a great success in modern science and engineering. The underlying mathematical

models are carefully designed to perform large scale computer simulations that

involve disparate scales of space and time. Such complexities often arise

when incorporating various multiphysical components which are represented by

classes of partial differential equations (PDE).

In this talk, I will show some of the key ideas and challenges of computational

mathematics in the framework of the University of Chicago's FLASH code.

FLASH is a highly-capable, massively parallel, publicly available open

source scientific code with a wide user base in the fields of astrophysics,

cosmology, and high-energy-density physics.

In the first part, I will discuss fundamental components of mathematical

algorithms to solve PDEs in order to construct numerical solutions

of computational fluid dynamics, gas dynamics and plasma physics.

Mathematical algorithms are going to be described with special

cares on two numerical approaches: first, the traditional

high-order polynomial based formulation, and second, a new innovative

exponentially converging formulation based on Gaussian Process.

In this part of my talk, I will show valuable importances of using

high-order accurate numerical methods that will be cruicial for future

high-performance (HPC) computing architectures.

In the second part, I will present laboratory astrophysical scientific simulations

using the numerical algorithms introduced in the first part. They will

include large scale computer simulations of astrophysics and

high-energy-density plasma physics, with special emphasis on

discussing laser-driven shock experiments to understand magnetic

fields generation and amplification.

END:VEVENT BEGIN:VEVENT DTSTART:20130822T150000 DTEND:20130822T180000 DTSTAMP:20130821T150000Z UID:efccd29e1e80d69881db6caa2287148b@cgp.ibs.re.kr SUMMARY:Semigroup theory and PDEs LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Juhi Jang, UC Riverside, USA\n\nEvent: PMI Lecture Series\n\nAbstract: Lecturer: Professor Juhi Jang, UC Riverside, USA

Place: Math. Bldg. # 312

Time: Aug. 22 Thur (3-6pm), Aug. 23 Fri (3-6pm)

Title: Semigroup theory and PDEs

Abstract: We present the classical semigroup theory by the Hille-Yosida theorem and its application to evolutionary PDEs.

Examples include the heat equation, wave equation, and Schrodinger equation. The heat equation with boundary conditions will be discussed in detail.

END:VEVENT BEGIN:VEVENT DTSTART:20130823T150000 DTEND:20130823T180000 DTSTAMP:20130822T150000Z UID:a43ef056b907b52f717aa26ecb1e250e@cgp.ibs.re.kr SUMMARY:Semigroup theory and PDEs LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Juhi Jang(UC Riverside)\n\nEvent: PMI Lecture Series\n\nAbstract: Lecture 1 - August 22 (Thursday) 3-6pm,Lecture 2 - August 23 (Friday) 3-6pmWe present the classical semigroup theory by the Hille-Yosida theorem and its application to evolutionary PDEs. Examples include the heat equation, wave equation, and Schrodinger equation. The heat equation with boundary conditions will be discussed in detail. END:VEVENT BEGIN:VEVENT DTSTART:20130826T160000 DTEND:20130826T180000 DTSTAMP:20130825T150000Z UID:cf79dd280c8ee885524fa0cb2e622014@cgp.ibs.re.kr SUMMARY:Lagrangian torus fibration and homological mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Lagrangian torus fibration and homological mirror symmetry\n\nAbstract: This is the first lecture of 4 lectures.I will discuss Lagrangian torus fibrations,tropical geometry, Strominger-Yau-Zaslow conjecture,and homological mirror symmetry.Lecture series begin with a gentle introduction for graduate students/non-expertsand/or discuss my recent joint project with Kwokwai Chan and Daniel Pomerleano,some part of which can be found in

http://arxiv.org/abs/1210.0652

http://arxiv.org/abs/1305.0968

END:VEVENT BEGIN:VEVENT DTSTART:20130827T160000 DTEND:20130827T180000 DTSTAMP:20130826T150000Z UID:bd8d5f582356aecb5d0652c815ca6861@cgp.ibs.re.kr SUMMARY:Lagrangian torus fibration and homological mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Lagrangian torus fibration and homological mirror symmetry\n\nAbstract: This is the first lecture of 4 lectures.I will discuss Lagrangian torus fibrations,tropical geometry, Strominger-Yau-Zaslow conjecture,and homological mirror symmetry.Lecture series begin with a gentle introduction for graduate students/non-expertsand/or discuss my recent joint project with Kwokwai Chan and Daniel Pomerleano,some part of which can be found inhttp://arxiv.org/abs/1210.0652

http://arxiv.org/abs/1305.0968

END:VEVENT BEGIN:VEVENT DTSTART:20130828T160000 DTEND:20130828T180000 DTSTAMP:20130827T150000Z UID:f6e1815cadcca5a0c0eff794f17944f3@cgp.ibs.re.kr SUMMARY:Lagrangian torus fibration and homological mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Lagrangian torus fibration and homological mirror symmetry\n\nAbstract: This is the first lecture of 4 lectures.I will discuss Lagrangian torus fibrations,tropical geometry, Strominger-Yau-Zaslow conjecture,and homological mirror symmetry.Lecture series begin with a gentle introduction for graduate students/non-expertsand/or discuss my recent joint project with Kwokwai Chan and Daniel Pomerleano,some part of which can be found inhttp://arxiv.org/abs/1210.0652

http://arxiv.org/abs/1305.0968

END:VEVENT BEGIN:VEVENT DTSTART:20130829T133000 DTEND:20130829T150000 DTSTAMP:20130828T150000Z UID:85aa7f536f3fa98d0ca55fb3c6ca3a62@cgp.ibs.re.kr SUMMARY:Lagrangian torus fibration and homological mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Lagrangian torus fibration and homological mirror symmetry\n\nAbstract: This is the first lecture of 4 lectures.I will discuss Lagrangian torus fibrations,tropical geometry, Strominger-Yau-Zaslow conjecture,and homological mirror symmetry.Lecture series begin with a gentle introduction for graduate students/non-expertsand/or discuss my recent joint project with Kwokwai Chan and Daniel Pomerleano,some part of which can be found inhttp://arxiv.org/abs/1210.0652

http://arxiv.org/abs/1305.0968

END:VEVENT BEGIN:VEVENT DTSTART:20130819T110000 DTEND:20130819T120000 DTSTAMP:20130818T150000Z UID:97b2eb2260849fe11baef0c57af790c9@cgp.ibs.re.kr SUMMARY:Vector bundles on non-Kaehler elliptic principal bundles LOCATION:CGP Main Hall DESCRIPTION:Speaker: Vasile Brinzanescu\n\nEvent: Seminar 2013\n\nAbstract: We shall describe moduli spaces of semi-stable vector bundles on non-Kaehler elliptic surfaces and elliptic principal bundles of arbitrary dimension. The main tools are a twisted Fourier-Mukai transform and spectral cover. END:VEVENT BEGIN:VEVENT DTSTART:20130820T110000 DTEND:20130820T120000 DTSTAMP:20130819T150000Z UID:86d9bb32028e5715b3416933dbd9f136@cgp.ibs.re.kr SUMMARY:Quantization in a magnetic field LOCATION:CGP Main Hall DESCRIPTION:Speaker: Radu Purice\n\nEvent: Seminar 2013\n\nAbstract: Together with Marius Mantoiu we have considered the description of quantum systems in magnetic fields starting from a gauge invariant classical picture given by the deformation of the canonical symplectic structure of the cotangent bundle, generalizing some former results from constant magnetic fields to bounded smooth magnetic fields. An interesting fact that we pointed out is that the algebra of observables is defined only in terms of the magnetic field without the need of a vector potential. A strict deformation quantization in the sense of Rieffel is put into evidence and a twisted pseudodifferetial calculus is developed. Some general abstract spectral results are obtained using operator algebra methods. END:VEVENT BEGIN:VEVENT DTSTART:20130822T160000 DTEND:20130822T180000 DTSTAMP:20130821T150000Z UID:b5793460aef37cbeb02b14578a604707@cgp.ibs.re.kr SUMMARY:The Analysis of Pseudo-holomorphic Curves in Contact Manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rui Wang\n\nEvent: CGP Seminar 2013\n\nAbstract: Pseudo-holomorphic curves in the symplectization of a contact manifold introduced by Hofer is an effective tool in the study of contact topology. We will revisit the analysis of pseudo-holomorphic curves in a tensorial method by using a new connection, named the contact triad connection, for every contact triad $(Q, \xi, \lambda)$. A priori estimates and the asymptotic behavior will be given under such analysis. Such analysis indicates a possible generalization of pseudo-holomorphic curves, which we call contact instantons living in a contact manifold itself without involving the symplectization. I will mention some current results of people related to this topic and some undergoing projects of ours . This is a joint project with Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20130819T160000 DTEND:20130819T175000 DTSTAMP:20130818T150000Z UID:dbe4323b119e70731456233f499bf857@cgp.ibs.re.kr SUMMARY:Divergent formal CR-mappings between infinite type hypersurfaces LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Ilya Kossvskiy(Wien Universitaet)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: As it was shown in the celebrated paper of Chern and Moser,a formal CR-mapping between Levi nondegenerate hypersurfaces is alwaysconvergent. In a large number of further works this result was generalized forhypersurfaces of finite type and CR manifolds of high codimension, satisfyingvarious nondegeneracy conditions. However, in the infinite type case thisphenomenon was not known. Using analytic theory of differential equations, weprovide elegant counterexamples to the convergence phenomenon in the infinitetype settings. END:VEVENT BEGIN:VEVENT DTSTART:20130820T160000 DTEND:20130820T175000 DTSTAMP:20130819T150000Z UID:f3fab240fa69c9a51e226161ddc21d40@cgp.ibs.re.kr SUMMARY:Analytic complexity for functions of two variables LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Professor Valeri Beloshapka (Moscow State University, Russia)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: In this talk we will define the analyticcomplexity for functions of two variables and discuss various methods forobtaining their upper and lower bounds. We will consider in detailthe functions of complexity 0, 1 and 2. We will also discuss itsconnection with the 13th Hilbert problem. END:VEVENT BEGIN:VEVENT DTSTART:20130819T130000 DTEND:20130819T150000 DTSTAMP:20130818T150000Z UID:29d09c2c97f50be1f1e55be1f9eee205@cgp.ibs.re.kr SUMMARY:10 Lectures on advanced topics in representations of algebraic groups LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: SRC-GAIA\n\nEvent: 10 Lectures on advanced topics in representations of algebraic groups\n\nAbstract:- Title: 10 Lectures on advanced topics inrepresentations of algebraic groups - Speaker: Professor - Time: 2013.8.19~23, 13:00~15:00 - Place: Math Bldg. Rm # Correspondence: 현동훈교수 (E-mail: dhyeon@postech.ac.kr) |

- Title: 10 Lectures on advanced topics inrepresentations of algebraic groups - Speaker: Professor - Time: 2013.8.19~23, 13:00~15:00 - Place: Math Bldg. Rm # Correspondence: 현동훈교수 (E-mail: dhyeon@postech.ac.kr) |

- Title: 10 Lectures on advanced topics inrepresentations of algebraic groups - Speaker: Professor - Time: 2013.8.19~23, 13:00~15:00 - Place: Math Bldg. Rm # Correspondence: 현동훈교수 (E-mail: dhyeon@postech.ac.kr) |

- Title: 10 Lectures on advanced topics inrepresentations of algebraic groups - Speaker: Professor - Time: 2013.8.19~23, 13:00~15:00 - Place: Math Bldg. Rm # Correspondence: 현동훈교수 (E-mail: dhyeon@postech.ac.kr) |

- Title: 10 Lectures on advanced topics inrepresentations of algebraic groups - Speaker: Professor - Time: 2013.8.19~23, 13:00~15:00 - Place: Math Bldg. Rm # Correspondence: 현동훈교수 (E-mail: dhyeon@postech.ac.kr) |

Speaker:** **Dong Sung Yoon, National Institute for Mathematical Sciences(NIMS)

Title: Hilbert's 12th Problem

Abstract: The Kronecker-Weber theorem shows that every abelian extension of Q is contained in the field generated by a special value. $\zeta=e^{2\pi i/N}$ of the exponential function. In 1900 Hilbert asked at the Paris ICM, as his 12-th problem, if the abelian extensions of other number fields can be generated by the special values of explicit transcendental functions. In this talk I will introduce chronicle topics from class field theory which is related to the Hilbert's 12-th problem and recent approaches as well.

END:VEVENT BEGIN:VEVENT DTSTART:20131127T163000 DTEND:20131127T173000 DTSTAMP:20131126T150000Z UID:e180e26499eb96319350df8fc5481ad4@cgp.ibs.re.kr SUMMARY:Adiabatic limits of vortex equation and its application in symplectic topology LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dongning Wang\n\nEvent: 2013 Fall T-Seminar\n\nAbstract: Vortex equation is generalisation of Yang-Mills equation. In this talk I will focus on Vortex equation over a disk and talk about the limit of their solutions when an adiabatic parameter in the equation changes. Then I will explain its application in the study of symplectic toric manifolds/orbifolds: Using Lagrangian FLoer theory one can define a potential function for a toric manifold/orbifold, at the same time one can always write down the Givental-Hori-Vafa potential function from the moment polytope of the toric manifold/orbifold. The solution moduli of vortex equations will provide a coordinate change between the two potential functions. If time allows, I will further explain how the identification of the two potential functions leads to a proof of the open crepant resolution conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20131211T163000 DTEND:20131211T173000 DTSTAMP:20131210T150000Z UID:b4630f501b6f2e32d45861df55baa783@cgp.ibs.re.kr SUMMARY:Generators for abelian extensions of number fields LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dong Hwa Shin (Hankuk University of Foreign Studies)\n\nEvent: 2013 Fall T-Seminar\n\nAbstract: Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a similar argument in terms of norm. As its applications we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension END:VEVENT BEGIN:VEVENT DTSTART:20130912T160000 DTEND:20130912T180000 DTSTAMP:20130911T150000Z UID:7e4c2bc03718652e376c05437ce5f379@cgp.ibs.re.kr SUMMARY:Singularity invariants related to Milnor fiber LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: CGP Seminar 2013\n\nAbstract: Singularities are everywhere. At the first part of talk we will discuss a general issues related to geometric singularity. Especially we focus on invariants related to Milnor fiber. A hyperplane arrangement is one of the simplest objects which has non isolated singular locus. We will discuss its singularity at the second part of talk. END:VEVENT BEGIN:VEVENT DTSTART:20130917T164000 DTEND:20130917T174000 DTSTAMP:20130916T150000Z UID:a38353420c2ca218cca2b192695b5f38@cgp.ibs.re.kr SUMMARY:Height of Units and Weber's Problem LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Takayuki Morisawa (Keio University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract:** " Height of Units and Weber's Problem"**

▶ Date : Sep. 17 16:40 pm

▶ Place : Math. Bldg. 312

▶ Contact : J.H.Coates@dpmms.cam.ac.uk)

END:VEVENT BEGIN:VEVENT DTSTART:20130829T160000 DTEND:20130829T170000 DTSTAMP:20130828T150000Z UID:b6d5206d99fa37ec78f3a62831d09fa8@cgp.ibs.re.kr SUMMARY:Retraction on a Banach space LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Sun Kwang Kim(KIAS)\n\nEvent: PMI Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131010T160000 DTEND:20131010T180000 DTSTAMP:20131009T150000Z UID:dc6e1ee506646d4e42280933c8b31370@cgp.ibs.re.kr SUMMARY:The uniqueness of the Fisher metric as information metric LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hong Van Le\n\nEvent: CGP Seminar 2013\n\nAbstract: Recent successful applications of information geometry, where the Fisher metric plays a fundamental role, motivate us to find an answer to the following long standing question. Is there another metric on statistical models with natural properties, which we could name information metric? This question has been solved by Chentsov in 1972 for statistical models associated with finite sample spaces. In this talk I shall discuss a conceptual approach developed jointly with Ay, Jost and Schwachhoefer to general statistical models and Fisher metrics, which leads us to the affirmative answer of the uniqueness of the Fisher metric. I also discuss some relation of the Fisher metric with statistical mechanics and string theory. END:VEVENT BEGIN:VEVENT DTSTART:20131011T140000 DTEND:20131011T153000 DTSTAMP:20131010T150000Z UID:578f4be3d3cbfac58348f8b92b778957@cgp.ibs.re.kr SUMMARY:Torus localization and the stable pairs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jinwon Choi\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: By the classical Bialynicki-Birula decomposition when we have an action of an algebraic torus, the topological invariants for the moduli space are obtained by classifying its torus fixed locus and computing the torus representation of the tangent space at each fixed point. In the first part of the talk, we explain this technique with examples such as the Hilbert schemes and the moduli spaces of stable pairs. In the second part, we extend the method to define the refined stable pair invariants for local toric Calabi-Yau threefolds. A product formula for their generating function is proposed as a generalization of the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local P^1. If time permits, we will also describe how the product formula can be understood by the wall-crossing in \alpha-stable pairs. This is joint work with Sheldon Katz and Albrecht Klemm. END:VEVENT BEGIN:VEVENT DTSTART:20131008T164000 DTEND:20131008T174000 DTSTAMP:20131007T150000Z UID:699bab1bbcb9cecc4cd6ed5e0c907a96@cgp.ibs.re.kr SUMMARY:The maximum size of Sidon subsets contained in a random subset of [n] LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Sang June Lee (ASARC, KAIST)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131010T143000 DTEND:20131010T164000 DTSTAMP:20131009T150000Z UID:77a38dfdd176b2b7d54ccce830050448@cgp.ibs.re.kr SUMMARY:Eisenstein series and p-adic Hecke L-functions LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Dohyeong Kim(POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: I will continue the weekly seminar. I will define the Eisenstein series of my interest by giving explicit formulae, compute their Fourier-Whittaker coefficient as well as the period integral. END:VEVENT BEGIN:VEVENT DTSTART:20131015T140000 DTEND:20131015T151500 DTSTAMP:20131014T150000Z UID:18664f163269f0df54d44faad1b779ac@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131017T140000 DTEND:20131017T151500 DTSTAMP:20131016T150000Z UID:966609c8489666b7cca5142615aaa59c@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131015T164000 DTEND:20131015T174000 DTSTAMP:20131014T150000Z UID:3510856dfa833d794bf49ae071f1933d@cgp.ibs.re.kr SUMMARY:Perturbation of the Maass and Selberg spectrum LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Roelof Bruggeman (Universiteit Utrecht)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: The talk concerns joint work with Markus Fraczek and Dieter Mayer. Fraczek did computations of the spectral parameters of Maass forms and of resonances for the congruence subgroup Gamma_0(4) in dependence of a one-parameter family of characters. These computations show some remarkable features in the movement of these spectral parameters as the character approaches the trivial character. This inspired us to look for analytical ways to understand this behavior. I'll show some of Fraczek's results and compare them with the asymptotic formulas that we could prove theoretically. END:VEVENT BEGIN:VEVENT DTSTART:20131014T190000 DTEND:20131014T210000 DTSTAMP:20131013T150000Z UID:712459bb3f178b720529c998c5e8f5be@cgp.ibs.re.kr SUMMARY:Non-Markovian categories of open quantum systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Quantum Monday 2013\n\nAbstract: I outline the problem of giving a mathematical description of the most general processes which can be undergone by open quantum systems and propose a category-theoretic solution. I also sketch a connection with the calculus of fractions of Gabriel and Zisman and with higher category theory. END:VEVENT BEGIN:VEVENT DTSTART:20131017T160000 DTEND:20131017T180000 DTSTAMP:20131016T150000Z UID:a1ab153bc1d03df8d65c1eec1717233b@cgp.ibs.re.kr SUMMARY:Hodge structure and arithmetic of abelian varieties: around the Morita conjecture LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dong Uk Lee\n\nEvent: CGP Seminar 2013\n\nAbstract: As exemplified in the Mordell conjecture and numerous other conjectures in arithmetic geometry, for an algebraic variety defined over a number field, its arithmetic and geometric properties are often intimately interrelated. In this talk, we discuss one vivid case of such phenomenon, a conjecture of Yasuo Morita which asserts that an abelian variety defined over a number field, if it does not generate geometrically, does not degenerate arithmetically either. Here, the specific structures to be considered for comparison are Hodge structures and Galois representations. A large part of the talk will be devoted to a review of these theories, insofar as relevant to our proof of this conjecture (esp. with geometers in mind). If time allows, we will also introduce certain conjectures along the same line as the Morita conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20131022T140000 DTEND:20131022T151500 DTSTAMP:20131021T150000Z UID:0f15e6c94a91ee6843ef824ccf0ad0b2@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131029T140000 DTEND:20131029T151500 DTSTAMP:20131028T150000Z UID:e1b47964547929eb2ccf97d5c5b04fd2@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131105T140000 DTEND:20131105T151500 DTSTAMP:20131104T150000Z UID:156f166761633183f8d878a2f34ea3d1@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131031T140000 DTEND:20131031T151500 DTSTAMP:20131030T150000Z UID:61382b14b2fb723e939f12c45c994211@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131022T164000 DTEND:20131022T174000 DTSTAMP:20131021T150000Z UID:60a8d42b271b8edeb78cd5ffde6fe55a@cgp.ibs.re.kr SUMMARY:Star products on quasimodular forms LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Emmanuel Royer(Blaise Pascal University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Rankin-Cohen brackets have been proved (Cohen-Manin & Zagier, Yao) to give the algebra of modular forms a formal deformation (Eholzer product). In a joint work with François Dumas, we construct formal deformations for quasimodular forms after having built and classified all the Poisson structures on their algebra. END:VEVENT BEGIN:VEVENT DTSTART:20131126T164000 DTEND:20131126T174000 DTSTAMP:20131125T150000Z UID:373571fb2caea048356db98cfd771b3c@cgp.ibs.re.kr SUMMARY:The congruences of congruent modular forms for non-ordinary primes LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Byoung Du Kim(Victoria University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: This is joint work with Suh Hyun Choi. Let p be a prime number. Suppose we have two modular forms whose weights are congruent modulo p^r(p-1), and q-expansions are congruent modulo p^r. (For example, consider modular forms given by topologically close points on an eigencurve.) People who do Iwasawa Theory believe that their p-adic L-functions are also congruent modulo p^r. In fact, if we push this idea further, we can also imagine there is a big p-adic L-function over an eigencurve which is integral and smooth. This is known in the ordinary prime case (i.e. the case where the slope of modular form is a p-adic unit), and in this case, the big p-adic L-function over the eigencurve is called the Kitagawa-Mazur p-adic L-function. In the non-ordinary case, so far we know relatively little. In this presentation, we will prove that the (non-integral) p-adic L-functions that I constructed are congruent for the above-said congruent modular forms assuming that Hecke algebras are Gorenstein. END:VEVENT BEGIN:VEVENT DTSTART:20131021T190000 DTEND:20131021T220000 DTSTAMP:20131020T150000Z UID:92001a22b7a18978a9a65655a156e04f@cgp.ibs.re.kr SUMMARY:Introduction to the method of descent LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: Quantum Monday 2013\n\nAbstract: The talk will be an informal introduction to the method of descent as it is used in arithmetic. The method of descent refers to a set of techniques that are used to solve Diophantine equations, which has evolved into various forms. The topics to be discussed include the classical descent on elliptic curves, the reciprocity laws, the role of special values of L-functions, Iwasawa theory, as well as the limitation of the classical/abelian theories and the two non-abelian generalizations of them. END:VEVENT BEGIN:VEVENT DTSTART:20131028T190000 DTEND:20131028T220000 DTSTAMP:20131027T150000Z UID:7956da54db349deb2626867560e64fff@cgp.ibs.re.kr SUMMARY:Introduction to the method of descent II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: Quantum Monday 2013\n\nAbstract: The talk will be an informal introduction to the method of descent as it is used in arithmetic. The method of descent refers to a set of techniques that are used to solve Diophantine equations, which has evolved into various forms. The topics to be discussed include the classical descent on elliptic curves, the reciprocity laws, the role of special values of L-functions, Iwasawa theory, as well as the limitation of the classical/abelian theories and the two non-abelian generalizations of them. END:VEVENT BEGIN:VEVENT DTSTART:20131030T140000 DTEND:20131030T160000 DTSTAMP:20131029T150000Z UID:f44c7deec07f458bec52d04c8f066446@cgp.ibs.re.kr SUMMARY:An introduction to Volume conjecture, its generalizations and related topics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Seminar 2013\n\nAbstract: Volume conjectue relates asymptotic behavior of a combinatorial object like colored Jones polynomial and a geometric quantity like hyperbolic volume and also involves Chern-Simons theory of theoritical physics. In fact, it seems to be difficult to answer directly the original question for the present. However, there are emerging many ideas and attempts to understand this phenomenon and generalize to more unified viewpoint. Nowaday this conjecture is an increasing prominent source giving new inspiration about various area. I'll give an introductory survey on volume conjecture and explain how to be adapted to knotted graph theory. END:VEVENT BEGIN:VEVENT DTSTART:20131031T100000 DTEND:20131031T120000 DTSTAMP:20131030T150000Z UID:450672ab82c44914b61805fbe2ac8ca7@cgp.ibs.re.kr SUMMARY:Optimistic limits of quantum invariants and volume potential functions for knotted graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Seminar 2013\n\nAbstract: Volume conjectue relates asymptotic behavior of a combinatorial object like colored Jones polynomial and a geometric quantity like hyperbolic volume and also involves Chern-Simons theory of theoritical physics. In fact, it seems to be difficult to answer directly the original question for the present. However, there are emerging many ideas and attempts to understand this phenomenon and generalize to more unified viewpoint. Nowaday this conjecture is an increasing prominent source giving new inspiration about various area. I'll give an introductory survey on volume conjecture and explain how to be adapted to knotted graph theory. END:VEVENT BEGIN:VEVENT DTSTART:20131031T160000 DTEND:20131031T180000 DTSTAMP:20131030T150000Z UID:71d774626bf399f1877da084ec8b97c9@cgp.ibs.re.kr SUMMARY:Hochschild-Witt complex LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: CGP Seminar 2013\n\nAbstract: The "de Rham-Witt complex" of Deligne and Illusie is a functorial complexof sheaves WΩ*(X) on a smooth algebraic variety X over a finite field, computing the cristalline cohomology of X. I am going to present a non-commutative generalization of this: even for a non-commutative ring A, one can define a functorial "Hochschild-Witt complex" with homology WHH*(A); if A is commutative, then WHHi(A)=WΩi(X), X = Spec A (this is analogous to the isomorphism HHi(A)=Ωi(X) discovered by Hochschild, Kostant and Rosenberg). Moreover, the construction of the Hochschild-Witt complex is actually simpler than the Deligne-Illusie construction, and it allows to clarify the structure of the de Rham-Witt complex. END:VEVENT BEGIN:VEVENT DTSTART:20131031T103000 DTEND:20131031T120000 DTSTAMP:20131030T150000Z UID:44df94e23b5097ab1cd11d26b3a11dbc@cgp.ibs.re.kr SUMMARY:Enriques K3 surfaces over odd characteristic LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Junmyeong Jang\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: In this talk, we will see a criterion for a K3 surface to be the cover of an Enriques surfaceover odd characteristic. END:VEVENT BEGIN:VEVENT DTSTART:20131104T160000 DTEND:20131104T180000 DTSTAMP:20131103T150000Z UID:9ca0f4bc4481b7cfb42fdac86e250bd4@cgp.ibs.re.kr SUMMARY:Homological methods in Non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Homological methods in Non-commutative geometry\n\nAbstract: I am going to give a brief introduction to what Kontsevich and Soibelman call "non-commutative algebraic geometry" -- the study of A_\infty and DG categories and the study of usual algebraic varieties via their derived categories of coherent sheaves. Here is a rough list of topics I want to cover:1. Motivations and basic examples2. Necessary facts about abstract homotopy theory3. Generalities about DG categories; smooth and proper DG categories4. Homological invariants: Hochschild and cyclic homology, Hochschild-Kostant-Rosenberg isomorphism5. Deformations and Hochschild cohomologyI will not assume any knowledge of non-commutative notions, and it should be possible to follow the lectures with very little background. A good reference for DG categories is B. Keller's talk at ICM 2006; for Hochschild and cyclic homology, there is a very good book "Cyclic Homology" by J.-L. Loday. END:VEVENT BEGIN:VEVENT DTSTART:20131106T160000 DTEND:20131106T180000 DTSTAMP:20131105T150000Z UID:417314a6dc9189d8e244fac77a6d0257@cgp.ibs.re.kr SUMMARY:Homological methods in Non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Homological methods in Non-commutative geometry\n\nAbstract: I am going to give a brief introduction to what Kontsevich and Soibelman call "non-commutative algebraic geometry" -- the study of A_\infty and DG categories and the study of usual algebraic varieties via their derived categories of coherent sheaves. Here is a rough list of topics I want to cover:1. Motivations and basic examples2. Necessary facts about abstract homotopy theory3. Generalities about DG categories; smooth and proper DG categories4. Homological invariants: Hochschild and cyclic homology, Hochschild-Kostant-Rosenberg isomorphism5. Deformations and Hochschild cohomologyI will not assume any knowledge of non-commutative notions, and it should be possible to follow the lectures with very little background. A good reference for DG categories is B. Keller's talk at ICM 2006; for Hochschild and cyclic homology, there is a very good book "Cyclic Homology" by J.-L. Loday. END:VEVENT BEGIN:VEVENT DTSTART:20131111T160000 DTEND:20131111T180000 DTSTAMP:20131110T150000Z UID:b5bb76986ea4f070781dc5b97d7cb640@cgp.ibs.re.kr SUMMARY:Homological methods in Non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Homological methods in Non-commutative geometry\n\nAbstract: I am going to give a brief introduction to what Kontsevich and Soibelman call "non-commutative algebraic geometry" -- the study of A_\infty and DG categories and the study of usual algebraic varieties via their derived categories of coherent sheaves. Here is a rough list of topics I want to cover:1. Motivations and basic examples2. Necessary facts about abstract homotopy theory3. Generalities about DG categories; smooth and proper DG categories4. Homological invariants: Hochschild and cyclic homology, Hochschild-Kostant-Rosenberg isomorphism5. Deformations and Hochschild cohomologyI will not assume any knowledge of non-commutative notions, and it should be possible to follow the lectures with very little background. A good reference for DG categories is B. Keller's talk at ICM 2006; for Hochschild and cyclic homology, there is a very good book "Cyclic Homology" by J.-L. Loday. END:VEVENT BEGIN:VEVENT DTSTART:20131113T160000 DTEND:20131113T180000 DTSTAMP:20131112T150000Z UID:12248b049fe80c99605ef41dfaefd9fc@cgp.ibs.re.kr SUMMARY:Homological methods in Non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Homological methods in Non-commutative geometry\n\nAbstract: I am going to give a brief introduction to what Kontsevich and Soibelman call "non-commutative algebraic geometry" -- the study of A_\infty and DG categories and the study of usual algebraic varieties via their derived categories of coherent sheaves. Here is a rough list of topics I want to cover:1. Motivations and basic examples2. Necessary facts about abstract homotopy theory3. Generalities about DG categories; smooth and proper DG categories4. Homological invariants: Hochschild and cyclic homology, Hochschild-Kostant-Rosenberg isomorphism5. Deformations and Hochschild cohomologyI will not assume any knowledge of non-commutative notions, and it should be possible to follow the lectures with very little background. A good reference for DG categories is B. Keller's talk at ICM 2006; for Hochschild and cyclic homology, there is a very good book "Cyclic Homology" by J.-L. Loday. END:VEVENT BEGIN:VEVENT DTSTART:20131107T160000 DTEND:20131107T180000 DTSTAMP:20131106T150000Z UID:cc68e37e3df738aaae05103bc69cd077@cgp.ibs.re.kr SUMMARY:Gromov─Witten Invariants of Toric fibrations (and Beyond) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jeff Brown\n\nEvent: CGP Seminar 2013\n\nAbstract: We consider a direct sum of complex line bundles over an arbitrary almost Kahler base; then its fiberwise symplectic reductions are well-defined, giving fibre bundles where the fiber is a toric variety. Given the datum of this construction, along with Gromov--Witten invariants of the base, we will write down a "closed-formula" generating function for Gromov--Witten invariants of the preceding fibre bundles. The formula was written down and conjectured by Givental to give Gromov--Witten invariants of the bundles, and the conjecture was proved in my thesis. We will describe some directions we are working in to generalize the result. END:VEVENT BEGIN:VEVENT DTSTART:20131104T190000 DTEND:20131104T210000 DTSTAMP:20131103T150000Z UID:d8983a9e806a1cc69b034040112ff880@cgp.ibs.re.kr SUMMARY:Introduction to the method of descent III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: Quantum Monday 2013\n\nAbstract: The talk will be an informal introduction to the method of descent as it is used in arithmetic. The method of descent refers to a set of techniques that are used to solve Diophantine equations, which has evolved into various forms. The topics to be discussed include the classical descent on elliptic curves, the reciprocity laws, the role of special values of L-functions, Iwasawa theory, as well as the limitation of the classical/abelian theories and the two non-abelian generalizations of them. END:VEVENT BEGIN:VEVENT DTSTART:20131105T150000 DTEND:20131105T160000 DTSTAMP:20131104T150000Z UID:61fd6899f6f7407a1fffe6c2f1a7e7ee@cgp.ibs.re.kr SUMMARY:Arithmetic of Heegner Points (I-IV) LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Ye Tian (Chinese Academy of Sciences)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Since Heenger proved that any positive integer congruent to 5, 6, 7 modulo 8 with exactly one odd prime factor is a congruent number, the study of Heegner points has played a very important role in arithemtic of elliptic curves. In these lectures, I will start with Heegner's work and mainly lecture on the works of Kolyvagin, Gross-Zagier, Yuan-Zhang-Zhang, Bertonili-Darmon, and W. Zhang etc on Heegner Points. END:VEVENT BEGIN:VEVENT DTSTART:20131107T140000 DTEND:20131107T151500 DTSTAMP:20131106T150000Z UID:ecd669155dee01e15c0e290df9cbf357@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131108T110000 DTEND:20131108T120000 DTSTAMP:20131107T150000Z UID:04f3ddf92fa360b78d7c5190834866bc@cgp.ibs.re.kr SUMMARY:Log canonical thresholds of complete intersection log del Pezzo surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: In-kyun Kim\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: We compute the global log canonical thresholds of quasi-smooth well- formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As a corollary we show the existence of orbitfold Kaehler- Einstein metrics on many of them. This presentation is a part of the speaker's defence of his dissertation. END:VEVENT BEGIN:VEVENT DTSTART:20131112T140000 DTEND:20131112T151500 DTSTAMP:20131111T150000Z UID:c71faa1027d471ea160ac486d6dc2c9b@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131114T140000 DTEND:20131114T151500 DTSTAMP:20131113T150000Z UID:17cd47b3d079e3736cd0e9bcf470c89f@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131111T190000 DTEND:20131111T210000 DTSTAMP:20131110T150000Z UID:5cd83502a76f5b2c494f6ef7ef6190c5@cgp.ibs.re.kr SUMMARY:Introduction to Operads LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Quantum Monday 2013\n\nAbstract: I'll provide (an attempt at) a gentle, expository introduction to operadic machinery, focusing on topological and differential graded operads. END:VEVENT BEGIN:VEVENT DTSTART:20131112T150000 DTEND:20131112T160000 DTSTAMP:20131111T150000Z UID:b59fc0c7ad47c0f8e9750b273d19cb91@cgp.ibs.re.kr SUMMARY:Arithmetic of Heegner Points (II) LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Ye Tian (Chinese Academy of Sciences)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Since Heenger proved that any positive integer congruent to 5, 6, 7 modulo 8 with exactly one odd prime factor is a congruent number, the study of Heegner points has played a very important role in arithemtic of elliptic curves. In these lectures, I will start with Heegner's work and mainly lecture on the works of Kolyvagin, Gross-Zagier, Yuan-Zhang-Zhang, Bertonili-Darmon, and W. Zhang etc on Heegner Points. END:VEVENT BEGIN:VEVENT DTSTART:20131114T154000 DTEND:20131114T164000 DTSTAMP:20131113T150000Z UID:e9cf263aba0178c38e741df566407455@cgp.ibs.re.kr SUMMARY:Numerical computations on the zeros of the Euler double zeta-function LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kohji Matsumoto (Nagoya university)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131119T140000 DTEND:20131119T151500 DTSTAMP:20131118T150000Z UID:3a4bfea5a683b2ea17af4ee924908d87@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131121T140000 DTEND:20131121T151500 DTSTAMP:20131120T150000Z UID:665b47df70f0c9560ccee0a29f33341b@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131126T140000 DTEND:20131126T151500 DTSTAMP:20131125T150000Z UID:f1c30dd0c305b1e76fd38fd0dbd79f5c@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131128T140000 DTEND:20131128T151500 DTSTAMP:20131127T150000Z UID:e22deaef99c84545d9506aa3fb3da2d6@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131203T140000 DTEND:20131203T151500 DTSTAMP:20131202T150000Z UID:867feb91ec4c368c64d9e9c9baef15a1@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131205T140000 DTEND:20131205T151500 DTSTAMP:20131204T150000Z UID:c1ace66a5461071d9d822e68a134b336@cgp.ibs.re.kr SUMMARY:Symplectic Algebraic Topology LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Algebraic Topology\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131118T190000 DTEND:20131118T210000 DTSTAMP:20131117T150000Z UID:492f9ebc901f85da3205df246bf2df4d@cgp.ibs.re.kr SUMMARY:Introduction to Operads II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Quantum Monday 2013\n\nAbstract: I'll provide (an attempt at) a gentle, expository introduction to operadic machinery, focusing on topological and differential graded operads. END:VEVENT BEGIN:VEVENT DTSTART:20131122T150000 DTEND:20131122T160000 DTSTAMP:20131121T150000Z UID:49ca059d27aca3a06a9c1fb33c90d661@cgp.ibs.re.kr SUMMARY:Arithmetic of Heegner Points (III) LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Ye Tian(Chinese Academy of Sciences)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Since Heenger proved that any positive integer congruent to 5, 6, 7 modulo 8 with exactly one odd prime factor is a congruent number, the study of Heegner points has played a very important role in arithemtic of elliptic curves. In these lectures, I will start with Heegner's work and mainly lecture on the works of Kolyvagin, Gross-Zagier, Yuan-Zhang-Zhang, Bertonili-Darmon, and W. Zhang etc onHeegner Points. END:VEVENT BEGIN:VEVENT DTSTART:20131122T140000 DTEND:20131122T153000 DTSTAMP:20131121T150000Z UID:6a6ee902ab4f8db2c144cf377ed09fdd@cgp.ibs.re.kr SUMMARY:The surjectivity of the reduction map for Alexeev's space LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jaeho Shin\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: A matroid is a combinatorial object that can be thought of as a generalization of a spanning set of a vector space. As many other mathematical objects, it turned out that hyperplane arrangements have the matroid structure.One can define a matroid using several different axiom systems such as independent sets, bases, span operator, flats, rank function, etc. I will show that two more descriptions of a matroid can be added that are characterized by edges of the associated convex polytope and quotient matroids, respectively, each of which leads us to a new combinatorial object, a puzzle-piece.We will see moreover that the associated convex polytopes which are called base polytopes have a special gluing property which is distinguished from that of the polytopes that are just convex.The gluing property tells us something about the surjectivity of the natural morphism, say the reduction morphism, defined between two moduli spaces $\bar M_{\beta}(k,n)\rightarrow \bar M_{\beta'}(k,n)$ with two weights $\beta>\beta'$, where $\bar M_{\beta}(k,n)$ is the moduli space of weighted stable hyperplane arrangements with rank $k$, which was generalized by the Valery Alexeev from the Hasset's moduli space of curves of genus 0 with weighted $n$ points with rank 2.For Hassett's space, the reduction map is surjective for any weight $\beta\ge \beta'$, but for $k\ge 3$, the answer was expected to be ``no'' by the Mnev's universality theorem. In this talk, I will show that for $k=3$ case, there is a counterexample to the surjectivity when $n=10$, and that the map is surjective when $n=4,5,6$. END:VEVENT BEGIN:VEVENT DTSTART:20131122T170000 DTEND:20131122T180000 DTSTAMP:20131121T150000Z UID:7798e6ed94c3006502d4d30f51d125cd@cgp.ibs.re.kr SUMMARY:Geometry of the Beta-deformation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Daniel Krefl\n\nEvent: Seminar 2013\n\nAbstract: I will give an introduction into the Beta-deformation (also known as Omega-deformation or refinement) of topological string theory from a geometric point of view. Key mathematical/geometric property of the deformation being the replacement of the usual Euler characteristic of the moduli spaces of complex curves with the parameterized Euler characteristic of Goulden, Harer and Jackson. If time permits, I will also introduce a special limit leading to a novel notion of 'semi-classical quantum' special geometry. END:VEVENT BEGIN:VEVENT DTSTART:20131125T190000 DTEND:20131125T210000 DTSTAMP:20131124T150000Z UID:ca3d8ba11b6d0ae11ada201fbb97e255@cgp.ibs.re.kr SUMMARY:Introduction to Operads III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Quantum Monday 2013\n\nAbstract: I'll provide (an attempt at) a gentle, expository introduction to operadic machinery, focusing on topological and differential graded operads. END:VEVENT BEGIN:VEVENT DTSTART:20131125T163000 DTEND:20131125T173000 DTSTAMP:20131124T150000Z UID:59d93f88a2c03522470e049449ebe47c@cgp.ibs.re.kr SUMMARY:Bergman Kernel asymptotics for lower energy forms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chin-Yu Hsiao\n\nEvent: Seminar 2013\n\nAbstract: In my work with Marinescu (Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles, 101 pages, to appear in CAG), we give for the first time a microlocal study of the complex Witten Laplacian. As an application, we obtain a full asymptotic expansion of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. From this result, we could deduce many classical results in complex geometry (eg Kodaira embedding and vanishing Theorems, Demailly's Morse inequalities, Bergman kernel asymptotics for ample line bundles...). In this talk, I will explain how to obtain these classical results from this result. In time is enough, I will also mention a new result obtained in this work: the existence of the full asymptotics expansion for Bergman kernel for a big line bundle twisted with a multiplier ideal sheaf. As a corollary, we could reprove the Shiffman conjecture, asserting that Moishezon manifolds can be characterized in terms of integral Kahler current. END:VEVENT BEGIN:VEVENT DTSTART:20131126T150000 DTEND:20131126T160000 DTSTAMP:20131125T150000Z UID:49b782797f7d41c572f39546f88e9817@cgp.ibs.re.kr SUMMARY:Arithmetic of Heegner Points (IV) LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Ye Tian (Chinese Academy of Sciences)\n\nEvent: PMI Seminar\n\nAbstract: Since Heenger proved that any positive integer congruent to 5, 6, 7 modulo 8 with exactly one odd prime factor is a congruent number, the study of Heegner points has played a very important role in arithemtic of elliptic curves. In these lectures, I will start with Heegner's work and mainly lecture on the works of Kolyvagin, Gross-Zagier, Yuan-Zhang-Zhang, Bertonili-Darmon, and W. Zhang etc onHeegner Points. END:VEVENT BEGIN:VEVENT DTSTART:20131129T140000 DTEND:20131129T150000 DTSTAMP:20131128T150000Z UID:19dc17de2e9fa4dd4c05401957e7bb04@cgp.ibs.re.kr SUMMARY:On the anticyclotomic main conjecture for modular forms LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Ming-Lun Hsieh (National Taiwan University)\n\nEvent: PMI Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131129T160000 DTEND:20131129T171500 DTSTAMP:20131128T150000Z UID:e79b9208c22f27f89faf932bb9f07d21@cgp.ibs.re.kr SUMMARY:Spatially homogeneous Boltzmann equation for relativistic particles LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seok-Bae Yun (Sungkyunkwan University)\n\nEvent: Fall 2013 POSTECH Math Colloquium\n\nAbstract: The relativistic Boltzmann equation describes the evolution of gaseous particles in the Minkowski space-time. In this talk, we will briefly overview the kinetic theory of collisional gases, and address several issues for the spatially homogeneous Boltzmann equation for relativistic particles such as initial value problem, propagation of L1-moments and propagation of L^infty bound. This is a joint work with Robert Strain. END:VEVENT BEGIN:VEVENT DTSTART:20131202T190000 DTEND:20131202T210000 DTSTAMP:20131201T150000Z UID:d95357f50f99537506239f6bcdd927e7@cgp.ibs.re.kr SUMMARY:Algebraic cycles and crystalline cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyun Park\n\nEvent: Quantum Monday 2013\n\nAbstract: Berthelot's crystalline cohomology theory is a Weil cohomology theory for smooth projective varieties over a field of characteristic p>0. In the late 70s, Bloch gave a description of it in terms of relative higher algebraic K-groups of Quillen, and Illusie gave a description in terms of the de Rham-Witt complexes. Subsequently, de Rham-Witt complexes were generalized to the big de Rham-Witt complexes by Hesselholt and Madsen. In this talk, we give a description of Zariski sheaf of big de Rham-Witt complexes on smooth varieties in terms of additive higher Chow groups. From this, we deduce a new description of crystalline cohomology in terms of algebraic cycles. END:VEVENT BEGIN:VEVENT DTSTART:20131209T190000 DTEND:20131209T210000 DTSTAMP:20131208T150000Z UID:c10c115daf308be976eed0cc77b4ad38@cgp.ibs.re.kr SUMMARY:What is homotopy probability space? LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2013\n\nAbstract: This is a sketch of my program to extend the notion of algebraic probability spaces from the vantage point of algebraic homotopy theory. END:VEVENT BEGIN:VEVENT DTSTART:20131211T100000 DTEND:20131211T120000 DTSTAMP:20131210T150000Z UID:e0d8a93cc5aea972da4f33bb6bec9672@cgp.ibs.re.kr SUMMARY:Intrinsically knotted graphs with 21 edges LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwa Jeong Lee\n\nEvent: Seminar 2013\n\nAbstract: A graph is called intrinsically knotted if every embedding of the graph in $R^3$ contains a knotted cycle. Conway and Gordon showd that $K_7$, the complete graph with seven vertices, is an intrinsically knotted graph. Jonson, Kidwell and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that $K_7$ and the thirteen graphs obtained from $K_7$ by $\nabla Y$ moves are intrinsically knotted graphs with $21$ edges. In this talk, we prove that only these $14$ graphs are intrinsically knotted graph with $21$ edges. This is a joint work with Hyoungjun Kim, Minjung Lee and Seungsang Oh. END:VEVENT BEGIN:VEVENT DTSTART:20131210T160000 DTEND:20131210T180000 DTSTAMP:20131209T150000Z UID:0d53c5cd9338fdec04e892bebe7689b2@cgp.ibs.re.kr SUMMARY:Arc presentations of knots and links LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwa Jeong Lee\n\nEvent: Seminar 2013\n\nAbstract: A knot or link $L$ can be embedded in a book with finitely many half planes in $R^3$ so that each half plane intersects $L$ in a single arc. We called such an embedding "arc presentation" of $L$. In this talk, we present a small survey of known results on arc presentation of knots and links. We also introduce some recent results. This is a joint work with Hideo Takioka. END:VEVENT BEGIN:VEVENT DTSTART:20131212T160000 DTEND:20131212T180000 DTSTAMP:20131211T150000Z UID:53fbe8a5655e3c2f77ab9db51b389b73@cgp.ibs.re.kr SUMMARY:An overview of Lagrangian cobordism in symplectic geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Wenfeng Jiang\n\nEvent: CGP Seminar 2013\n\nAbstract: Cobordism theory of Lagrangian Immersion is introduced by Arnold, we are going to compared it to Cobordism theory of Lagrangian Embedding. The category of Lagrangian cobordism is related to the derived Fukaya category by Biran and Cornea, and in monotone case the relation of this two category is quite clear. END:VEVENT BEGIN:VEVENT DTSTART:20131213T140000 DTEND:20131213T153000 DTSTAMP:20131212T150000Z UID:149a5e6b377b230c12ee171f01bbc570@cgp.ibs.re.kr SUMMARY:Semi-terminal modifications of demi-normal pairs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kento Fujita\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: It is a classical result that for a normal algebraic surface there exists the minimal resolution. In this talk, we want to talk about its reducible and higher-dimensional version. END:VEVENT BEGIN:VEVENT DTSTART:20131213T160000 DTEND:20131213T171500 DTSTAMP:20131212T150000Z UID:06a21175c170e50d29f8a098fc045d0a@cgp.ibs.re.kr SUMMARY:Geometry and complexity of limits of ideals LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donghoon Hyeon (POSTECH)\n\nEvent: Fall 2013 POSTECH Math Colloquium\n\nAbstract: Ideals of polynomial rings are central objects of study in algebraic geometry and commutative algebra. Much information about the algebra and combinatorics of an ideal can be read off from the initial terms of its elements - Macaulay already realized this in the early 20th century, and this powerful idea was prominently used in Hironaka's work on the resolution of singularities of algebraic varieties. I will explain the basic concepts and applications from a geometer's point of view, and reprove important properties by using geometry of algebraic groups and homogeneous spaces. END:VEVENT BEGIN:VEVENT DTSTART:20131217T160000 DTEND:20131217T180000 DTSTAMP:20131216T150000Z UID:2ab5b3ef9c20f0b012084e7cc2aa77f2@cgp.ibs.re.kr SUMMARY:Survey on birational rigid Fano complete intersections LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Algebraic Geometry Seminar 2013\n\nAbstract: We survey some results of birational rigidity on Fano complete intersections in projective space by Pukhlikov. END:VEVENT BEGIN:VEVENT DTSTART:20131219T160000 DTEND:20131219T180000 DTSTAMP:20131218T150000Z UID:6b0b364a90090b4bd89ff785dfd9c797@cgp.ibs.re.kr SUMMARY:Integrable systems and non-minimal rational elliptic surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Adrian Stefan Carstea\n\nEvent: CGP Seminar 2013\n\nAbstract: Integrability of dynamical systems can be studied by resolution of singularities which allows construction of invariants and symmetries. However in many cases rational surfaces obtained by desingularization of birational dynamical systems are not relatively minimal.We propose a method to obtain coordinates of relatively minimal rational surfaces by using blowing down structure. We apply this method to the study of various integrable systems, including discrete versions of reduced Nahm equations. END:VEVENT BEGIN:VEVENT DTSTART:20131218T163000 DTEND:20131218T173000 DTSTAMP:20131217T150000Z UID:2c11752aedd5af13a5da3fb60ef9ed38@cgp.ibs.re.kr SUMMARY:Generators for abelian extensions of number fields LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dong Hwa Shin(Hankuk University of Foreign Studies)\n\nEvent: 2013 Fall T-Seminar\n\nAbstract: Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a similar argument in terms of norm. As its applications we investigate towers of ray class fields over imaginary quadratic fields. And, we further present a new method of finding a normal element for the extension $U/L$. END:VEVENT BEGIN:VEVENT DTSTART:20140106T100000 DTEND:20140106T120000 DTSTAMP:20140105T150000Z UID:cac6e53e817df0ee0a311ad77cc0325f@cgp.ibs.re.kr SUMMARY:Family Floer cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Family Floer cohomology\n\nAbstract: Floer cohomology assigns a group to a pair of Lagrangians (under certain technical hypotheses). To two families of Lagrangians, Family Floer cohomology should assign a sheaf on to the product of the two parameter spaces. I will explain some motivation behind trying to construct these groups, what has been done so far in the literature (mostly work of Fukaya), and some work in progress to construct these groups. END:VEVENT BEGIN:VEVENT DTSTART:20140107T100000 DTEND:20140107T120000 DTSTAMP:20140106T150000Z UID:49ecf43a0f16ec435394b5552b68bbca@cgp.ibs.re.kr SUMMARY:Family Floer cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Family Floer cohomology\n\nAbstract: Floer cohomology assigns a group to a pair of Lagrangians (under certain technical hypotheses). To two families of Lagrangians, Family Floer cohomology should assign a sheaf on to the product of the two parameter spaces. I will explain some motivation behind trying to construct these groups, what has been done so far in the literature (mostly work of Fukaya), and some work in progress to construct these groups. END:VEVENT BEGIN:VEVENT DTSTART:20140108T100000 DTEND:20140108T120000 DTSTAMP:20140107T150000Z UID:728756e5a5624857553a7c3b51cdbea9@cgp.ibs.re.kr SUMMARY:Family Floer cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Family Floer cohomology\n\nAbstract: Floer cohomology assigns a group to a pair of Lagrangians (under certain technical hypotheses). To two families of Lagrangians, Family Floer cohomology should assign a sheaf on to the product of the two parameter spaces. I will explain some motivation behind trying to construct these groups, what has been done so far in the literature (mostly work of Fukaya), and some work in progress to construct these groups. END:VEVENT BEGIN:VEVENT DTSTART:20140109T100000 DTEND:20140109T120000 DTSTAMP:20140108T150000Z UID:0a22caea4deca669543bba138ff3aab1@cgp.ibs.re.kr SUMMARY:Family Floer cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Family Floer cohomology\n\nAbstract: Floer cohomology assigns a group to a pair of Lagrangians (under certain technical hypotheses). To two families of Lagrangians, Family Floer cohomology should assign a sheaf on to the product of the two parameter spaces. I will explain some motivation behind trying to construct these groups, what has been done so far in the literature (mostly work of Fukaya), and some work in progress to construct these groups. END:VEVENT BEGIN:VEVENT DTSTART:20131221T160000 DTEND:20131221T180000 DTSTAMP:20131220T150000Z UID:5d35ba5d89feb2e1f3d4d44b54ec7e80@cgp.ibs.re.kr SUMMARY:Localized Mirror Functors for Lagrangian Immersions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hansol Hong\n\nEvent: Seminar 2013\n\nAbstract: In this talk, I introduce a construction of a homological mirror functorfrom the Fukaya category to the matrix factorization category associatedwith a weakly unobstructed Lagrangian immersions. As an application,we prove the homological mirror symmetry for orbifold projective lines P^1_a, b, c with 1/a+1/b+1/c≤1. END:VEVENT BEGIN:VEVENT DTSTART:20140127T160000 DTEND:20140127T180000 DTSTAMP:20140126T150000Z UID:8a1119296bff06403ee2f25df9bb1e66@cgp.ibs.re.kr SUMMARY:Introduction to weak KAM theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Albert Fathi\n\nEvent: Introduction to Weak KAM Theory\n\nAbstract: Weak KAM theory makes the link between the theory of Lagrangian Dynamical Systems (in the Mather framework) and the theory of viscosity solutions of the Hamilton-Jacobi equation.We will show how to find non-smooth solutions to the Hamilton-Jacobi equation, and to obtain from this non-smooth solutions the Aubry-Mather invariant sets that do always exist even in the absence of invariant tori given by the KAM theorem.We will give a presentation of the subject with a strong emphasis on the Dynamical Systems point of view. No previous knowledge on the subject will be assumed.A familiarity with ODEs and the rudiments of the Calculus of Variations might be helpful.My lecture notes on the subject can be obtained from http://tinyurl.com/AFnotesWeakKamThere is also a nice introduction in Alain Chenciner “Calculus of variations in the convex case : an introduction to Fathi’s weak KAM theory and Mather’s theory of minimal invariant measures” 5 conferences at Universitat Politecnica de Catalunya, Barcelone, June 26 – July 2 2004http://www.bdl.fr/Equipes/ASD/person/chenciner/chenciner.html END:VEVENT BEGIN:VEVENT DTSTART:20140204T140000 DTEND:20140204T155000 DTSTAMP:20140203T150000Z UID:e013fcb4d44683ea3b01a2e1885117b8@cgp.ibs.re.kr SUMMARY:Introduction to weak KAM theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Albert Fathi\n\nEvent: Introduction to Weak KAM Theory\n\nAbstract: Weak KAM theory makes the link between the theory of Lagrangian Dynamical Systems (in the Mather framework) and the theory of viscosity solutions of the Hamilton-Jacobi equation.We will show how to find non-smooth solutions to the Hamilton-Jacobi equation, and to obtain from this non-smooth solutions the Aubry-Mather invariant sets that do always exist even in the absence of invariant tori given by the KAM theorem.We will give a presentation of the subject with a strong emphasis on the Dynamical Systems point of view. No previous knowledge on the subject will be assumed.A familiarity with ODEs and the rudiments of the Calculus of Variations might be helpful.My lecture notes on the subject can be obtained from http://tinyurl.com/AFnotesWeakKamThere is also a nice introduction in Alain Chenciner “Calculus of variations in the convex case : an introduction to Fathi’s weak KAM theory and Mather’s theory of minimal invariant measures” 5 conferences at Universitat Politecnica de Catalunya, Barcelone, June 26 – July 2 2004http://www.bdl.fr/Equipes/ASD/person/chenciner/chenciner.html END:VEVENT BEGIN:VEVENT DTSTART:20140203T160000 DTEND:20140203T180000 DTSTAMP:20140202T150000Z UID:733b17613db635410f2e73c432646edb@cgp.ibs.re.kr SUMMARY:Introduction to weak KAM theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Albert Fathi\n\nEvent: Introduction to Weak KAM Theory\n\nAbstract: Weak KAM theory makes the link between the theory of Lagrangian Dynamical Systems (in the Mather framework) and the theory of viscosity solutions of the Hamilton-Jacobi equation.We will show how to find non-smooth solutions to the Hamilton-Jacobi equation, and to obtain from this non-smooth solutions the Aubry-Mather invariant sets that do always exist even in the absence of invariant tori given by the KAM theorem.We will give a presentation of the subject with a strong emphasis on the Dynamical Systems point of view. No previous knowledge on the subject will be assumed.A familiarity with ODEs and the rudiments of the Calculus of Variations might be helpful.My lecture notes on the subject can be obtained from http://tinyurl.com/AFnotesWeakKamThere is also a nice introduction in Alain Chenciner “Calculus of variations in the convex case : an introduction to Fathi’s weak KAM theory and Mather’s theory of minimal invariant measures” 5 conferences at Universitat Politecnica de Catalunya, Barcelone, June 26 – July 2 2004http://www.bdl.fr/Equipes/ASD/person/chenciner/chenciner.html END:VEVENT BEGIN:VEVENT DTSTART:20140205T140000 DTEND:20140205T160000 DTSTAMP:20140204T150000Z UID:dfd8d81e5d4728399b9a28c4dc5e0f14@cgp.ibs.re.kr SUMMARY:Introduction to weak KAM theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Albert Fathi\n\nEvent: Introduction to Weak KAM Theory\n\nAbstract: Weak KAM theory makes the link between the theory of Lagrangian Dynamical Systems (in the Mather framework) and the theory of viscosity solutions of the Hamilton-Jacobi equation.We will show how to find non-smooth solutions to the Hamilton-Jacobi equation, and to obtain from this non-smooth solutions the Aubry-Mather invariant sets that do always exist even in the absence of invariant tori given by the KAM theorem.We will give a presentation of the subject with a strong emphasis on the Dynamical Systems point of view. No previous knowledge on the subject will be assumed.A familiarity with ODEs and the rudiments of the Calculus of Variations might be helpful.My lecture notes on the subject can be obtained from http://tinyurl.com/AFnotesWeakKamThere is also a nice introduction in Alain Chenciner “Calculus of variations in the convex case : an introduction to Fathi’s weak KAM theory and Mather’s theory of minimal invariant measures” 5 conferences at Universitat Politecnica de Catalunya, Barcelone, June 26 – July 2 2004http://www.bdl.fr/Equipes/ASD/person/chenciner/chenciner.html END:VEVENT BEGIN:VEVENT DTSTART:20140204T160000 DTEND:20140204T180000 DTSTAMP:20140203T150000Z UID:b3a54f8892fc7df572c7edf4fd92ae0a@cgp.ibs.re.kr SUMMARY:Tau function and Chern-Simons invariant LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinsung Park\n\nEvent: CGP Seminar 2014\n\nAbstract: In this talk I will explain an equality relating the Bergman tau function for a Riemann surfaceto the complex valued Chern-Simons invariant and Zograf F-function for a bounding Schottky hyperbolic 3-manifold.This equality can be understood as an generalization of the defining equality of the Dedekind eta function.This is a joint work with A. Mcintyre. END:VEVENT BEGIN:VEVENT DTSTART:20140110T140000 DTEND:20140110T153000 DTSTAMP:20140109T150000Z UID:35121c92b357790454eb0af2abeea6b4@cgp.ibs.re.kr SUMMARY:Fano threefold hypersurfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: In 1979 Reid discovered the 95 families of K3 surfaces in three dimensional weighted projective spaces. After this, Fletcher, who was a Ph.D. student of Ried, discovered the 95 families of weighted Fano threefold hypersurfaces in his Ph.D. dissertation in 1988. These are quasi-smooth hypersurfaces of degrees d with only terminal singularities in weighted projective spaces P(1,a1,a2,a3,a4), where d=a1+a2+a3+a4. The 95 families are determined by the quadruples of non-decreasing positive integers (a1, a2, a3, a4). All Reid’s 95 families of K3 surfaces arises as anticanonical divisors in Fletcher’s 95 families of Fano threefolds.In my talk, non-rationality of quasi-smooth hypersurfaces in the 95 families will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20140114T160000 DTEND:20140114T180000 DTSTAMP:20140113T150000Z UID:1dfa93899e475a25ed55a46abadffc40@cgp.ibs.re.kr SUMMARY:Lagrangian caps and flexibility in high dimensional symplectic geometry I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Emmy Murphy\n\nEvent: Lagrangian Caps and Flexibility in High Dimensional Symplectic Geometry\n\nAbstract: Does there exist a Lagrangian disk in $C^n−B^{2n}$, which is Legendrian at the boundary? When n=2 the answer is no, but in all higher dimensions the answer is yes. This is an example of a more general existence theorem for Lagrangian embeddings with loose Legendrian concave boundary. Over two talks we discuss applications of this theorem, and sketch a proof.During the first talk, we will set up the context and statement of the theorem. We then discuss applications to Lagrangian embeddings and immersions in $C^n$. As examples we construct Lagrangians in $C^n$ which are not uniruled by holomorphic disks, and show any closed 3-manifold exactly immerses into $C^3$ as a Lagrangian with a single transverse self-intersection.During the second talk we will sketch a proof of the main theorem. Following this we then discuss applications to Weinstein manifolds. We show that any Weinstein manifold is only geometrically interesting in a topological collar of the boundary, and also prove theorems about embedding Weinstein domains into other symplectic manifolds, even compact ones. END:VEVENT BEGIN:VEVENT DTSTART:20140116T160000 DTEND:20140116T180000 DTSTAMP:20140115T150000Z UID:a7955745b1e9533bed4c4279cafe1904@cgp.ibs.re.kr SUMMARY:Lagrangian caps and flexibility in high dimensional symplectic geometry II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Emmy Murphy\n\nEvent: Lagrangian Caps and Flexibility in High Dimensional Symplectic Geometry\n\nAbstract: Does there exist a Lagrangian disk in $C^n−B^{2n}$, which is Legendrian at the boundary? When n=2 the answer is no, but in all higher dimensions the answer is yes. This is an example of a more general existence theorem for Lagrangian embeddings with loose Legendrian concave boundary. Over two talks we discuss applications of this theorem, and sketch a proof.During the first talk, we will set up the context and statement of the theorem. We then discuss applications to Lagrangian embeddings and immersions in $C^n$. As examples we construct Lagrangians in $C^n$ which are not uniruled by holomorphic disks, and show any closed 3-manifold exactly immerses into $C^3$ as a Lagrangian with a single transverse self-intersection.During the second talk we will sketch a proof of the main theorem. Following this we then discuss applications to Weinstein manifolds. We show that any Weinstein manifold is only geometrically interesting in a topological collar of the boundary, and also prove theorems about embedding Weinstein domains into other symplectic manifolds, even compact ones. END:VEVENT BEGIN:VEVENT DTSTART:20140108T110000 DTEND:20140108T120000 DTSTAMP:20140107T150000Z UID:6dbaccc31b03e9b614611fbe8fbe025b@cgp.ibs.re.kr SUMMARY:Intensity non-uniformity correction method for brain MR imaging LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yunho Kim (School of Medicine, Yale University)\n\nEvent: Math Seminar\n\nAbstract: MR (Magnetic Resonance) images often contain an artifact called intensity non-uniformity. Possible causes include RF coil inhomogeneity, gradient driven eddy currents, interactions within the body. In brain MR images, we are often interested in the classification of the brain into white matter, gray matter, cerebro-spinal fluid. However, this artifact makes vague distinction between the regions and segmentation results are not usually satisfactory without preprocessing the data to correct it. In this talk, we model the artifact as a smooth and slowly varying function and characterize a set that contains such a unique function with a practical assumption. We then propose and analyze an optimization problem to find it. At the end, we provide numerical experiments and a comparison result with a popular state-of-the-art method called N3. END:VEVENT BEGIN:VEVENT DTSTART:20140117T094500 DTEND:20140117T170000 DTSTAMP:20140116T150000Z UID:ba9694d71c4201dc77516ad30c17c46d@cgp.ibs.re.kr SUMMARY:1st Brainstorming Meeting between Mathematics and Fluid Dynamics (1st BM²F) LOCATION:POSTECH DESCRIPTION:Speaker: \n\nEvent: PMI Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140115T140000 DTEND:20140115T160000 DTSTAMP:20140114T150000Z UID:784c6e4d4fbf97ffa4d5e64119d49b53@cgp.ibs.re.kr SUMMARY:Arithmetic of elliptic curves and L-functions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: Seminar 2014\n\nAbstract: An elliptic curve is, roughly speaking, a cubic equation in two variables. Given an elliptic curve with rational coefficients, the task of finding all rational solutions of it has remained one of the number theorists' favorite since the work of Diophantus. The way number theorists understand this ancient problem changed in a fundamental way in 60's when Birch and Swinnerton-Dyer formulated their famous conjecture on the relationship between solutions of an elliptic curve and the Hasse-Weil L-function of it. The aim of this talk is to explain their conjecture and one modest generalization of it, to a general audience. If time permits, I will talk about the role of Iwasawa theory in the proof of special cases of the conjecture, including its non-commutative generalizations. END:VEVENT BEGIN:VEVENT DTSTART:20140120T100000 DTEND:20140120T110000 DTSTAMP:20140119T150000Z UID:54e944a3d5df4449cac7daec89121fab@cgp.ibs.re.kr SUMMARY:Aubry-Mather theory and Lipschitz Lagrangian manifolds LOCATION:POSTECH DESCRIPTION:Speaker: Patrick Bernard\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140120T111500 DTEND:20140120T121500 DTSTAMP:20140119T150000Z UID:04093f15ef520a9dd984523997267e7c@cgp.ibs.re.kr SUMMARY:$C^0$ integrability under a convexity assumption LOCATION:POSTECH DESCRIPTION:Speaker: Marie-Claude Arnaud\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140120T140000 DTEND:20140120T150000 DTSTAMP:20140119T150000Z UID:2e7af9d4652a99824fa11724b708b9a2@cgp.ibs.re.kr SUMMARY:On the Multiplicity of Isometry-Invariant Geodesics LOCATION:POSTECH DESCRIPTION:Speaker: Marco Mazzucchelli\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: The problem of isometry-invariant geodesics, introduced by K. Grove in the 70s, is a generalization of the closed geodesics one: given an isometry of a closed Riemannian manifold, one looks for geodesics on which the isometry acts as a non-trivian translation. In this talk, after recalling the framework of the problem and possible contact-geometric generalizations, we shall present a few new multiplicity results on certain Riemannian manifolds homeomorphic to a non-trivial product, and on Riemannian manifolds with infinite abelian fundamental group. END:VEVENT BEGIN:VEVENT DTSTART:20140120T153000 DTEND:20140120T160000 DTSTAMP:20140119T150000Z UID:801da8049cc57be889e6c676128fdcb3@cgp.ibs.re.kr SUMMARY:Optimal Transformation for Generalized Lagrangian LOCATION:POSTECH DESCRIPTION:Speaker: Ji Li\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: We study the optimal transportation for generalized Lagrangian $L=L(x, u,t)$, and consider the cost function as following:$$c(x, y)=\inf_{\substack{x(0)=x\\x(1)=y\\u\in\mathcal{U}}}\int_0^1L(x(s), u(x(s),s), s)ds.$$Where $\mathcal{U}$ is a control set, and $x$ satisfies the following ordinary equation:$$\dot{x}(s)=f(x(s),u(x(s),s),s).$$We prove that under the condition that the initial measure $\mu_0$ is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation:$$\begin{cases}V_t(t, x)+\sup_{\substack{u\in\mathcal{U}}}\lt V_x(t, x), f(x, u(x(t), t),t)-L(x(t), u(x(t), t),t)\gt =0.&\\V(0,x)=\phi_0(x)&\end{cases}$$ END:VEVENT BEGIN:VEVENT DTSTART:20140120T161500 DTEND:20140120T171500 DTSTAMP:20140119T150000Z UID:e73d70359f1b5ab6166456c28c20a33c@cgp.ibs.re.kr SUMMARY:Algebraic properties and geometric invariants of classical diffeomorphism groups LOCATION:POSTECH DESCRIPTION:Speaker: Tomasz Rybicki\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: First well-known results concerning the symplectomorphism group and the volume preserving diffeomorphism group are presented. Next the automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced.In particular the simplicity of the kernels of these homomorphisms is proved. In the second part of my talk the contactomorphism group and the strict contactomorphism group are investigated. The latter group is viewed as the quantomorphism group of the total space of a prequantization bundle in the case of a closed integral symplectic manifold.The compactly supported identity component of the contactomorphism group is simple while it is not the case of its strict subgroup. The properties of an invariant being an obstacle to the simplicity of the strict contactomorphism group are proved. Some applications to symplectic geometry and topology are presented. END:VEVENT BEGIN:VEVENT DTSTART:20140121T100000 DTEND:20140121T110000 DTSTAMP:20140120T150000Z UID:17f74e87dfd0739db4e1bc836e85e78b@cgp.ibs.re.kr SUMMARY:Non-finite energy pseudoholomorphic curves LOCATION:POSTECH DESCRIPTION:Speaker: Barney Bramham\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: In this mainly speculative talk I will discuss a situation where it seems natural in applications to dynamical systems to consider pseudoholomorphic curves in symplectizations that do not have finite energy. We will begin to explore what a "theory" of such curves might be like and how they might be used. END:VEVENT BEGIN:VEVENT DTSTART:20140121T111500 DTEND:20140121T121500 DTSTAMP:20140120T150000Z UID:64207e0e5504a17d5ba351ee781c3ac6@cgp.ibs.re.kr SUMMARY:Topological contact dynamics and its applications LOCATION:POSTECH DESCRIPTION:Speaker: Stefan Müller\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: This talk will explain the complications inherent in adapting topological Hamiltonian dynamics to topological contact dynamics, and show how they are overcome. We then explore applications of topological contact dynamics, which arise from a contact version of the energy-capacity inequality and/or uniqueness of the topological conformal factor. In particular, we discuss a rigidity result for geodesic flows. END:VEVENT BEGIN:VEVENT DTSTART:20140121T140000 DTEND:20140121T150000 DTSTAMP:20140120T150000Z UID:ab3a2ff6e9955cc31f72b8e1a0a2272d@cgp.ibs.re.kr SUMMARY:Topological rigidity of contact and symplectic isotopies LOCATION:POSTECH DESCRIPTION:Speaker: Peter Spaeth\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: A contact or symplectic manifold carries with it distinguished groups of topological isotopies that are defined via metric completions of the associated groups of smooth contact or symplectic isotopies of the manifold. We will explore different aspects of rigidity of these groups of topological isotopies and their time-one maps, and applications to smooth and topological dynamics. In particular we will explain the implications of topological contact dynamics on the helicity invariant from fluid mechanics, and a simple criterion to detect non-contractible loops of strictly contact diffeomorphisms. New displacement energies for contact and symplectic manifolds will also be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20140121T153000 DTEND:20140121T160000 DTSTAMP:20140120T150000Z UID:c7fefc4616b81ab1a1a37a74aa05f036@cgp.ibs.re.kr SUMMARY:Superheavy Lagrangian immersion in 2-torus LOCATION:POSTECH DESCRIPTION:Speaker: Morimichi Kawasaki\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: M. Entov and L. Polterovich defined heaviness and superheaviness of closed subsets in closed symplectic manifolds to solve the problem of non-displaceability of lagrangian submanifolds. To define heaviness and superheaviness, they used the Oh-Schwarz spectral invariants which are from the Hamitonian Floer theory. We explain our method to give superheavy subsets by using noncontractible Hamitonian circle actions. One of our examples is the sum of the meridian curve and the longitude curve in the 2-torus. By this example, we give the non-trivial result about non-displaceability. END:VEVENT BEGIN:VEVENT DTSTART:20140121T161500 DTEND:20140121T171500 DTSTAMP:20140120T150000Z UID:38808338073ab638ac5d340cd8e402d9@cgp.ibs.re.kr SUMMARY:Action for hamiltonian homeomorphisms on surfaces LOCATION:POSTECH DESCRIPTION:Speaker: Frédéric Le Roux\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: We will discuss the following result: for a surface homeomorphism belonging to the $C^0$ closure of hamiltonian diffeomorphisms, the action function may be defined for a dense set of contractible fixed points. END:VEVENT BEGIN:VEVENT DTSTART:20140123T100000 DTEND:20140123T110000 DTSTAMP:20140122T150000Z UID:b15945519eb7609c4cc3e127e1f44287@cgp.ibs.re.kr SUMMARY:Submanifolds and the Hofer norm LOCATION:POSTECH DESCRIPTION:Speaker: Michael Usher\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: The Hofer norm on the Hamiltonian diffeomorphism group of a symplectic manifold induces a natural pseudometric on the orbit of any submanifold under the action of the group. It is easy to see that the pseudometric vanishes identically when the submanifold is a point, whereas Chekanov showed that for a compact Lagrangian submanifold of a tame symplectic manifold the pseudometric is nondegenerate. I will discuss the situation for more general submanifolds, showing on the one hand that the pseudometric continues to be nondegenerate for many classes of coisotropic submanifolds, and on the other that it vanishes identically for appropriately generic submanifolds having codimension at least two. END:VEVENT BEGIN:VEVENT DTSTART:20140123T111500 DTEND:20140123T121500 DTSTAMP:20140122T150000Z UID:7f665f2506505c5872994efbb0045992@cgp.ibs.re.kr SUMMARY:A variant of the energy-capacity inequality and applications to $C^0$-symplectic topology. LOCATION:POSTECH DESCRIPTION:Speaker: Vincent Humilière\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: I will present the following statement: if a Hamiltonian is equal to a sufficiently large constant on some open set, then the Hofer energy of its time one map is bounded from below. I will also talk about a Lagrangian version of this result and show some applications to $C^0$-symplectic topology. This is joint work with Rémi Leclercq and Sobhan Seyfaddini. END:VEVENT BEGIN:VEVENT DTSTART:20140123T140000 DTEND:20140123T150000 DTSTAMP:20140122T150000Z UID:8a7b96e198922ab2e913abce983ddacc@cgp.ibs.re.kr SUMMARY:Rigidity of coisotropic submanifolds LOCATION:POSTECH DESCRIPTION:Speaker: Rémi Leclercq\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: In a joint work with Vincent Humilière and Sobhan Seyfaddini, we showed that not only symplectic homeomorphisms preserve coisotropic submanifolds but also map characteristic foliations to characteristic foliations. I will discuss this result and in particular I will show that it relies on continuous analogs of dynamical properties satisfied by coisotropics. Then I will discuss some consequences of this rigidity phenomenon. END:VEVENT BEGIN:VEVENT DTSTART:20140123T161500 DTEND:20140123T171500 DTSTAMP:20140122T150000Z UID:2e4521b595e1edc4857f706d08c56f50@cgp.ibs.re.kr SUMMARY:Variations on Eliashberg-Gromov theorem I LOCATION:POSTECH DESCRIPTION:Speaker: Lev Buhovsky\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: I will discuss a joint work with E. Opshtein, concerned with rigidity and flexibility of smooth submanifolds under the action of symplectic homeomorphisms. I will start with the celebrated Eliashberg-Gromov theorem and with a recent coisotropic rigidity result of Humili ère-Leclercq-Seyfaddini, and then I will formulate our results and state some related questions. END:VEVENT BEGIN:VEVENT DTSTART:20140124T100000 DTEND:20140124T110000 DTSTAMP:20140123T150000Z UID:b2fb7f0aeaea78c78a43df8253a9c206@cgp.ibs.re.kr SUMMARY:Variations on Eliashberg-Gromov's theorem II LOCATION:POSTECH DESCRIPTION:Speaker: Emmanuel Opshtein\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: I will discuss a joint work with L. Buhovsky, concerned with some quantitative aspects of the rigidity of symplectic homeomorphisms. The basic question is the following: when a symplectic homeomorphism takes some symplectic submanifold to a smooth symplectic submanifold, what can be said on the action of its restriction on capacities ? I will mainly explain a flexibility result: there are symplectic homeomorphisms that fix symplectic discs (or even codimension 4 symplectic submanifolds), and contract the restriction of the symplectic form. On the other hand, there is some rigidity in codimension 2. END:VEVENT BEGIN:VEVENT DTSTART:20140124T111500 DTEND:20140124T121500 DTSTAMP:20140123T150000Z UID:f6e31c6e67c29f28e486675ffc4bc672@cgp.ibs.re.kr SUMMARY:Reduction for quasi-morphisms on contactomorphism groups and contact rigidity LOCATION:POSTECH DESCRIPTION:Speaker: Frol Zapolsky\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: I'll formulate a framework for nondisplaceability phenomena in contact manifolds using quasi-morphisms on contactomorphism groups. Then I'll explain how to construct such quasi-morphisms using reduction and Givental's nonlinear Maslov index. Based on joint work with M. Strom Borman. END:VEVENT BEGIN:VEVENT DTSTART:20140124T140000 DTEND:20140124T150000 DTSTAMP:20140123T150000Z UID:b2bc237895247ba8a1f1568f0f1cac73@cgp.ibs.re.kr SUMMARY:The displaced disks problem via symplectic topology LOCATION:POSTECH DESCRIPTION:Speaker: Sobhan Seyfaddini\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: We will show that a $C^0$-small area preserving homeomorphism of $S^2$ cannot displace a disk of large area. This resolves the displaced disks problem posed by F. Béguin, S. Crovisier, and F. Le Roux. END:VEVENT BEGIN:VEVENT DTSTART:20140124T151500 DTEND:20140124T161500 DTSTAMP:20140123T150000Z UID:efb166bdab8fa1e1f99454575b3f619f@cgp.ibs.re.kr SUMMARY:Non-convex Aubry Mather theory LOCATION:POSTECH DESCRIPTION:Speaker: Claude Viterbo\n\nEvent: $C^0$-symplectic topology and dynamical systems\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20120913T200000 DTEND:20120913T220000 DTSTAMP:20120912T150000Z UID:8fd7487bc358e92d82c203c7edffc8ba@cgp.ibs.re.kr SUMMARY:Simulacra And Simulation on the Quantum World I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20120917T200000 DTEND:20120917T220000 DTSTAMP:20120916T150000Z UID:5764b919e0c7db8137b55eb97dec6500@cgp.ibs.re.kr SUMMARY:Between Strings, Categories and Topology LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20120920T200000 DTEND:20120920T220000 DTSTAMP:20120919T150000Z UID:c96147c064017d6b9dadffc8d189eb93@cgp.ibs.re.kr SUMMARY:Periods of Certain Representations of Lie Algebras I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121011T200000 DTEND:20121011T220000 DTSTAMP:20121010T150000Z UID:baaffeda68488e87a9999be6ca4b365a@cgp.ibs.re.kr SUMMARY:Periods of Certain Representations of Lie Algebras II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121019T110000 DTEND:20121019T120000 DTSTAMP:20121018T150000Z UID:787748089bfb332aa5301a532ae2cf63@cgp.ibs.re.kr SUMMARY:How to find counterfeit coins? An algorithmic version. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeong Han Kim\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121025T200000 DTEND:20121025T220000 DTSTAMP:20121024T150000Z UID:9b8b8ab5ab179b277bcdb1af38ffafcc@cgp.ibs.re.kr SUMMARY:Simulacra And Simulation Of The Quantum World II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121031T170000 DTEND:20121031T190000 DTSTAMP:20121030T150000Z UID:cf5eda572302cde6220d063d2bc4f462@cgp.ibs.re.kr SUMMARY:Periods Of Certain Representations Of Lie Algebras III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121107T153000 DTEND:20121107T163000 DTSTAMP:20121106T150000Z UID:dc9d979f25b18768af0655ff8a876695@cgp.ibs.re.kr SUMMARY:Derived deformation theory and homotopy probability LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: John Terilla\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121109T151500 DTEND:20121109T161500 DTSTAMP:20121108T150000Z UID:ade2b2eaa07c95c12dd529ff3fd3e50a@cgp.ibs.re.kr SUMMARY:A Beginner's Guide to Physics and Mathematics of Scattering Amplitudes LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sangmin Lee\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121109T161500 DTEND:20121109T171500 DTSTAMP:20121108T150000Z UID:1ff2f3ec795669200097f94172fe5aea@cgp.ibs.re.kr SUMMARY:이론물리와 순수수학의 만남(Theoretical Physics Meets Pure Mathematics) LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Seung Joon Hyun\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121115T200000 DTEND:20121115T220000 DTSTAMP:20121114T150000Z UID:28d7e1bef016f62bedaa2c3fae408a3b@cgp.ibs.re.kr SUMMARY:Periods Of Certain Representations Of Lie Algebras IV LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121217T160000 DTEND:20121217T180000 DTSTAMP:20121216T150000Z UID:d8d8ab328a6971426d535723444d9a21@cgp.ibs.re.kr SUMMARY:Hodge Theory and Number Theory I LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Dong Uk Lee\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121218T160000 DTEND:20121218T180000 DTSTAMP:20121217T150000Z UID:1146c3d7a2ffda539c1b265cfba88995@cgp.ibs.re.kr SUMMARY:Hodge Theory and Number Theory II LOCATION:Math. Bldg. #310 DESCRIPTION:Speaker: Dong Uk Lee\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20121221T170000 DTEND:20121221T180000 DTSTAMP:20121220T150000Z UID:e84351c461d64a3fab7a5de24b5ac328@cgp.ibs.re.kr SUMMARY:Euler-Maclaurin formula and a cocycle given by Todd series LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byungheup Jun\n\nEvent: Quantum Monday 2012\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20130108T160000 DTEND:20130108T180000 DTSTAMP:20130107T150000Z UID:1e46e1633c55efc339eee1c0e6587717@cgp.ibs.re.kr SUMMARY:I.Thin instantons in G2 manifolds and Seiberg-Witten invariants II.Thick-thin decomposition of Floer trajectories and adiabatic gluing LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ke Zhu\n\nEvent: Seminar 2013\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20130109T160000 DTEND:20130109T180000 DTSTAMP:20130108T150000Z UID:7b7e4c3e3dc532e4e4edd77e24637c74@cgp.ibs.re.kr SUMMARY:I.Introduction to Homological Mirror Symmetry, Semi-orthgonal Decompositions, and Birational Geometry II.Variation of Geometric Invariant Theory Quotients and Derived Categories LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: David Favero\n\nEvent: Seminar 2013\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20130227T160000 DTEND:20130227T180000 DTSTAMP:20130226T150000Z UID:a050c64e4982b476d70f84262ee9b38d@cgp.ibs.re.kr SUMMARY:Floer-Gromov theory and field theory I, II LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Yakov Savelyev\n\nEvent: Seminar 2013\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20131114T160000 DTEND:20131114T180000 DTSTAMP:20131113T150000Z UID:e44381360827300e625224d3363276b0@cgp.ibs.re.kr SUMMARY:Toward an E_infty minimal model LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: CGP Seminar 2013\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20130124T140000 DTEND:20130124T150000 DTSTAMP:20130123T150000Z UID:a7bc8e06cb9d194a85e92dd4fd76c203@cgp.ibs.re.kr SUMMARY:Considerations when building an IT system for IBS LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Seminar 2013\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20130523T170000 DTEND:20130523T180000 DTSTAMP:20130522T150000Z UID:48d5b2253b717c990a79de4ef22fbdb3@cgp.ibs.re.kr SUMMARY:한국 수학의 국제화와 IBS 기하학수리물리연구단의 역할 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyungju Park\n\nEvent: Seminar 2013\n\nAbstract: 현대적인 의미의 수학이 한국에서 시작되어 나름의 어려움을 겪으며 성장한 과정을 정리해볼 것이다. 이제 21세기의 한국 수학이 다음 단계로 도약하기 위해 필요한 것들이 무엇인지를 살펴보고 세계적인 수학 연구소들의 역할을 정리해보고자 한다. 그리고, 이로부터 IBS 기하학수리물리연구단의 역할과 미래에 대한 제언을 하고자 한다. END:VEVENT BEGIN:VEVENT DTSTART:20140320T160000 DTEND:20140320T180000 DTSTAMP:20140319T150000Z UID:991f144f385a909571ff4f25ff96c492@cgp.ibs.re.kr SUMMARY:Complex structures as homotopy algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joan Millès\n\nEvent: CGP Seminar 2014\n\nAbstract: A complex structure is an almost complex structure which is integrable. A local description of such a structure reveals a lot of algebraic equations. Sergei Merkulov has studied the Nijenhuis integrability condition and he has proposed a simple interpretation of the equations characterizing Nijenhuis structures in terms of homotopy algebras. Following this attempt to define "homotopy geometry", we make use of the curved Koszul duality to describe complex structures as homotopy algebras. END:VEVENT BEGIN:VEVENT DTSTART:20140217T160000 DTEND:20140217T180000 DTSTAMP:20140216T150000Z UID:f3bee4fd6f9a04c0193afd761e5042ba@cgp.ibs.re.kr SUMMARY:Some aspects of mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Changzheng Li\n\nEvent: Seminar 2014\n\nAbstract: In this talk, I will talk about two seemingly very different classical mathematical subjects which nonetheless can be put together under the same framework of mirror symmetry: (1) (quantum) Schubert calculus (2) the theory of primitive forms in singularity theory. More specifically, I will explain functorial properties among quantum cohomology of homogenous varieties which led to new results in quantum Schubert calculus, and a new formulation of primitive forms and its applications to mirror symmetry for Arnold's exceptional unimodular singularities. This talk is based on my various works joint with Naichung Conan Leung, Si Li, Kyoji Saito and Yefeng Shen. END:VEVENT BEGIN:VEVENT DTSTART:20140218T160000 DTEND:20140218T180000 DTSTAMP:20140217T150000Z UID:232e443da7b2e57a36c859f3855358a9@cgp.ibs.re.kr SUMMARY:I. Some topological problems in symplectic geometryII. Finite subgroups of symplectic Cremona group LOCATION:CGP Main Hall DESCRIPTION:Speaker: Weiwei Wu\n\nEvent: Seminar 2014\n\nAbstract: I. In this lecture I will discuss some topological aspects in symplectic geometry, surrounding problems on symplectomorphism groups and Lagrangian embeddings. Problems I will discuss stemmed from Arnold's nearby Lagrangian conjecture and Gromov's original work. We will focus more on the particular case of dimension four, where existing techniques in symplectic geometry yield more geometric information than higher dimensions.II. Finite subgroup of Cremona group is a classical topic in algebraic geometry since the 19th century. In this talk we explain an extension of this problem to the symplectic category. In particular, we will explain the symplectic counterparts of two classical theorems. The first one due to Noether, says a plane Cremona map is decomposed into a sequence of quadratic transformations, which is generalized to the symplectic category on the homological level. The second one is due to Castelnuovo and Kantor, which says a minimal $G$-surface either has a conic bundle structure or is a Del Pezzo surface. The latter theorem lies the ground of classifications of finite Cremona subgroups due to Dolgachev and Iskovskikh. This is an ongoing program joint with Weimin Chen and Tian-Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20140219T160000 DTEND:20140219T180000 DTSTAMP:20140218T150000Z UID:167acc0e57029e3195666d2946eed8ae@cgp.ibs.re.kr SUMMARY:A few remarks on Lagrangian cobordisms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Roman Golovko\n\nEvent: Seminar 2014\n\nAbstract: We will discuss some obstructions to the existence of exact Lagrangian cobordisms in the symplectization of PxR, where P is an exact symplectic manifold, and some constructions of exact Lagrangian cobordisms. In addition, we will say a few words about rigidity and flexibility of Lagrangian cobordisms whose ends are Legendrian isotopic. Some of the results are joint work with B. Chantraine, G. Dimitroglou Rizell, and P. Ghiggini. END:VEVENT BEGIN:VEVENT DTSTART:20140303T190000 DTEND:20140303T210000 DTSTAMP:20140302T150000Z UID:89e7c8163bb23496dfc2ae4cec6cec2a@cgp.ibs.re.kr SUMMARY:Nodal domains and eigenfunctions of negatively curved surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Junehyuk Jung\n\nEvent: Quantum Monday 2014\n\nAbstract: In this talk I'll discuss the nodal set (the zero set) and the nodal domains of eigenfunctions on negatively curved surfaces. By giving a graph structure on the nodal set and using the Euler's inequality for embedded graph, we show that the number of nodal domains is bounded from below by the number of certain singular points of the eigenfunction. The number of such points can be understood by combining recent results on Quantum Ergodic Restriction Theorems and generalized Kuznecov sum formulae. This is a joint work with Steve Zelditch. END:VEVENT BEGIN:VEVENT DTSTART:20140317T160000 DTEND:20140317T180000 DTSTAMP:20140316T150000Z UID:92f76f513b00d54be407322c4ffa86e2@cgp.ibs.re.kr SUMMARY:Givental action and trivialization of the circle action I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bruno Vallette\n\nEvent: Quantum Monday 2014\n\nAbstract: During the first hour, I will explain, to a wide audience, what happens when one mixes Algebra with Homotopy. New interesting higher structures appear naturally, which require to introduce a new mathematical object to encode their intricate combinatorics: this is the notion of an operad. I will introduce two examples of operads: the moduli space of genus 0 stable curves which encodes the category of hypercommutative algebras (also called formal Frobenius manifolds or genus 0 Cohomological Field Theories) and the framed little disks operad which encodes Batalin-Vilkovisky algebras. I will conclude with the definition of Givental action of hypercommutative algebras and formulate two conjectures of Costello and Kontsevich.During the second hour, I will explain, on two toy models (multi complexes and homotopy associative algebras) how one does homotopical algebra with operads. This will open the doors to the Koszul duality theory for operads, which will be used to produce a nice resolution for the operad encoding Batalin-Vilkovisky algebras. END:VEVENT BEGIN:VEVENT DTSTART:20140324T160000 DTEND:20140324T180000 DTSTAMP:20140323T150000Z UID:e308ac1e36751221bd3446b604b4065b@cgp.ibs.re.kr SUMMARY:Givental action and trivialization of the circle action II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bruno Vallette\n\nEvent: Quantum Monday 2014\n\nAbstract: I will begin the first hour with the most canonical resolution of the Batalin-Vilkovisky operad: its minimal model. The associated notion of homotopy Batalin-Vilkovisky algebras is made up of two parts: a homotopy circle action and an action of the moduli space of genus 0 curves. This will allow us to give a proof (over the rationals) of one conjecture mentioned at the end of the first talk: compute the homotopy quotient of the framed little disks operad with respect to the action of the circle. I will then introduce a necessary and sufficient condition, inspired by gauge theory, for the vanishing of this homotopy circle action and apply it to endow the de Rham cohomology of a Poisson manifold with faithful higher structures.The second hour will be devoted to the proof of the second conjecture: give an interpretation of Givental action in terms of trivializations of the circle action. The main step lies in the equality between two worlds: the infinitesimal Given action and the gauge action of homotopy Batalin-Vilkovisky algebras. The rest of the proof is given by integrating properly this infinitesimal action. END:VEVENT BEGIN:VEVENT DTSTART:20140220T160000 DTEND:20140220T180000 DTSTAMP:20140219T150000Z UID:f87c251e5b1a8be6d555efa7e71c59e2@cgp.ibs.re.kr SUMMARY:When is a Stein manifold merely symplectic? LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chris Wendl\n\nEvent: CGP Seminar 2014\n\nAbstract: Stein manifolds are objects originating in complex geometry that also naturally carry symplectic structures. In recent years, the study of Stein structures has increasingly been dominated by the question of "rigid vs. flexible": on the flexible side, the so-called "subcritical" Stein manifolds satisfy an h-principle in higher dimensions, so their Stein homotopy type is determined by the homotopy class of the underlying almost complex structure, and all "interesting" invariants of such structures vanish. At the other end of the spectrum, one should expect to find pairs of Stein manifolds that are symplectomorphic but not Stein deformation equivalent, though no examples are yet known. In this talk, I will explain where NOT to look for examples: in complex dimension 2, there is a large class of Stein domains that exist somewhere between rigid and flexible, meaning that while the h-principle does not hold in any strict sense, their Stein deformation type is completely determined by their symplectic deformation type. This result depends on some joint work with Sam Lisi and Jeremy Van Horn-Morris involving the relationship between Stein structures and Lefschetz fibrations, which can sometimes be realised as foliations by J-holomorphic curves. END:VEVENT BEGIN:VEVENT DTSTART:20140304T140000 DTEND:20140304T150000 DTSTAMP:20140303T150000Z UID:67a7111a0d154f1c7255f8dc83143aa3@cgp.ibs.re.kr SUMMARY:Factorization homology for stratified manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Seminar 2014\n\nAbstract: Factorization homology, also known as topological chiral homology, is a relatively new family of invariants for manifolds. Just as any abelian group provides coefficients for a homology theory, different algebras provide coefficients for factorization homology. However, factorization homology is a much more sensitive invariant than ordinary homology: For instance, by work of Costello and Francis, factorization homology for 3-manifolds recovers the famous Reshetikhin-Turaev invariants for knots. In this talk, I will discuss fundamental examples of factorization homology, as developed in work of David Ayala, Kevin Costello, John Francis, Owen Gwilliam, and Jacob Lurie. I will then discuss joint work with David Ayala and John Francis, which generalizes factorization homology to give invariants of stratified manifolds, analogous to how singular homology generalizes to intersection homology END:VEVENT BEGIN:VEVENT DTSTART:20140306T160000 DTEND:20140306T180000 DTSTAMP:20140305T150000Z UID:2cf9f1ea34745ad3179d706a84aaf2a9@cgp.ibs.re.kr SUMMARY:Lagrangian cobordisms, the Fukaya category, and dreams about mirror symmetry over ring spectra LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: CGP Seminar 2014\n\nAbstract: In this two-part talk, I will talk about recent work on cobordisms between Lagrangian submanifolds. For instance, for every exact symplectic manifold M, one can construct a triangulated category whose objects are Lagrangian branes in M, and whose morphisms are certain Lagrangian cobordisms between them. We discuss a functor from this category of cobordisms to the Fukaya category of M; as a corollary, we prove that any two compact Lagrangian branes related by a compact Lagrangian cobordism are equivalent objects in the Fukaya category. In the second part of my talk, I will discuss connections with Lagrangian correspondences, which are expected to define functors between Fukaya categories. We state a theorem-in-progress showing that Lagrangian correspondences define functors between cobordism categories (and respect compositions of Lagrangian correspondences). Finally, we discuss a road map that suggests the theory of Lagrangian cobordisms provides a family of invariants with maps to bordered Heegard-Floer invariants. END:VEVENT BEGIN:VEVENT DTSTART:20140220T130000 DTEND:20140220T140000 DTSTAMP:20140219T150000Z UID:dee046fefff22811fc840afba37cb684@cgp.ibs.re.kr SUMMARY:Supersonic flow for euler-poisson system LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Jingjing Xiao (Chinese University of Hong Kong)\n\nEvent: Math Seminar\n\nAbstract: In this talk we will discuss some results on supersonic potential flow for steady Euler-Poisson system in a nozzle of a finite length. Prescribing suitable boundary conditions, we establish the existence of one-dimensional supersonic solution and then study the stability of the background solution for multi-dimensional case. END:VEVENT BEGIN:VEVENT DTSTART:20140221T140000 DTEND:20140221T153000 DTSTAMP:20140220T150000Z UID:2d631d8a4b7ee9370074996795cb5549@cgp.ibs.re.kr SUMMARY:Steady subsonic Euler flows with large vorticity in physical domains LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Chunjing Xie (Shanghai Jiao Tong University)\n\nEvent: PMI Seminar\n\nAbstract: In this talk, I will discuss some results on subsonic Euler flows in physical domains, such as the flows in nozzles or past a wall. The focus is on the flows with large vorticity. END:VEVENT BEGIN:VEVENT DTSTART:20140224T160000 DTEND:20140224T180000 DTSTAMP:20140223T150000Z UID:61bc4fd289185f177825877dd67bcd9e@cgp.ibs.re.kr SUMMARY:Modeling Random Noises 1 LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Kijung Lee (Ajou University)\n\nEvent: PMI Seminar\n\nAbstract: In a stochastic parabolic equation the temporal noise of the inhomogeneous term dominates the regularity of the diusion especially in time direction. For a long time white noise has been used in most of modelings. However, at the stage of modeling, the statistical information about the actual noise may not match with white noise and we simply can not use the white noise anymore. In this talk we discuss two ways of modeling more general Gaussian noises; series and colored noises. We also discuss issues related to the regularity of resulting processes from the noises. The discussion will be heuristic. END:VEVENT BEGIN:VEVENT DTSTART:20140225T160000 DTEND:20140225T180000 DTSTAMP:20140224T150000Z UID:eba31ade8793a3be8bd8d42d5ea00d03@cgp.ibs.re.kr SUMMARY:Modeling Random Noises 2 LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Kijung Lee (Ajou Univ.)\n\nEvent: PMI Seminar\n\nAbstract: In a stochastic parabolic equation the temporal noise of the inhomogeneous term dominates the regularity of the diusion especially in time direction. For a long time white noise has been used in most of modelings. However, at the stage of modeling, the statistical information about the actual noise may not match with white noise and we simply can not use the white noise anymore. In this talk we discuss two ways of modeling more general Gaussian noises; series and colored noises. We also discuss issues related to the regularity of resulting processes from the noises. The discussion will be heuristic. END:VEVENT BEGIN:VEVENT DTSTART:20140225T140000 DTEND:20140225T153000 DTSTAMP:20140224T150000Z UID:726c856aff2cfc39e635f203d403e0c8@cgp.ibs.re.kr SUMMARY:Boltzmann equation: classical and relativistic 1 LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Seok Bae Yun (Sungkyunkwan Univ.)\n\nEvent: PMI Seminar\n\nAbstract: In this series of lectures, we are concerned with the spatially homogeneous theory of the relativistic Boltzmann equation, which is a fundamental equation describing the time evolution of the phase space distribution of relativistic particles. The lecture will be divided into the following two parts: 1. Introduction to the Boltzmann equation:I will start with the overview of the kinetic theory of gases. Then the derivation of the Boltzmann equation will be considered and physical and mathematical properties of the Boltzmann equation will be discussed. If time allows, I will briefly introduce some model equations in the kinetic theory. 2. Recent results on the L^1 and L^{infty} moments propagation for the relativistic Boltzmann equation: In the second part of the lecture, my recent work with Robert Strain on the spatially homogeneous relativistic Boltzmann equation for will be presented. Several mathematical issues such as the relativistic Povzner inequality or the relativistic Carlemann representation of the collision operator will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20140226T140000 DTEND:20140226T153000 DTSTAMP:20140225T150000Z UID:e612fc4d2658821f32a89d782de259eb@cgp.ibs.re.kr SUMMARY:Boltzmann equation: classical and relativistic 2 LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Seok Bae Yun (Sungkyunwan Univ.)\n\nEvent: PMI Seminar\n\nAbstract: In this series of lectures, we are concerned with the spatially homogeneous theory of the relativistic Boltzmann equation, which is a fundamental equation describing the time evolution of the phase space distribution of relativistic particles. The lecture will be divided into the following two parts:1. Introduction to the Boltzmann equation:I will start with the overview of the kinetic theory of gases. Then the derivation of the Boltzmann equation will be considered and physical and mathematical properties of the Boltzmann equation will be discussed. If time allows, I will briefly introduce some model equations in the kinetic theory.2. Recent results on the L^1 and L^{infty} moments propagation for the relativistic Boltzmann equation: In the second part of the lecture, my recent work with Robert Strain on the spatially homogeneous relativistic Boltzmann equation for will be presented. Several mathematical issues such as the relativistic Povzner inequality or the relativistic Carlemann representation of the collision operator will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20140227T140000 DTEND:20140227T153000 DTSTAMP:20140226T150000Z UID:c931572fb26e9016a8473706fccc8a83@cgp.ibs.re.kr SUMMARY:Boltzmann equation: classical and relativistic 3 LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Seok Bae Yun (Sungkyunkwan University)\n\nEvent: PMI Seminar\n\nAbstract: In this series of lectures, we are concerned with the spatially homogeneous theory of the relativistic Boltzmann equation, which is a fundamental equation describing the time evolution of the phase space distribution of relativistic particles. The lecture will be divided into the following two parts:1. Introduction to the Boltzmann equation:I will start with the overview of the kinetic theory of gases. Then the derivation of the Boltzmann equation will be considered and physical and mathematical properties of the Boltzmann equation will be discussed. If time allows, I will briefly introduce some model equations in the kinetic theory.2. Recent results on the L^1 and L^{infty} moments propagation for the relativistic Boltzmann equation: In the second part of the lecture, my recent work with Robert Strain on the spatially homogeneous relativistic Boltzmann equation for will be presented. Several mathematical issues such as the relativistic Povzner inequality or the relativistic Carlemann representation of the collision operator will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20140327T160000 DTEND:20140327T170000 DTSTAMP:20140326T150000Z UID:b5b35158628677c52105dab4e12858d1@cgp.ibs.re.kr SUMMARY:Isometric Reeb Flow and Contact Hypersurfaces in Hermitian Symmetric Spaces LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Young Jin Suh (Kyungpook National University)\n\nEvent: PMI Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140307T160000 DTEND:20140307T171500 DTSTAMP:20140306T150000Z UID:d95ca823afcc8c211ec6f03d9cbc1928@cgp.ibs.re.kr SUMMARY:Generalizations of Forelli's theorem LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kang-Tae Kim (POSTECH)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: Second only to the celebrated Hartogs' analyticity theorem in several complex variables, Forelli’s theorem has its unique position in complex geometry. However it was generally believed that it is impossible to generalize since its initial appearance in 1977. Then a generalization took place by E. Chirka of Russia in 2005/2006 in complex dimension 2 and the higher dimension was posed as an open problem. Now at least two directions are well understood through the papers by Kim-Poletsky-Schmalz (2008), also by Joo-Kim-Schmalz (2013, 2014). I would like to give a report on the whole account of this line of research. END:VEVENT BEGIN:VEVENT DTSTART:20140314T163000 DTEND:20140314T171500 DTSTAMP:20140313T150000Z UID:ff94979acc690e23b2727184a855ce07@cgp.ibs.re.kr SUMMARY:L-functions and modular forms LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Winfried Kohnen (Univ. of Heidelberg)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: We will report about useful applications of L-functions, both from aclassical and also modern point of view, in particular in the connection of modular forms. No pre-knowledge of the theory of L-series or modular forms will be assumed. END:VEVENT BEGIN:VEVENT DTSTART:20140321T163000 DTEND:20140321T171500 DTSTAMP:20140320T150000Z UID:c65e6b311aaaa3bd422b0812a006d4ad@cgp.ibs.re.kr SUMMARY:Homotopy theory of Batalin—Vilkovisky algebras and applications LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Bruno Vallette (Université de Nice-Sophia Antipolis)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: The notion of Batalin—Vilkovisky algebras is a type of algebraic structures which appears in many fields of Mathematics: Differential Geometry (de Rham complex), Mathematical Physics (renomalization), Algebraic Geometry (moduli spaces of curves), and Algebra (cohomology of Lie algebras), to name but a few. The goal of the homotopy theory of Batalin—Vilkovisky algebras is to study how this algebraic structure behaves with respect to deformations of underlying spaces. Deformations make higher operations appear, which carry of lot of informations. The purpose of this talk is to provide a gentle introduction to this theory, including applications to Algebra, Geometry, Topology and Mathematical Physics . END:VEVENT BEGIN:VEVENT DTSTART:20140328T163000 DTEND:20140328T171500 DTSTAMP:20140327T150000Z UID:4d6ea9350dcffa19ddb753904ae93cdd@cgp.ibs.re.kr SUMMARY:Partial differential equations in Sobolev spaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Doyoon Kim (Kyunghee University)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: Since their introduction in the early 20th century, Sobolev spaces,together with the Sobolev imbedding theorem, have become one of the most powerful tools in the theory of partial differential equations(PDEs), and many approaches have been developed to deal with PDEs in Sobolev spaces.In this talk we will discuss elliptic and parabolic PDEs whensolutions are sought in Sobolev spaces, and show the advantages ofconsidering PDEs in Sobolev spaces, especially, when PDEs haverelatively rough coefficients and data. We will also discuss variousapproaches for PDEs in Sobolev spaces and some recent results about the solvability of elliptic and parabolic PDEs when the coefficients are very rough. Some counterexamples will be given to illustrate the regularity of solutions one can or cannot expect when PDEs do not have good coefficients. END:VEVENT BEGIN:VEVENT DTSTART:20140305T160000 DTEND:20140305T170000 DTSTAMP:20140304T150000Z UID:1ae91e53dc449b4d33dfdc2bf6340aa7@cgp.ibs.re.kr SUMMARY:Effective computation of period integrals of elliptic curves LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Abstract: Let E be an elliptic curve over Q. Griffiths' theorem says that the first homology group H_1(E) can be embedded into the dual of the cohomology H^2(P^2-E),where P^2 is the projective space of dimension 2. In this talk I will describe how to compute an element in the dual of H^2(P^2-E) by using a new description of H^2(P^2-E) and explain a relation with the L-values of E. This can be seen as an application of the general work regarding "period integrals of smooth projective hypersurfaces and homotopyLie algebras" with Jae-Suk Park. END:VEVENT BEGIN:VEVENT DTSTART:20140311T160000 DTEND:20140311T180000 DTSTAMP:20140310T150000Z UID:af5b0dd46eb93ca62b7b2c22906299ef@cgp.ibs.re.kr SUMMARY:Construction of simply connected non-Kähler symplectic manifolds with vanishing odd Betti numbers LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Seminar 2014\n\nAbstract: Due to the work of W. Thurston, R. Gompf, D. McDuff, M. Fernández, V. Muñoz, G. Cavalcanti and many other people, it is quite well-known that the category of symplectic manifolds is much bigger than the category of Kähler manifolds. Almost of their work can be done by constructing symplectic manifolds which violate certain Käherian properties. In this talk, we construct a simply connected 6-dimensional compact symplectic manifold (M, ω) such that [ω] does not satisfy the hard Lefschetz property and every odd Betti number of M vanishes. In particular, our manifold has a semifree Hamiltonian circle action with only two fixed components. As a consequence, there is a smooth compact non-Kähler symplectic manifold which is simply connected and every odd Betti number vanishes for each dimension bigger than four. END:VEVENT BEGIN:VEVENT DTSTART:20140310T160000 DTEND:20140310T180000 DTSTAMP:20140309T150000Z UID:cb39a5012779e02b54ac0eefbc50e406@cgp.ibs.re.kr SUMMARY:Factorization homology for stratified manifolds II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Quantum Monday 2014\n\nAbstract: Factorization homology, also known as topological chiral homology, is a relatively new family of invariants for manifolds. Just as any abelian group provides coefficients for a homology theory, different algebras provide coefficients for factorization homology. However, factorization homology is a much more sensitive invariant than ordinary homology: For instance, by work of Costello and Francis, factorization homology for 3-manifolds recovers the famous Reshetikhin-Turaev invariants for knots. In this talk, I will discuss fundamental examples of factorization homology, as developed in work of David Ayala, Kevin Costello, John Francis, Owen Gwilliam, and Jacob Lurie. I will then discuss joint work with David Ayala and John Francis, which generalizes factorization homology to give invariants of stratified manifolds, analogous to how singular homology generalizes to intersection homology. END:VEVENT BEGIN:VEVENT DTSTART:20140311T140000 DTEND:20140311T150000 DTSTAMP:20140310T150000Z UID:f278f1cddfc4005afbbaa5dfd1e4d28a@cgp.ibs.re.kr SUMMARY:Geometry of the moduli space of pure sheaves supported on quartic curves in $\mathbb{P}^3$ LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kiryong Chung\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: Let $\mathbf{M}_d$ be the moduli space of stable sheaves on $PP^3$ with Hilbert polynomial $dm+1$. By the general result of the Simpson, the moduli space $\mathbf{M}_d$ is a projective scheme for all $d\geq 1$. By the lack of the geometry of the boundary of the space $\mathbf{M}_d$, there are very few results about the geometry of the moduli space. As the first non-trivial case, when $d=3$, Freiermuth and Trautmann showed that the space $\mathbf{M}_3$ is isomorphic to the Hilbert scheme of connected curves with degree $d=3$ and genus $g=0$. The later space consists of two irreducible components: the space of twisted cubic curves and planar cubic curves with an embedded point. In this talk, as a generalization of this one, we study the geometry of the moduli space $\mathbf{M}_4$ for $d=4$. We show that the space $\mathbf{M}_4$ has at least three irreducible components. This is working in progress with J. Choi and M. Maican. END:VEVENT BEGIN:VEVENT DTSTART:20140313T160000 DTEND:20140313T180000 DTSTAMP:20140312T150000Z UID:0d4b40dbb4c268c1760e8adc94295cbc@cgp.ibs.re.kr SUMMARY:Lagrangian cobordisms, the Fukaya category, and dreams about mirror symmetry over ring spectra II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: CGP Seminar 2014\n\nAbstract: In this two-part talk, I will talk about recent work on cobordisms between Lagrangian submanifolds. For instance, for every exact symplectic manifold M, one can construct a triangulated category whose objects are Lagrangian branes in M, and whose morphisms are certain Lagrangian cobordisms between them. We discuss a functor from this category of cobordisms to the Fukaya category of M; as a corollary, we prove that any two compact Lagrangian branes related by a compact Lagrangian cobordism are equivalent objects in the Fukaya category. In the second part of my talk, I will discuss connections with Lagrangian correspondences, which are expected to define functors between Fukaya categories. We state a theorem-in-progress showing that Lagrangian correspondences define functors between cobordism categories (and respect compositions of Lagrangian correspondences). Finally, we discuss a road map that suggests the theory of Lagrangian cobordisms provides a family of invariants with maps to bordered Heegard-Floer invariants. END:VEVENT BEGIN:VEVENT DTSTART:20140417T160000 DTEND:20140417T180000 DTSTAMP:20140416T150000Z UID:c8d6efdc623f8fef57fb6febfd4bc454@cgp.ibs.re.kr SUMMARY:Curvature and contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Patrick Massot\n\nEvent: CGP Seminar 2014\n\nAbstract: This talk will explore relations between global topological features of contact structures and the curvature of suitably compatible Riemannian metrics. This subject is still in its infancy but I will explain an analogue of the sphere theorem (by Rauch, Berger and Klingenberg) in this context. It uses methods from topology, geometry and analysis. This is a joint work with John Etnyre and Rafał Komendarczyk. END:VEVENT BEGIN:VEVENT DTSTART:20140312T160000 DTEND:20140312T170000 DTSTAMP:20140311T150000Z UID:afe857ce89f762a8633c5427070b3e1b@cgp.ibs.re.kr SUMMARY:Non-emptiness of Newton stratification of Shimura varieties of Hodge type. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dong Uk Lee\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140313T163000 DTEND:20140313T173000 DTSTAMP:20140312T150000Z UID:6e33e151ebd21c3d90709aaed1fad531@cgp.ibs.re.kr SUMMARY:Unimodality of the Betti Numbers for Hamiltonian circle actionwith isolated fixed points LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: YunHyung Cho (KIAS)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: In this talk, we will discuss about the following conjectural question due to S. Tolman.Question. Let (M, ω) be a 2n-dimensional smooth compact symplectic manifold equipped with a Hamiltonian circle action with only isolated ﬁxed points. Then is the sequence of even Betti numbers unimodal?, i.e. b_k(M) ≤ b_{k+2}(M) for every k ≤ n − 2?We will show that the answer for the question above is true in the case when dim(M) = 8. Also, we will discuss about future works related to the question in higher dimensional cases. END:VEVENT BEGIN:VEVENT DTSTART:20140319T160000 DTEND:20140319T170000 DTSTAMP:20140318T150000Z UID:a0cf722c6f66f94080d76a597d1a7439@cgp.ibs.re.kr SUMMARY:Hecke bound and cuspidality of vector-valued modular forms LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jongryul Lim (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140327T170000 DTEND:20140327T180000 DTSTAMP:20140326T150000Z UID:8a60bca6af63c8ab991feb569ec51357@cgp.ibs.re.kr SUMMARY:The geometry of the Hilbert scheme of points in the plane LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: İzzet Coşkun\n\nEvent: Special Lecture\n\nAbstract: The Hilbert scheme of points in the plane is a smooth compactification of the configuration space of unordered points in the plane. It plays an important role in combinatorics (such as in Haiman's proof of the n! conjecture), mathematical physics and representation theory (such as in Nakajima's work on the cohomology of the Hilbert scheme) and in algebraic geometry. In this talk, I will give a broad introduction to the geometry of the Hilbert scheme of points in the plane and then describe recent work on its birational geometry. This talk will be based on joint work with Daniele Arcara, Aaron Bertram, Jack Huizenga and Matthew Woolf. END:VEVENT BEGIN:VEVENT DTSTART:20140331T160000 DTEND:20140331T180000 DTSTAMP:20140330T150000Z UID:b1d703b46117d177678d6d724bb7cf52@cgp.ibs.re.kr SUMMARY:M5-branes, holography and knots LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dongmin Gang\n\nEvent: Quantum Monday 2014\n\nAbstract: First, I will give brief introduction to "3d-3d relations" (ref. arXiv:1108.4389) which relate topological invariants on a 3-manifold M to supersymmetric quantities of the corresponding 3-dimensional quantum field theory T[M]. The relation can be heuristically derived from physics of M5-branes. Then, basic ideas of "holographic principle"(ref. arXiv:hep-th/9711200) will be explained. Finally combining the "3d-3d relations" and the "holographic principal" , I will propose a mathematical conjecture on invariants of perturbative Chern-Simons theory defined on knot complements M. The talk is based on arXiv:1401.3595. END:VEVENT BEGIN:VEVENT DTSTART:20140326T160000 DTEND:20140326T170000 DTSTAMP:20140325T150000Z UID:1ebb72a4759ea471448e1c7365d6cbdb@cgp.ibs.re.kr SUMMARY:Property RD LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Irine Peng(POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: I will define what it means for a group to have property RD (Rapid Decay), the history of how this notion came about, and a conjecture of Valette concerning RD of lattices in semisimple Lie groups. END:VEVENT BEGIN:VEVENT DTSTART:20140326T130000 DTEND:20140326T150000 DTSTAMP:20140325T150000Z UID:769751b09a160576f5a0b5c73ef507e9@cgp.ibs.re.kr SUMMARY:Informal introduction to Bridgeland stability I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: İzzet Coşkun\n\nEvent: Seminar 2014\n\nAbstract: In this talk, I will describe the basic geometry of the Hilbert scheme of points on the plane. I will discuss the ample and effective cones and how to run the minimal model program and give interpretations to the models in terms of moduli spaces of Bridgeland stable objects. This is joint work with Arcara, Bertram and Huizenga. END:VEVENT BEGIN:VEVENT DTSTART:20140328T110000 DTEND:20140328T130000 DTSTAMP:20140327T150000Z UID:8bf341fb25df6da18f0862c39f3e7280@cgp.ibs.re.kr SUMMARY:Informal introduction to Bridgeland stability II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: İzzet Coşkun\n\nEvent: Seminar 2014\n\nAbstract: In this talk, I will introduce Bridgeland stability conditions and describe joint work with Jack Huizenga on determining the stable base decomposition of the Hilbert scheme of points on the plane. END:VEVENT BEGIN:VEVENT DTSTART:20140410T160000 DTEND:20140410T180000 DTSTAMP:20140409T150000Z UID:7b8136087046373544b4f9eb20ebc954@cgp.ibs.re.kr SUMMARY:Localized mirror functors LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: CGP Seminar 2014\n\nAbstract: We will explain the formalism of localized mirror functors. Namely, given a good Lagrangian immersion or a torus L, we can define a localized Floer potential W(L) using holomorphic polygons or discs. Then, the formalism provides a canonical functor from Fukaya category of a symplectic manifold to the category of matrix factorizations of the localized Floer potential W(L). END:VEVENT BEGIN:VEVENT DTSTART:20140404T163000 DTEND:20140404T174500 DTSTAMP:20140403T150000Z UID:c62c99163792c4352c92dc203d176600@cgp.ibs.re.kr SUMMARY:Homotopy theory of period integrals of algebraic varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Park (POSTECH)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: P. Griffiths studied the periods of certain rational integrals in his celebrated Annals papers. We approach his period integrals with a different optic (quantum field theoretic and homotopy Lie theoretic) and reveal hidden new structures on them.As a main theorem, we prove that the period integral of a hypersurface X can be enhanced to a homotopy Lie algebra morphism (so called an L_infty-morphism), which governs its correlations and new extended deformations.I will try to make this colloquium as elementary as possible so that graduate students who know the basic definitions of singular (co)homologies and Lie algebras can get some ideas behind the main theorem. This is a joint work with Jae-Suk Park. END:VEVENT BEGIN:VEVENT DTSTART:20140402T160000 DTEND:20140402T170000 DTSTAMP:20140401T150000Z UID:1dead4c4eef3bc8f8fdc97065400b118@cgp.ibs.re.kr SUMMARY:Construction of unramified extensions with a prescribed Galois group LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kim Kwang-Sob (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: We shall prove that for any finite solvable group $G$, there exist infinitely many abelian extensions $K/\Q$ and Galois extensions $M/\Q$ such that the Galois group $\Gal(M/K)$ is isomorphic to $G$ and $M/K$ is unramified. END:VEVENT BEGIN:VEVENT DTSTART:20140403T160000 DTEND:20140403T180000 DTSTAMP:20140402T150000Z UID:533f30ddb5b687b3d18fad5ac595dbfc@cgp.ibs.re.kr SUMMARY:Homotopy theory of the Griffiths period integrals of hypersurfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: CGP Seminar 2014\n\nAbstract: P. Griffiths studied the periods of certain rational integrals in his celebrated Annals papers. We approach his period integrals with a different optic (quantum field theoretic and homotopy Lie theoretic) and reveal hidden new structures on them. As a main theorem, we prove that the period integral of a hypersurface X can be enhanced to a homotopy Lie algebra morphism (so called an L_\infty-morphism), which governs its correlations and new extended deformations. In theoretical physics language, the main theorem amounts to constructing a (0+0)-dimensional quantum field theory where the classical action function is given by a certain polynomial, whose partition functionis exactly the Griffiths period integral of a hypersurface. Main ingredient for our approach is to construct a certain functor from the category of linear representations of Lie algebras to the category of homotopy Lie algebras and develop its general theory. We make a relevant Lie algebra representation attached to the hypersurface X. Then we apply the functor to it and run the generalmachine carefully to verify the main theorem. Also, as an application, an efficient computation algorithm for the period integrals will be given. This is a joint work with Jae-Suk Park. END:VEVENT BEGIN:VEVENT DTSTART:20140502T140000 DTEND:20140502T153000 DTSTAMP:20140501T150000Z UID:56ab814fef810f8d5d0a2a6b12ece837@cgp.ibs.re.kr SUMMARY:An analytic approach to the study of Iitaka's $C_{m,n} ^+$ conjecture LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Junyan Cao\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: Let $f: X\rightarrow Y$ be a fibration between two projective manifolds. The Iitaka's conjecture, one of the main conjectures in birational geometry, states that the Kodaira dimension of $X$ is larger than the sum of the Kodaira dimension of $X$ and the Kodaira dimension of the generic fiber. It has been proved by Kollar that the Iitaka's conjecture is true if the generic fiber is of general type by using some deep results in mixed Hodge theory. By using some analytic methods, we give an alternative proof (without using Hodge thoery). The advantage of our methods is that we can generalise the main result of the article of Kollar to the klt pair case. END:VEVENT BEGIN:VEVENT DTSTART:20140508T160000 DTEND:20140508T180000 DTSTAMP:20140507T150000Z UID:bfc5579d8fd96cf6b36fb4aacd40cd21@cgp.ibs.re.kr SUMMARY:Hyperbolic volume for Knotted graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: CGP Seminar 2014\n\nAbstract: Hyperbolic volume of knots or links is defined by the integration of the hyperbolic volume form over their complement in the 3-sphere where the hyperbolic volume form means an induced 3-form of a complete Riemannian metric whose sectional curvature is constantly negative one. We can regard this metric invariant as a topological invariant by Mostow's rigidity theorem. In practice, it plays a crucial role in classifying 3-manifolds or knots. In this talk we will generalize the notion of hyperbolic volume to knotted graphs as an isotopy invariant. Moreover, we suggest a volume formula written directly from knotted graph diagrams, which is inspired by the volume conjecture relating the hyperbolic volume and the Jones polynomial. END:VEVENT BEGIN:VEVENT DTSTART:20140407T160000 DTEND:20140407T180000 DTSTAMP:20140406T150000Z UID:8a6bd825dbc3c729abe159f96408276e@cgp.ibs.re.kr SUMMARY:Lectures on (0+0)-dimensional quantum field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2014\n\nAbstract: The purpose of this series of lectures is to introduce and develop mathematics of a class of (0+0)-dimensional quantum field theories over an algebraically closed field k. Such a theory governs the space of maps from a point, a (0+0-dimensional space, to an affine, or projective, or toric variety X, which (homogeneous) coordinate ring corresponds to the algebra of classical observables. We shall study the algebra of quantum observables and "quantised points" as primer to quantum algebraic geometry. As an intermediate byproduct, we will have a theory of "extended formal variations of homotopy polarised Hodge structures” on X, which structure encodes generating function of all genus correlation functions of extended topological string theory. END:VEVENT BEGIN:VEVENT DTSTART:20140411T163000 DTEND:20140411T174500 DTSTAMP:20140410T150000Z UID:f0279b52cb674f8871b930864a7315d5@cgp.ibs.re.kr SUMMARY:Investigation of Rheological Behaviors for Powder-Binder Separation and Particle Orientation on Powder Injection Molding LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seong Jin Park (POSTECH)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: Powder injection molding (PIM) is one of the manufacturing technologies to mass-produce near-net-shape metallic or ceramic components at a low cost. The PIM consists of four processing steps: (i) mixing—producing the pelletized feedstock of the powder and organic binders; (ii) molding—injecting the feedstock melt into the mold cavity, similar with thermoplastics; (iii) debinding—extracting or removing the organic binders out of the injection-molded part via solvents or the thermal energy; and (iv) sintering—densifying the debound part from the low initial density to the high final density, close to the full density. Among all the processes, the injection molding is one of the key steps for fabricating defect-free components. One problem in the injection molding is a powder-binder separation (P-B separation) resulted in defects such as voids, cracks and distortion. Even though there are a lot of attempts to predict the P-B separation affected by many factors including mold geometry, solid loading and injection pressure, this problem still remains to be explained. Therefore, it is important to investigate the relationship between those factors and P-B separation phenomenon. In addition, the orientation of the powder, especially for magnetic PIM components, is another consideration for successful injection molding process. Magnetic powder is prone to be aligned for the direction in magnetic field during injection molding. The final alignment of magnetic powders decides the intensity of magnets. The particle-particle, particle-flow, and magnetic field-particle interactions affect to this phenomenon. Even though a few hydrodynamic orientation models for nonmagnetic particles have been suggested to describe the particle orientation, the rheological model considering the effect of magnetic interactions did not exist. Therefore, a new model to describe the powder orientation in a magnetic field is required. In this presentation, the injection molding problem with respect to P-B separation and particle orientation will be introduced and discussed with several mathematical attempts. END:VEVENT BEGIN:VEVENT DTSTART:20140502T160000 DTEND:20140502T180000 DTSTAMP:20140501T150000Z UID:8cf054f803f3adcc3cb6d35a54ef0b0b@cgp.ibs.re.kr SUMMARY:Filtered Hopf algebras and growth of Reeb chords LOCATION:CGP Main Hall DESCRIPTION:Speaker: Urs Frauenfelder\n\nEvent: Seminar 2014\n\nAbstract: This is joint work with Felix Schlenk. We prove a uniform lower bound on the growth of Reeb chords on the spherization of a closed manifold whose universal cover is not homotopy equivalent to a finite CW-complex. Our proof uses the Hopf algebra structure of the based loop space. END:VEVENT BEGIN:VEVENT DTSTART:20140418T133000 DTEND:20140418T143000 DTSTAMP:20140417T150000Z UID:742b902d322b4013ccfc2c778b9ec4c8@cgp.ibs.re.kr SUMMARY:Topics on smooth transonic Euler-Poisson flows LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ben Duan (POSTECH)\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: In this talk, we consider the steady Euler-Poisson system. The aim is to find out a subsonic-sonic-supersonic smooth solution in a given flat nozzle. Our main result is the unique existence of such flow containingsonic curve, the framework of the proof will be given briefly. This is a joint work with Myoungjean Bae at POSTECH and Chunjing Xie at Shanghai Jiaotong Universtity. END:VEVENT BEGIN:VEVENT DTSTART:20140418T163000 DTEND:20140418T174500 DTSTAMP:20140417T150000Z UID:155a6cef94d6174e5c051a46b622f758@cgp.ibs.re.kr SUMMARY:Ramsey-type theorem for graphs without splits LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sang-il Oum (KAIST)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: Ramsey’s theorem (1930) states that every sufficient large graph must contain n pairwise adjacent vertices or n pairwise non-adjacent vertices. We aim to prove a variation of Ramsey’s theorem in which graphs satisfy certain connectivity requirement. A split of a graph is a partition (A,B) of its vertex set such that |A|,|B|≥2 and vertices in A having neighbors in B have the exactly same set of neighbors in B. We will describe an unavoidable structure in all sufficiently large graphs without splits. This is a joint work with O-joung Kwon. END:VEVENT BEGIN:VEVENT DTSTART:20140522T140000 DTEND:20140522T153000 DTSTAMP:20140521T150000Z UID:a407d90b4c9f3edd62cb781c492c452e@cgp.ibs.re.kr SUMMARY:Introduction to tropical algebraic geometry and some applications I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mounir Nisse\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: The goal of this series of lectures is to provide a quick overview of tropical geometry through some examples with the maximum of details ([IMS], [MS], [SS], and [RST]). More precisely, the question that many people ask are e.g., with what kind of problems deals this geometry? And why is it useful to use this geometry in several area of mathematics? After defining a basic objects in tropical geometry, weexplain their relations to the classical algebraic geometry via the notion of amoebas and coamoebas of algebraic varieties ([NS], and [M1]). We will give some applications of tropical geometry to real andenumerative geometry ([M2]) and mirror symmetry.References[IMS] I. Itenberg, G Mikhalkin, and E. Shustin, Tropical Algebraic Geometry, volume bf 35 of Oberwolfach Seminars Series. BirkhŠuser, 2007.[MS] D. Maclagan and B. Sturmfels, Introduction to tropical geometry. Book in progress, available inBernd Sturmfels Homepage.[M1] G. Mikhalkin, Enumerative tropical algebraic geometry in R2. J. Amer. Math. Soc., 18(2), 313Ð377,2005.[M2] G. Mikhalkin, Tropical geometry and its applications. In International Congress of Mathematicians. Vol. II, pages 827Ð852. Eur. Math. Soc., Zurich, 2006.[NS] M. Nisse and F. Sottile, The phase limit set of a variety, Algebra & Number Theory, 7, (2013), 339–352.[RST] J. Richter-Gebert, B. Sturmfels, and T. Theobald, First steps in tropical geometry. In Idempotent mathematics and mathematical physics, volume 377 of Contemp. Math., 289Ð317. Amer. Math. Soc.,Providence, RI, 2005.[SS] D. Speyer and B. Sturmfels, The tropical Grassmannian. Adv. Geom., 4(3), 389Ð 411, 2004. END:VEVENT BEGIN:VEVENT DTSTART:20140605T140000 DTEND:20140605T153000 DTSTAMP:20140604T150000Z UID:c523c3b4b1e661baa56ed2489ffef16b@cgp.ibs.re.kr SUMMARY:Small $\mathbb{Q}$-factorial modifications of Quot schemes of trivial bundles on $\mathbb{P}^1$ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Atsushi Ito\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: In this talk, we construct all small $\mathbb{Q}$-factorial modifications of Quot schemes of trivial bundles on $\mathbb{P}^1$ and interpret them as moduli spaces. As a corollary, we can show that the Quot schemes are Mori dream spaces and give the chamber decompositions of the cones of divisors. END:VEVENT BEGIN:VEVENT DTSTART:20140523T103000 DTEND:20140523T120000 DTSTAMP:20140522T150000Z UID:b3bf94cf27906f974dc888ecb0b00fec@cgp.ibs.re.kr SUMMARY:Introduction to tropical algebraic geometry and some applications II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Mounir Nisse\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: The goal of this series of lectures is to provide a quick overview of tropical geometry through some examples with the maximum of details ([IMS], [MS], [SS], and [RST]). More precisely, the question that many people ask are e.g., with what kind of problems deals this geometry? And why is it useful to use this geometry in several area of mathematics? After defining a basic objects in tropical geometry, weexplain their relations to the classical algebraic geometry via the notion of amoebas and coamoebas of algebraic varieties ([NS], and [M1]). We will give some applications of tropical geometry to real andenumerative geometry ([M2]) and mirror symmetry.References[IMS] I. Itenberg, G Mikhalkin, and E. Shustin, Tropical Algebraic Geometry, volume bf 35 of Oberwolfach Seminars Series. BirkhŠuser, 2007.[MS] D. Maclagan and B. Sturmfels, Introduction to tropical geometry. Book in progress, available inBernd Sturmfels Homepage.[M1] G. Mikhalkin, Enumerative tropical algebraic geometry in R2. J. Amer. Math. Soc., 18(2), 313Ð377,2005.[M2] G. Mikhalkin, Tropical geometry and its applications. In International Congress of Mathematicians. Vol. II, pages 827Ð852. Eur. Math. Soc., Zurich, 2006.[NS] M. Nisse and F. Sottile, The phase limit set of a variety, Algebra & Number Theory, 7, (2013), 339–352.[RST] J. Richter-Gebert, B. Sturmfels, and T. Theobald, First steps in tropical geometry. In Idempotent mathematics and mathematical physics, volume 377 of Contemp. Math., 289Ð317. Amer. Math. Soc.,Providence, RI, 2005.[SS] D. Speyer and B. Sturmfels, The tropical Grassmannian. Adv. Geom., 4(3), 389Ð 411, 2004. END:VEVENT BEGIN:VEVENT DTSTART:20140523T140000 DTEND:20140523T153000 DTSTAMP:20140522T150000Z UID:2cd64f9a53ab8d84a8989cd343a0d6c8@cgp.ibs.re.kr SUMMARY:Introduction to tropical algebraic geometry and some applications III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Mounir Nisse\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: The goal of this series of lectures is to provide a quick overview of tropical geometry through some examples with the maximum of details ([IMS], [MS], [SS], and [RST]). More precisely, the question that many people ask are e.g., with what kind of problems deals this geometry? And why is it useful to use this geometry in several area of mathematics? After defining a basic objects in tropical geometry, weexplain their relations to the classical algebraic geometry via the notion of amoebas and coamoebas of algebraic varieties ([NS], and [M1]). We will give some applications of tropical geometry to real andenumerative geometry ([M2]) and mirror symmetry.References[IMS] I. Itenberg, G Mikhalkin, and E. Shustin, Tropical Algebraic Geometry, volume bf 35 of Oberwolfach Seminars Series. BirkhŠuser, 2007.[MS] D. Maclagan and B. Sturmfels, Introduction to tropical geometry. Book in progress, available inBernd Sturmfels Homepage.[M1] G. Mikhalkin, Enumerative tropical algebraic geometry in R2. J. Amer. Math. Soc., 18(2), 313Ð377,2005.[M2] G. Mikhalkin, Tropical geometry and its applications. In International Congress of Mathematicians. Vol. II, pages 827Ð852. Eur. Math. Soc., Zurich, 2006.[NS] M. Nisse and F. Sottile, The phase limit set of a variety, Algebra & Number Theory, 7, (2013), 339–352.[RST] J. Richter-Gebert, B. Sturmfels, and T. Theobald, First steps in tropical geometry. In Idempotent mathematics and mathematical physics, volume 377 of Contemp. Math., 289Ð317. Amer. Math. Soc.,Providence, RI, 2005.[SS] D. Speyer and B. Sturmfels, The tropical Grassmannian. Adv. Geom., 4(3), 389Ð 411, 2004. END:VEVENT BEGIN:VEVENT DTSTART:20140414T160000 DTEND:20140414T170000 DTSTAMP:20140413T150000Z UID:33fbfcd8909caa205386382afe347e55@cgp.ibs.re.kr SUMMARY:Lectures on (0+0)-dimensional quantum field theory II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2014\n\nAbstract: The purpose of this series of lectures is to introduce and develop mathematics of a class of (0+0)-dimensional quantum field theories over an algebraically closed field k. Such a theory governs the space of maps from a point, a (0+0-dimensional space, to an affine, or projective, or toric variety X, which (homogeneous) coordinate ring corresponds to the algebra of classical observables. We shall study the algebra of quantum observables and "quantised points" as primer to quantum algebraic geometry. As an intermediate byproduct, we will have a theory of "extended formal variations of homotopy polarised Hodge structures” on X, which structure encodes generating function of all genus correlation functions of extended topological string theory. END:VEVENT BEGIN:VEVENT DTSTART:20140428T160000 DTEND:20140428T180000 DTSTAMP:20140427T150000Z UID:e6d25b401beae89b23f9e8e2643a4f75@cgp.ibs.re.kr SUMMARY:Lectures on (0+0)-dimensional quantum field theory III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2014\n\nAbstract: The purpose of this series of lectures is to introduce and develop mathematics of a class of (0+0)-dimensional quantum field theories over an algebraically closed field k. Such a theory governs the space of maps from a point, a (0+0-dimensional space, to an affine, or projective, or toric variety X, which (homogeneous) coordinate ring corresponds to the algebra of classical observables. We shall study the algebra of quantum observables and "quantised points" as primer to quantum algebraic geometry. As an intermediate byproduct, we will have a theory of "extended formal variations of homotopy polarised Hodge structures” on X, which structure encodes generating function of all genus correlation functions of extended topological string theory. END:VEVENT BEGIN:VEVENT DTSTART:20140423T160000 DTEND:20140423T170000 DTSTAMP:20140422T150000Z UID:5a3cea034368c7c233e53683fa74aaec@cgp.ibs.re.kr SUMMARY:Schubert classes in the algebraic cobordism of flag bundles LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Thomas Hudson (KAIST)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Let V be a vector bundle over a smooth scheme X. In order to establish a Schubert calculus for the full flag bundle FL V it is necessary to identify a basis for CH^*(FL V) as a module over CH^*(X). For this purpose one considers the fundamental classes of Schubert varieties, which can be described by means of double Schubert polynomials. Analogous constructions are also available for the generalized flag bundles associated to each of the classical groups. In this talk I will illustrate one possible way of defining Schubert classes in the context of a general oriented cohomology theory and more specifically in algebraic cobordism, by making use of Bott-Samelson resolutions. END:VEVENT BEGIN:VEVENT DTSTART:20140424T163000 DTEND:20140424T173000 DTSTAMP:20140423T150000Z UID:ecfdeec91c5e375c03c9374c890aedb3@cgp.ibs.re.kr SUMMARY:Landau Damping LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Emre Esenturk\n\nEvent: T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140428T200000 DTEND:20140428T220000 DTSTAMP:20140427T150000Z UID:c3be5793b19cc3414a4b60a055f5445b@cgp.ibs.re.kr SUMMARY:Scaling methods and more LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kang-Hyurk Lee (Gyeongsang National U.)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140430T160000 DTEND:20140430T190000 DTSTAMP:20140429T150000Z UID:2043d47d8111cf2250510a217bc4b7a4@cgp.ibs.re.kr SUMMARY:A characterization of Iwasawa algebras LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: PMI Number Theory Seminar\n\nAbstract: In Iwasawa theory, one considers certain inverse limit of finite group rings, which is called an Iwasawa algebra. I will characterize an Iwasawa algebra as the completion of certain operator algebra. This is parallel to the C*-algebra approach to the non-commutative character space of a countable discrete group. Perhaps this elementary observation has been known for a while, but I do not know a reference. END:VEVENT BEGIN:VEVENT DTSTART:20140512T200000 DTEND:20140512T220000 DTSTAMP:20140511T150000Z UID:e6f82f660c4a7c8ececf116a20a0de64@cgp.ibs.re.kr SUMMARY:Existence of Bergman metric on unbounded domains LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Taeyong Ahn\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140502T163000 DTEND:20140502T174500 DTSTAMP:20140501T150000Z UID:5134f75ac2cde498022c1e8f2ecd1c7a@cgp.ibs.re.kr SUMMARY:Graphs that can be drawn with few crossings LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Otfried Cheong\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: If you can draw a graph on n vertices in the plane such that it has no crossings, then it is a planar graph, and Euler's formula implies that it has at most 3n-6 edges. What can be said if we relax this restriction - that is, if we permit some crossings in a restricted way?Examples of such graphs are k-planar graphs, where an edge is allowed to cross k other edges but not more, k-quasi-planar graphs, which can be drawn without k pairwise crossing edges, right-angle crossing graphs, where edges are allowed to cross at right angles only, and k-fan-crossing free graphs. We discuss known bounds on the number of edges of such graphs and the relationship between these families. END:VEVENT BEGIN:VEVENT DTSTART:20140509T163000 DTEND:20140509T174500 DTSTAMP:20140508T150000Z UID:a5d62cd2fc072c5683aa3e030b9a2737@cgp.ibs.re.kr SUMMARY:Boltzmann equation in some cosmological settings LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ho Lee (Kyunghee University)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: In this talk we study the Boltzmann equation in several different cosmological settings.The main purpose of this study is to understand the time evolution of matter distribution in our universe.The Boltzmann equation will describe the time evolution of matter distribution, while Poisson's equation or Einstein's equations will describe the time evolution of our universe.Recent results on existence and asymptotic behaviors of solutions of the Boltzmann equation will be reviewed. END:VEVENT BEGIN:VEVENT DTSTART:20140512T160000 DTEND:20140512T180000 DTSTAMP:20140511T150000Z UID:134f3d7b5e9c0ce0408a360bad3fa32c@cgp.ibs.re.kr SUMMARY:Lectures on (0+0)-dimensional quantum field theory IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2014\n\nAbstract: The purpose of this series of lectures is to introduce and develop mathematics of a class of (0+0)-dimensional quantum field theories over an algebraically closed field k. Such a theory governs the space of maps from a point, a (0+0-dimensional space, to an affine, or projective, or toric variety X, which (homogeneous) coordinate ring corresponds to the algebra of classical observables. We shall study the algebra of quantum observables and "quantised points" as primer to quantum algebraic geometry. As an intermediate byproduct, we will have a theory of "extended formal variations of homotopy polarised Hodge structures” on X, which structure encodes generating function of all genus correlation functions of extended topological string theory. END:VEVENT BEGIN:VEVENT DTSTART:20140507T160000 DTEND:20140507T170000 DTSTAMP:20140506T150000Z UID:2390f711d718f37a021fdeb3d0b40b6f@cgp.ibs.re.kr SUMMARY:A Waldspurger formula for the quadratic twist families of the elliptic curve LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Junhwa Choi\n\nEvent: PMI Number Theory Seminar\n\nAbstract: In the case of twisted GL(2) L-functions, J.Waldspurger made the formula which explain how the central value of a L-function should be related to the period integral. S.Zhang generalized this Waldspurger formula and Y.Tian gave the idea to apply it to the BSD conjecture for certain elliptic curve. In this talk, I will explain how to get an appropriate Gross-Prasad test vector and the explicit Waldspurger formula for it. From this, one can compute L(E,1) of some quadratic twists E of X_0(49) and prove the 2-part of BSD conjecture for these quadratic twists combining the result of 2-descent. END:VEVENT BEGIN:VEVENT DTSTART:20140508T163000 DTEND:20140508T173000 DTSTAMP:20140507T150000Z UID:782c1caf6bab7cfc0174943911817841@cgp.ibs.re.kr SUMMARY:Fourier-Finite Element Method for the heat equation LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyungjun Choi\n\nEvent: T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140516T133000 DTEND:20140516T143000 DTSTAMP:20140515T150000Z UID:ee898b137a29fbbda0ad1dfd777b7190@cgp.ibs.re.kr SUMMARY:Singularity formation for the incompressible Hall-MHD equations without resistivity LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Shangkun Weng (Seoul National University)\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: In this talk, we show that the incompressible Hall-MHD system without resistivity is not globally in time well-posed in any Sobolev space $H^{m}(mathbb{R}^3)$ for any $m>frac{7}{2}$. Namely, either the system is locally ill-posed in $H^{m}(mathbb{R}^3)$, or it is locally well-posed, but there exists an initial data in $H^{m}(mathbb{R}^3)$, for which the $H^{m}(mathbb{R}^3)$ norm of solution blows-up in finite time if $m>7/2$. In the latter case we choose an axisymmetric initial data $u_0(x)=u_{0r}(r,z)e_r+ b_{0z}(r,z)e_z$ and $B_0(x)=b_{0theta}(r,z)e_{theta}$, and reduce the system to the axisymmetric setting. If the convection term survives sufficiently long time, then the Hall term generates the singularity on the axis of symmetry and we have $ limsup_{tto t_*} sup_{zin Bbb R}|partial_zpartial_r b_theta(r=0,z)|=infty$ for some $t_*>0$. END:VEVENT BEGIN:VEVENT DTSTART:20140519T200000 DTEND:20140519T220000 DTSTAMP:20140518T150000Z UID:0d2950b8c28515508af1790348bb59fd@cgp.ibs.re.kr SUMMARY:On a Forelli-Rudin type formula and Roos' open problem LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Atsushi Yamamori\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140523T163000 DTEND:20140523T174500 DTSTAMP:20140522T150000Z UID:5b515ab76de58b4dc228b65ec0f50b68@cgp.ibs.re.kr SUMMARY:Oscillatory integrals with polynomial phases LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Junil Kim (Yonei University)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: Consider vector polynomials P : R2 ! Rd de ned byP = (P1; ; Pd) where P(t1; t2) =Xm2Z2+cmtm with = 1; ; d:The locally de ned oscillatory integrals associated with P with d = 3 are given by Iloc(P; ; 3) =Z eih;P i (t)dt where 2 Rd and 2 C1c (R2) with small support.We shall rst discuss about the problem for the optimal decay rate: Find the number a > 0 satisfying: Iloc(P; (0.1) ; 3) = O(jj END:VEVENT BEGIN:VEVENT DTSTART:20140530T163000 DTEND:20140530T174500 DTSTAMP:20140529T150000Z UID:2822b6c2326ef8f082571cee7eb51f24@cgp.ibs.re.kr SUMMARY:Fano varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ivan Cheltsov (University of Edinburgh)\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: I will speak about Fano varieties and their roles in modern mathematics. END:VEVENT BEGIN:VEVENT DTSTART:20140602T200000 DTEND:20140602T220000 DTSTAMP:20140601T150000Z UID:f45c28c7b1c2f990ff1fddb1cdfd9390@cgp.ibs.re.kr SUMMARY:Bergman geometry of a certain unbounded domain LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Hyeseon Kim\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140609T200000 DTEND:20140609T220000 DTSTAMP:20140608T150000Z UID:97983d103f91327b9f6c55eeb2f7f489@cgp.ibs.re.kr SUMMARY:Fiber-preserving property of automorphisms of the total space of fibration LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Seungjae Lee\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140613T133000 DTEND:20140613T143000 DTSTAMP:20140612T150000Z UID:a7e17234bca77fc468db4c74c3a84874@cgp.ibs.re.kr SUMMARY:A mathematical model for an immune system LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 이성원\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140522T160000 DTEND:20140522T180000 DTSTAMP:20140521T150000Z UID:cae21bcae15cce4b4cbafec2c0ccfb88@cgp.ibs.re.kr SUMMARY:Mirror maps and disk counting LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kwokwai Chan\n\nEvent: CGP Seminar 2014\n\nAbstract: In this talk, I will explain the proof of a conjecture of Gross and Siebert, which asserts an enumerative meaning of mirror maps in terms of counts of holomorphic disks, in the case of toric Calabi-Yau manifolds. This talk is based on various joint works with Cheol-Hyun Cho, Siu-Cheong Lau, Conan Leung and Hsian-HuaTseng. END:VEVENT BEGIN:VEVENT DTSTART:20140612T160000 DTEND:20140612T180000 DTSTAMP:20140611T150000Z UID:d3face591837b49530cc1db9d1f6a81a@cgp.ibs.re.kr SUMMARY:Knot contact homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Michael Sullivan\n\nEvent: CGP Seminar 2014\n\nAbstract: One can `lift' a smooth submanifold to a Legendrian submanifold in the unit cotangent bundle endowed with the standard contact structure. Legendrians in contact manifolds play a role similar to Lagrangians in symplectic manifold, and in particular, one can study Legendrians using pseudo-holomorphic curves. When the Legendrian is the lift of a smooth knot in Euclidean 3-space, I will discuss how a count of such curves, known as knot contact homology, produces a knot invariant rich enough to detect the unknot. If time permits, I will discuss the following: how knot contact homology connects to string topology; how it can be filtered if the original knot is transverse to the standard contact structure in Euclidean 3-space; and speculations on how it connects to ``physics." Most of this work is joint with T. Ekholm, J. Etnyre and L. Ng. The string topology is joint with S. Basu, J. McGibbon and D. Sullivan. The ``string" speculation is not my own, but an idea of M. Aganic, T. Ekholm, L. Ng and C. Vafa. This talk is independent of my other one. END:VEVENT BEGIN:VEVENT DTSTART:20140526T101500 DTEND:20140526T111500 DTSTAMP:20140525T150000Z UID:b25547741afb4e8dd995cd186eb56cd1@cgp.ibs.re.kr SUMMARY:Noncommutative linear systems, base loci, and Okounkov bodes LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Ludmil Katzarkov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: In this talk, we suggest a theory on noncommutative linear systems. END:VEVENT BEGIN:VEVENT DTSTART:20140526T143000 DTEND:20140526T153000 DTSTAMP:20140525T150000Z UID:0a84b4de060c93ff49edbe69c795ba34@cgp.ibs.re.kr SUMMARY:Categories of Factorizations from Abelian Categories LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: David Favero\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I will discuss the "derived category" of a triple $(A, L, w)$ where $A$ is an Abelian category, $L$ is an autoequivalence of $A$, and $w$ is a natural transformation from the identity to $A$. A good example to have in mind is the "derived category" of a Landau-Ginzburg model, i.e when $A$ is coherent sheaves on a scheme, $L$ is tensoring with a line bundle, and $w$ is the natural transformation corresponding to a section of that line bundle. I will discuss how we can bootstrap results on such categories from results on usual derived categories and some interesting examples. This is joint work with Ballard, Deliu, Isik, and Katzarkov. END:VEVENT BEGIN:VEVENT DTSTART:20140527T160000 DTEND:20140527T170000 DTSTAMP:20140526T150000Z UID:da74bde3be2fedc3089fb74e454c9a6c@cgp.ibs.re.kr SUMMARY:Bounded groups of birational automorphisms LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: A classical theorem by H.Minkowski says that the orders of finite subgroups of the group GL_N(Q) are bounded by a constant that depends only on N. Another classical theorem by C.Jordan says that for any finite subgroup G of GL_N(C) there is an abelian subgroup whose index in G is bounded by a constant that depends only on N. It is partially known and partially expected that birational automorphism groups of many varieties over Q and C, respectively, enjoy similar properties. I will survey some relevant results (due to many people) including low-dimensional cases, higher dimensional cases modulo standard conjectures of birational geometry, estimates for the relevant constants, counter-examples, and analogous results in other settings. END:VEVENT BEGIN:VEVENT DTSTART:20140527T113000 DTEND:20140527T123000 DTSTAMP:20140526T150000Z UID:4af9c0b703e0bcaacf36129b1d2cace1@cgp.ibs.re.kr SUMMARY:On Kuchle fourfolds of K3 type LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Alexander Kuznetsov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: In 1995 O. Kuchle classified all Fano fourfolds of index 1 which are zeros of regular sections of equivariant bundles in Grassmannians. In his list there are 3 varieties which have the Hodge diamond of a K3 surface inside their own Hodge diamond (similar to a cubic forufold). In the talk I will discuss the geometry of these varieties and the structure of their derived categories. END:VEVENT BEGIN:VEVENT DTSTART:20140526T113000 DTEND:20140526T123000 DTSTAMP:20140525T150000Z UID:9b017eb63a5e8cbc1a7ab5858f07b467@cgp.ibs.re.kr SUMMARY:Prime divisors and birational geometry in Fano manifolds LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Cinzia Casagrande\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: Let $X$ be a smooth, complex Fano variety, $D$ a prime divisor in $X$, and set $c(D):=\dim \ker(r: H^2(X,R)-> H^2(D,R))$, where r is the natural restriction map. It is a special property of Fano manifolds that the presence of a prime divisor $D$ with large $c(D)$ has consequences on the geometry of $X$. More precisely, we define: $c_X:=\max\{c(D)|D\text{ is a prime divisor in }X\}$. Then $c_X$ is at most 8, and if $c_X$ is at least 2, then we get some special properties of $X$. We will explain this result, which relies on a construction in birational geometry; then we will focus on the case $c_X=2$, which is new. END:VEVENT BEGIN:VEVENT DTSTART:20140528T090000 DTEND:20140528T100000 DTSTAMP:20140527T150000Z UID:00cca88cac37c334ae69dc7ce6d51633@cgp.ibs.re.kr SUMMARY:Cosection localization of virtual fundamental classes LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: Since 1995, enumerative invariants in algebraic geometry, such as Gromov-Witten and Donaldson-Thomas invariants, have been mostly defined as integrals on virtual fundamental classes on suitable moduli spaces. I will talk about a technique to handle virtual fundamental classes, called localization by cosection, and discuss several applications. This talk is based on joint work with Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20140527T143000 DTEND:20140527T153000 DTSTAMP:20140526T150000Z UID:e368f16a474ebb4654b7f1686d44c9ed@cgp.ibs.re.kr SUMMARY:Homological Mirrors of toric GIT quotients and Lagrangian Skeleta LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Colin Diemer\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: This talk will consider various attempts to understand the homological mirror symmetry underlying Geometric Invariant Theory. On the side of algebraic geometry, the foundational work has recently been investigated by Ballard, Favero, Katzarkov, and Halpern-Leistner. The mirror symplectic theory is less understood. We'll discuss some recent proposals of Kontsevich to develop the mirror theory at the level Lagrangian skeleta. This is based on various ongoing collaborations with Ballard, Favero, Katzarkov, Kerr, and Kontsevich. END:VEVENT BEGIN:VEVENT DTSTART:20140526T160000 DTEND:20140526T170000 DTSTAMP:20140525T150000Z UID:04612982c88e2eaf1c85019fa8d5be54@cgp.ibs.re.kr SUMMARY:Birational geometry of Q-Fano 3-fold weighted complete intersections LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I will talk about explicit studies on the birational geometry of Q-Fano 3-fold weighted complete intersections of codimension 2. Compared to the case of weighted hypersurfaces, many Q-Fano WCIs are birationally non-rigid: among 85 families of Q-Fano WCIs, 19 families consist of birationally rigid varieties and the remaining 66 families consist of birationally non-rigid varieties. I will explain some results on the complete determination of ``birational Mori fiber structures" of birationally non-rigid Q-Fano WCIs. END:VEVENT BEGIN:VEVENT DTSTART:20140529T090000 DTEND:20140529T100000 DTSTAMP:20140528T150000Z UID:fb53581a2a8e86a166e6d58c43ae1fac@cgp.ibs.re.kr SUMMARY:Stable and unstable log del Pezzo surfaces. LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: We describe some results about stable and unstable log del Pezzo surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20140527T101500 DTEND:20140527T111500 DTSTAMP:20140526T150000Z UID:e1eab71acb623c5ed960f55f9acff31d@cgp.ibs.re.kr SUMMARY:Mirrors to weighted flips and blow-ups LOCATION:Outside POSTECH DESCRIPTION:Speaker: Gabriel Kerr\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: Any toric DM stack has a minimal model sequence consisting of weighted flips, blow-ups and projective bundle projections. It is known that any such sequence introduces a semi-orthogonal decomposition of the derived category of the stack. In ``Symplectomorphism group relations and degenerations of Landau-Ginzburg models'', a joint work with C. Diemer and L. Katzarkov, a decomposition of the mirror Landau-Ginzburg model was defined. It was conjectured that there is a quasi-equivalence between the A and B model categories that respects these decompositions. In this talk I will discuss this conjecture and sketch a partial proof. END:VEVENT BEGIN:VEVENT DTSTART:20140529T143000 DTEND:20140529T153000 DTSTAMP:20140528T150000Z UID:6284e39a7e7d81f36ee802c2a4f02bd2@cgp.ibs.re.kr SUMMARY:Local VGIT and derived categories LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Matthew Ballard\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I will discuss how recent work of B.-Favero-Katzarkov and Halpern-Leinster can be extended to a slightly more general, that where the unstable strata are determined by VGIT locally on the moduli space of semi-stable objects in the wall. If time allows, I will discuss applications to well understood examples of wall crossing for Bridgeland moduli spaces. Part of this work is joint with Arend Bayer. END:VEVENT BEGIN:VEVENT DTSTART:20140529T101500 DTEND:20140529T111500 DTSTAMP:20140528T150000Z UID:7c77ba56eb4152ae6df1dbab8600d489@cgp.ibs.re.kr SUMMARY:Toric Landau—Ginzburg models and birational geometry of Fano varieties LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Victor Przyjalkowski\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: There are several points of view on what is a mirror correspondence between Fano varieties and their Landau—Ginzburg models. We discuss one of the simplest ones called Mirror Symmetry of Variations of Hodge structures. From its point of view mirror dual for Fano variety is just a specific Laurent polynomial related to Fano’s toric degeneration. We discuss when this dual Laurent polynomial is proven to exist and (possibly conjectural) output for studying birational transformations of (degenerations of) Fano varieties. In particular we observe a new view on a structure of a classification of smooth Fano threefolds and give examples of relations with Minimal Model Program. END:VEVENT BEGIN:VEVENT DTSTART:20140529T160000 DTEND:20140529T170000 DTSTAMP:20140528T150000Z UID:5128baeddf12cefa9c8cd1cc966df4d6@cgp.ibs.re.kr SUMMARY:Q-Gorenstein deformation and its applications LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Yongnam Lee\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: In this talk, we will discuss Q-Gorenstein schemes and Q-Gorenstein morphisms in a general setting. Based on the notion of Q-Gorenstein morphism, we define the notion of Q-Gorenstein deformation and discuss its properties. Versal property of Q-Gorenstein deformation and its applications on higher dimensional varieties are also considered. This is joint work with Noboru Nakayama. END:VEVENT BEGIN:VEVENT DTSTART:20140530T090000 DTEND:20140530T100000 DTSTAMP:20140529T150000Z UID:81c17bd50a6243f2cf1db01757644462@cgp.ibs.re.kr SUMMARY:Mori dream spaces and maps between Mori fibrations LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Francesco Zucconi\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I presents some results obtained in a joint work with H. Ahmadinezhad where we highlight a strong relation between finite generation of certain Cox rings and existence of maps between Mori fiber spaces and Fano Varieties. This can be used to obtain some rigidity or non-rigidity results. In particular we can complete the birational rigidity results of Okada for Fano three folds of codimension 2 replacing generality assumption by quasi-smoothness. END:VEVENT BEGIN:VEVENT DTSTART:20140528T101500 DTEND:20140528T111500 DTSTAMP:20140527T150000Z UID:955da9106f5ec5b2af6d6361290f31a2@cgp.ibs.re.kr SUMMARY:Construction of Sarkisov links LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Hamid Ahmadinezhad\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: Maps between Mori fibre spaces, and Fano varieties in particular, are decomposed as finite sequences of Sarkisov links. I explain how a Sarkisov link can be obtained via variation of geometric invariant theory, and show some explicit methods. This can be used for both constructing Sarkisov links from a given Mori fibre space or showing the non-existence of such links. For illustration, I show some examples of our joint work with Kaloghiros on links from quartic threefolds with compound Du Val singularities. END:VEVENT BEGIN:VEVENT DTSTART:20140527T090000 DTEND:20140527T100000 DTSTAMP:20140526T150000Z UID:c4501d5606eb6e99c45a354fe67dd1c3@cgp.ibs.re.kr SUMMARY:Automorphisms of Fano varieties and and Jordan properties of Cremona groups LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I'll start by recalling known facts on classification of (singular) Fano threefolds. I then discuss some possible ways to describe their automorphism groups and explain some important applications. END:VEVENT BEGIN:VEVENT DTSTART:20140529T113000 DTEND:20140529T123000 DTSTAMP:20140528T150000Z UID:4e9be1dce2277f6c56c26487205257d5@cgp.ibs.re.kr SUMMARY:Nonrational quotients of del Pezzo surfaces LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Andrey Trepalin\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: We study quotients of del Pezzo surfaces by finite groups of automorphisms over algebraically nonclosed fields. We find all cases when the quotient is not rational surface over ground field and construct minimal models. END:VEVENT BEGIN:VEVENT DTSTART:20140530T113000 DTEND:20140530T123000 DTSTAMP:20140529T150000Z UID:8c37ff8c1870a54699570a4b932a2095@cgp.ibs.re.kr SUMMARY:DG categorical Hitchin system LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Alexander Efimov\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: First, we construct a family of associative algebras, which are formally smooth (Qulllen-smooth), and whose representation spaces are (affine charts of) moduli spaces of semi-stable vector bundles on a smooth projective curve, with trivialization of a single fiber. Then we construct a noncommutative version of Hitchin system, which induces the usual one (for GL_n) by taking its "trace". Our construction is closely related with some generalization (actually, extension) of the DG Lie algebra of Hochschild cochains.of a small DG category. END:VEVENT BEGIN:VEVENT DTSTART:20140530T101500 DTEND:20140530T111500 DTSTAMP:20140529T150000Z UID:9018279eb41625c74afc0ebd1e731e88@cgp.ibs.re.kr SUMMARY:Fukaya categories of surfaces and Teichmüller theory LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Fabian Haiden\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I will discuss several ways in which the topology and geometry of surfaces is reflected in properties of their Fukaya categories. These categories allow an elementary, axiomatic definition based only on topology and homotopical algebra. Representations of the category over a field are classified in terms of immersed curves with local system. The main result is a correspondence between CY-structures and stability conditions. As a special case, this gives a geometric construction of stability conditions on derived categories associated with some LG-models. Part of joint work with L. Katzarkov and M. Kontsevich. END:VEVENT BEGIN:VEVENT DTSTART:20140530T143000 DTEND:20140530T153000 DTSTAMP:20140529T150000Z UID:bf1782336a629b2435b5d848f499af3f@cgp.ibs.re.kr SUMMARY:On conjectures of Dubrovin and Ostrover-Tyomkin LOCATION:Hotel Hyundai, Gyeongju, Korea DESCRIPTION:Speaker: Sergey Galkin\n\nEvent: Landau-Ginzburg Theory and Fano Varieties\n\nAbstract: I will briefly review three recent works:arXiv:1404.7388,arXiv:1405.3857 (with Anton Mellit and Maxim Smirnov),arXiv:1404.6407 (with Vasily Golyshev and Hiroshi Iritani).Next four algebraic properties of quantum cohomology of a Fano manifold are all distinct:1. Big quantum cohomology is generically semi-simple (the condition of Dubrovin's conjecture)2. Small quantum cohomology is generically semi-simple3. "Very small" quantum cohomology (i.e. QH of the monotome symplectic manifold) is semi-simple4. A small quantum cohomology algebra (of a monotone symplectic manifold) has a field as a direct summandIn 1404.7388 using mirror symmetry and a simple argument from Ginzburg-Landau theory I show that property (4) should also hold for all Fano manifolds, and prove it for all toric Fano manifolds, thus confirming conjecture of Ostrover-Tyomkin.This is also related to Conjecture O (of 1404.6407) that roughly says that the structure sheaf of a Fano manifoldis mirror dual to the Lagrangian thimble formed by the locus of real positive points.Ostrover and Tyomkin shown that for some toric Fano fourfolds (3) fails, but (2) is true. In 1405.3857 we show that for isotropic Grassmannian IG(2,6) (2) fails, but (1) is true; and also the derived category of coherent sheaves has a full exceptional collection, so it is the first case where one needs big quantum cohomology to formulate the first part of Dubrovin's conjecture. Finally, in 1404.3857 I will formulate Gamma Conjecture I (related to Conjecture O)and also Gamma Conjecture II (which is the exact formulation of the third part of Dubrovin's conjecture).I will provide some confirming examples, and give some ways that could lead to proving these conjectures. END:VEVENT BEGIN:VEVENT DTSTART:20140519T163000 DTEND:20140519T180000 DTSTAMP:20140518T150000Z UID:365e67e2fbbe7ead3bfb1da4212fe837@cgp.ibs.re.kr SUMMARY:A Guide to Normal Surface Singularities 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: DongSeon Hwang (Ajou University)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Normal surface singularities 'link' surfaces to 3-folds by means of smoothings and to 3-manifolds through links. In this lecture, I will present the classical foundation of the theory of normal surface singularities developed by Mumford, Artin, and Laufer with an emphasis on topological aspects, and then talk about the singularities coming from the developments of MMP. If time permits, I will sketch the proof of the classification of (log) terminal/canonical surface singularities. END:VEVENT BEGIN:VEVENT DTSTART:20140520T103000 DTEND:20140520T120000 DTSTAMP:20140519T150000Z UID:6e4d6dddd326caee341d3e9e37dbf603@cgp.ibs.re.kr SUMMARY:A Guide to Normal Surface Singularities LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: DongSeon Hwang (Ajou University)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Normal surface singularities 'link' surfaces to 3-folds by means of smoothings and to 3-manifolds through links. In this lecture, I will present the classical foundation of the theory of normal surface singularities developed by Mumford, Artin, and Laufer with an emphasis on topological aspects, and then talk about the singularities coming from the developments of MMP. If time permits, I will sketch the proof of the classification of (log) terminal/canonical surface singularities. END:VEVENT BEGIN:VEVENT DTSTART:20140514T160000 DTEND:20140514T170000 DTSTAMP:20140513T150000Z UID:0edc158f0ec1d6543fc35ec6fd271e39@cgp.ibs.re.kr SUMMARY:2-Selmer groups and Gross-Zagier weak conjecture LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donggeon Yhee (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: I want to sketch a partial result on the conjecture and Selmer group for elliptic curves with rational torsion points of order 2. The results are not completed yet, and I will introduce the problems I have met. END:VEVENT BEGIN:VEVENT DTSTART:20140515T163000 DTEND:20140515T173000 DTSTAMP:20140514T150000Z UID:9a776ea94f180efb2a27df2bd6d80420@cgp.ibs.re.kr SUMMARY:Bergman geometry of unbounded pseudoconvex domains LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyeseon Kim (POSTECH)\n\nEvent: T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140609T160000 DTEND:20140609T180000 DTSTAMP:20140608T150000Z UID:4677f802486d9ab9d28e8f065ab221d1@cgp.ibs.re.kr SUMMARY:Legendrian contact homology, generating families and augmentations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Michael Sullivan\n\nEvent: Quantum Monday 2014\n\nAbstract: Legendrian submanifolds of contact manifolds play a role similar to Lagrangians in symplectic manifold, and in particular, one can study Legendrians using pseudo-holomorphic curves. One such count, known as Legendrian contact homology (equivalent to knot contact homology in my other talk) has proved useful to show that Legendrian submanifolds are much more rigid than smooth submanifolds. A common problem symplectic/contact geometers must face is how to find (count/classify) these pseudo-holomorphic curves. Thankfully, when the Legendrian is a knot is standard contact 3-space, the differential graded algebra (DGA) underlying Legendrian contact homology has a combinatorial reformulation. This has led to many results for Legendrian knots. I will discuss how using a Van-Kampen theorem, computing the DGA can be reduced to localized computations. In particular, for 2-dimensional Legendrians, the DGA has a combinatorial/cellular reformulation. As an application of this reformulation, I will outline how to prove a Legendrian surface has a DGA-augmentation (similar to a Lagrangian filling) if and only if it has a generating family. All terms to be defined. This is joint work with D. Rutherford. This talk is independent of my other one. END:VEVENT BEGIN:VEVENT DTSTART:20140613T163000 DTEND:20140613T174500 DTSTAMP:20140612T150000Z UID:805d6b03f835c257a7179c73bb4fc641@cgp.ibs.re.kr SUMMARY:Partial differential equations arising in applied fields LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyung Ju Hwang\n\nEvent: Spring 2014 POSTECH Math Colloquium\n\nAbstract: I will talk on two different perspectives for doing mathematics - towards versus with mathematics. I will introduce several examples in the appied areas such as physics, biology, and engineering, where mathematics is used at different levels. In particular, I will describe how to apply mathematical methods to a variety of real-world problems with a focus on partial differential equations.For instance, we will discuss PDEs motivated from plasma physics, fluid mechanics, and medicine. END:VEVENT BEGIN:VEVENT DTSTART:20140602T170000 DTEND:20140602T180000 DTSTAMP:20140601T150000Z UID:c30ff5a7e035a52c499c2445fa13ca9e@cgp.ibs.re.kr SUMMARY:Rozansky-Witten-type invariants from symplectic Lie pairs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ping Xu\n\nEvent: Quantum Monday 2014\n\nAbstract: We introduce symplectic structures on pairs of Lie algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a g-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds given by weight systems. END:VEVENT BEGIN:VEVENT DTSTART:20140602T160000 DTEND:20140602T170000 DTSTAMP:20140601T150000Z UID:9bd2ef903e9a5e60c8d617d9ea89d527@cgp.ibs.re.kr SUMMARY:Poincaré-Birkhoff-Witt isomorphisms and $L_\infty$ algebras associated to Lie pairs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mathieu Stiénon\n\nEvent: Quantum Monday 2014\n\nAbstract: We will explain how the Atiyah classes relative to pairs of Lie algebroids give rise to strong homotopy Lie algebras. In particular, we will explain why, for every pair of Lie algebroids $(L,A)$, the graded manifold $A[1]\oplus L/A$ acquires an essentially canonical structure of dg-manifold. END:VEVENT BEGIN:VEVENT DTSTART:20140728T160000 DTEND:20140728T180000 DTSTAMP:20140727T150000Z UID:e09eefc31020a3ce534e3f3e6441bf29@cgp.ibs.re.kr SUMMARY:Reflexive polytopes and semistable degenerations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ursula Whitcher\n\nEvent: Quantum Monday 2014\n\nAbstract: The Batyrev-Borisov construction uses the combinatorial information of pairs of polar dual polytopes to construct mirror families of Calabi-Yau varieties. We'll begin by reviewing this construction and its implications for the mirror symmetry of K3 surfaces. If the intersection of a reflexive polytope with a hyperplane through the origin yields a lower-dimensional reflexive polytope, then the corresponding Calabi-Yau varieties are fibered by lower-dimensional Calabi-Yau varieties. A top generalizes the idea of splitting a reflexive polytope into two pieces. Tops may be used to describe either fibrations or degenerations of Calabi-Yau varieties. We give a simple combinatorial condition on tops which produces semistable degenerations of K3 surfaces, and, when appropriate smoothness conditions are met, semistable degenerations of Calabi-Yau threefolds. Our method is constructive: given a fixed reflexive polytope which will lie on the boundary of the top, we describe an algorithm for constructing tops which yields semistable degenerations of the corresponding hypersurfaces. END:VEVENT BEGIN:VEVENT DTSTART:20140616T160000 DTEND:20140616T180000 DTSTAMP:20140615T150000Z UID:ea74e0e872bb761271737ad7129bc2f1@cgp.ibs.re.kr SUMMARY:Introduction to the volume conjecture I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Roland van der Veen\n\nEvent: Quantum Monday 2014\n\nAbstract: The volume conjecture is one of the major open problems in low dimensional topology. One way to state it is that a certain limit of the Jones polynomials of a knot determine the hyperbolic volume of its complement. I will try to motivate and illustrate the conjecture from several points of view coming from both mathematics and physics. END:VEVENT BEGIN:VEVENT DTSTART:20140617T160000 DTEND:20140617T180000 DTSTAMP:20140616T150000Z UID:03faeda91c2468ab709f38ff7972038e@cgp.ibs.re.kr SUMMARY:Introduction to the volume conjecture II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Roland van der Veen\n\nEvent: Seminar 2014\n\nAbstract: The volume conjecture is one of the major open problems in low dimensional topology. One way to state it is that a certain limit of the Jones polynomials of a knot determine the hyperbolic volume of its complement. I will try to motivate and illustrate the conjecture from several points of view coming from both mathematics and physics. END:VEVENT BEGIN:VEVENT DTSTART:20140717T160000 DTEND:20140717T180000 DTSTAMP:20140716T150000Z UID:eecbf9c8418c25ac2a8871ba32318a64@cgp.ibs.re.kr SUMMARY:Compactified combinatorial string topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kate Poirier\n\nEvent: CGP Seminar 2014\n\nAbstract: String topology studies algebraic structures arising from intersecting loops in manifolds. Godin and Kupers have shown that thehomology of the moduli space of Riemann surfaces acts on the homology of the loop space of a manifold. It is thought that this action isjust the shadow of an explicit action of the chains on a compactification of moduli space on the chains on the loop space. In this talk, we report on recent work with Nathaniel Rounds and current work with Gabriel C. Drummond-Cole to define this chain-level action and the corresponding algebraic structure. END:VEVENT BEGIN:VEVENT DTSTART:20140724T160000 DTEND:20140724T180000 DTSTAMP:20140723T150000Z UID:f9bbea9ede6dda8bcd7b00f7a9fe959c@cgp.ibs.re.kr SUMMARY:Koszul duality and completion LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joseph Hirsh\n\nEvent: CGP Seminar 2014\n\nAbstract: After an introduction to completions via Goodwillie calculus, we discuss the completion functor in the category of algebras over an operad and relate it to Koszul duality. END:VEVENT BEGIN:VEVENT DTSTART:20140731T160000 DTEND:20140731T170000 DTSTAMP:20140730T150000Z UID:34b8cebfc406e91cff7c7e8806909329@cgp.ibs.re.kr SUMMARY:Some remarks about Bridgeland stability conditions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: CGP Seminar 2014\n\nAbstract: We'll review the basics of Bridgeland stability conditions and talk about some work in progress. We may talk about possible applications to 2-Segal spaces, or about what appears to be a factorization algebra on the real line induced by the space of stability conditions. END:VEVENT BEGIN:VEVENT DTSTART:20140828T160000 DTEND:20140828T173000 DTSTAMP:20140827T150000Z UID:4af639652bc4cd82f23b1b23e6e16776@cgp.ibs.re.kr SUMMARY:PreLie deformation theory (from an idea gotten at the CGP in March 2014) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bruno Vallette\n\nEvent: CGP Seminar 2014\n\nAbstract: The Deligne—Grothedieck philosophy asserts that any deformation problem over a field of characteristic 0 can be encoded by a differential graded Lie algebra (see the recent work of Lurie for a proof using higher algebra). Many of the objects of deformation theory can actually be built from associative algebras: exponentials, gauge group, Baker–Campbell–Hausdorff product, etc. In this talk, I will explain what happens when the dg Lie algebra comes from a dg preLie algebra. In this context, by refining the arguments, one can also consider preLie exponentials, gauge group action, etc. The main motivation of this preLie calculus is homotopical algebra: it provides simple formulas and a conceptual explanation for the homotopy transfer theorem. (This is a joint work with Vladimir Dotsenko and Sergey Shadrin). END:VEVENT BEGIN:VEVENT DTSTART:20140825T140000 DTEND:20140825T160000 DTSTAMP:20140824T150000Z UID:1d7222f02afe4e1ee5ed9a69fa58d7ba@cgp.ibs.re.kr SUMMARY:Geometric Langlands from $N=4$ gauge theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Philsang Yoo\n\nEvent: Quantum Monday 2014\n\nAbstract: Geometric Langlands conjecture arises as geometric analogue of the Langlands program in number theory. From a completely different direction, Kapustin-Witten found a physical theory which led to a version of the geometric Langlands correspondence. One of our goals is to rigorously analyze the physical theory using derived algebraic geometry and to obtain the up-to-date version of the conjecture, which was not possible from the original investigation of Kapustin-Witten.The first part of the talk will be a gentle introduction to the geometric Langlands conjecture for anyone interested in the subject. We will start the second part by reviewing some of Kapustin-Witten's main ideas and then provide some hints for how one could have conjectured the geometric Langlands correspondence purely out of physics, without knowing any number theory. No knowledge of number theory or physics is assumed. The main results are based on a joint work in progress with Chris Elliott. END:VEVENT BEGIN:VEVENT DTSTART:20140825T160000 DTEND:20140825T180000 DTSTAMP:20140824T150000Z UID:28e3b59a5b041fbadd620899448f86cb@cgp.ibs.re.kr SUMMARY:A universal approach to universal algebra LOCATION:CGP Main Hall DESCRIPTION:Speaker: Emily Riehl\n\nEvent: Quantum Monday 2014\n\nAbstract: A large variety of "algebraic" structures can be encode as algebras for a monad - rings, group actions, sheaves, compact Hausdorff spaces - and this encoding implies a number of formal properties in each context. A general category of mathematical objects can be recognized as a category of algebras by means of the monadity theorem. In this talk I'll describe joint work with Dominic Verity that gives a "context free" proof of the monadicity theorem, applying in any 2-category or any (oo,2)-category, as in the setting of abstract homotopy theory. Monads, algebras, and adjunctions in this latter context are called "homotopy coherent." Time permitting I'll explain how this work specializes to Grothendieck's descent theory. END:VEVENT BEGIN:VEVENT DTSTART:20140710T140000 DTEND:20140710T153000 DTSTAMP:20140709T150000Z UID:2a32cff50bb6505b244cae770c08e3ab@cgp.ibs.re.kr SUMMARY:On quantum cohomology ring of ellipitic $\mathbb{P}^1$ orbifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hyung-Seok Shin\n\nEvent: CGP Seminar 2014\n\nAbstract: The Gromov-Witten theory of orbifolds was introduced in the symplectic setting by Weimin Chen and Yongbin Ruan. In this talk, I will briefly recall the orbifold Gromov-Witten theory. Then, I will compute 3-point genus-0 Gromov-Witten invariants of elliptic $\mathbb{P}^1$ orbifolds by directly counting holomorphic orbi-curves.Those terms are already known from the computation of potentials: Satake-Takahashi for $\mathbb{P}^1_{2,2,2,2}$ and $\mathbb{P}^1_{3,3,3}$ cases and Krawitz-Shen for $\mathbb{P}^1_{3,3,3}$, $\mathbb{P}^1_{2,4,4}$, and $\mathbb{P}^1_{2,3,6}$ cases. Their techniques are based on some algebraic relations of the potential, for example, the WDVV equation, divisor equation, etc.We choose more direct method for the computation, namely, classifying holomorphic orbi-spheres. It turns out that these orbi-spheres have an ono-to-one correspondence with the solutions of certain Diophantine equations.This is a joint work with Hansol Hong. END:VEVENT BEGIN:VEVENT DTSTART:20140725T160000 DTEND:20140725T180000 DTSTAMP:20140724T150000Z UID:5f5dd2a1243c22734bd14fdccf3841c3@cgp.ibs.re.kr SUMMARY:Alternative compactifications of the moduli space of pointed rational curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Han-Bom Moon\n\nEvent: Seminar 2014\n\nAbstract: Mori's program for moduli spaces aims to find and classify modular birational models of given moduli space. On Mori's program for the moduli of curves, most of modular birational models have been obtained by allowing worse singularities. In this talk, I will explain a new type of birational model appears in the case of the moduli space of pointed stable rational curves. END:VEVENT BEGIN:VEVENT DTSTART:20140624T160000 DTEND:20140624T173000 DTSTAMP:20140623T150000Z UID:4806a9012e1a806e0d9b8e2ec0051e2d@cgp.ibs.re.kr SUMMARY:Newton-Okounkov bodies and Toric degenerations of Bott-Samelson varieties 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihyeon Yang (McMaster University)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: In the first talk, we will study the introduction of Newton-Okounkov body theory, which is about assigning a convex body to an algebraic object (for example, a semigroup of integral points, an algebraic variety with a linear system, etc). The construction was motivated by the study of representations of reductive algebraic groups and it has been actively developed recently and has many different perspectives. In the second talk, we focus on the study of Bott-Samelson varieties. In a certain case (original construction) they are desingularizations of Schubert varieties. Based on Grossberg-Karshon's work, Pasquier constructed toric degenerations of Bott-Samelson varieties. We will study how these toric degenerations provide the explicit descriptions of Newton-Okounkov bodies of Bott-Samelson varieties. END:VEVENT BEGIN:VEVENT DTSTART:20140625T103000 DTEND:20140625T120000 DTSTAMP:20140624T150000Z UID:71b3d66900361d4a6a7a6650260f40bb@cgp.ibs.re.kr SUMMARY:Newton-Okounkov bodies and Toric degenerations of Bott-Samelson varieties 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihyeon Yang (McMaster University)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: In the first talk, we will study the introduction of Newton-Okounkov body theory, which is about assigning a convex body to an algebraic object (for example, a semigroup of integral points, an algebraic variety with a linear system, etc). The construction was motivated by the study of representations of reductive algebraic groups and it has been actively developed recently and has many different perspectives. In the second talk, we focus on the study of Bott-Samelson varieties. In a certain case (original construction) they are desingularizations of Schubert varieties. Based on Grossberg-Karshon's work, Pasquier constructed toric degenerations of Bott-Samelson varieties. We will study how these toric degenerations provide the explicit descriptions of Newton-Okounkov bodies of Bott-Samelson varieties. END:VEVENT BEGIN:VEVENT DTSTART:20140801T140000 DTEND:20140801T153000 DTSTAMP:20140731T150000Z UID:e86b6f9a4b9cb4708a746126398b0ee3@cgp.ibs.re.kr SUMMARY:EPW sextics and Hilbert squares of K3 surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Carlo Madonna\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: We prove that the Hilbert square $S^{[2]}$ of a very general primitively polarized K3 surface S of degree $d(n)=2(4n^2+8n+5)$, $n≥1$ is birational to a double Eisenbud-Popescu-Walter sextic. Our result implies a positive answers, in the case when $r$ is even, to a conjecture of O'Grady: On the Hilbert square of a very general K3 surface of genus $r^2+2$, $r≥1$ there is an antisymplectic involution. We explicitly give this involution on $S^{[2]}$ in term of the corresponding EPW polarization on it. This is the main result of a joint work with A.Iliev. END:VEVENT BEGIN:VEVENT DTSTART:20140714T160000 DTEND:20140714T180000 DTSTAMP:20140713T150000Z UID:9d79a1ee29449a272c0544355c1db6c3@cgp.ibs.re.kr SUMMARY:Gopakumar-Vafa invariant and perverse sheaves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Quantum Monday 2014\n\nAbstract: In 1998, Gopakumar-Vafa proposed a method to enumerate curves in a Calabi-Yau 3-fold by using a cohomology theory equipped with an action of $\mathfrak{sl}_2\times\mathfrak{sl}_2$. The invariant thus defined should give the Gromov-Witten invariants of all genera. The problem of finding such a cohomology theory remained open. In this talk, I will discuss our recent proposal to use perverse sheaves to provide a mathematical theory of Gopakumar-Vafa invariants. This talk is based on a joint work with Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20140717T140000 DTEND:20140717T153000 DTSTAMP:20140716T150000Z UID:20982a11d9493cf7f1ad71c4fdc4240c@cgp.ibs.re.kr SUMMARY:A + B model in conifold transitions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuan-Pin Lee\n\nEvent: CGP Seminar 2014\n\nAbstract: I will discuss the changes of Gromov-Witten theory and variations of Hodge structures under projective conifold transitions. This is a joint project with Hui-Wen Lin and Chin-Lung Wang from National Taiwan University. END:VEVENT BEGIN:VEVENT DTSTART:20140731T140000 DTEND:20140731T153000 DTSTAMP:20140730T150000Z UID:a1892cacaa686c58021b0f1e1bab7983@cgp.ibs.re.kr SUMMARY:Symplectic topologist's tales of quantum mechanics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Leonid Polterovich\n\nEvent: CGP Seminar 2014\n\nAbstract: We focus on constraints on the Poisson brackets found within symplectic topology. Their interpretation and proof are related to quantum mechanics. In the talk we discuss an exchange of ideas between these fields. END:VEVENT BEGIN:VEVENT DTSTART:20140716T140000 DTEND:20140716T153000 DTSTAMP:20140715T150000Z UID:0974b0bf0e1fa39161c4838646c6f169@cgp.ibs.re.kr SUMMARY:Mirror symmetry of toric A-model and Laudau-Ginzburg B model I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Special Lecture\n\nAbstract: I will explain (homological) Mirror symmetry where we take toric manifold as a symplectic manifold and a version of singularity theory in the complex side. The talk include some of (hopeful most of) the following topic.A summary of Lagrangian Floer homology. How we include open closed and closed open map to it. How we can calculate them in case of toric manifold. How we use rigid analytic family version to construct mirror functor. Application of cardy relation to study Lagrangian Floer theory on toric manifolds. How we can work out equivariant version of virtual fundamental chain technique. Cyclic homology of Floer complex and its relation to open closed map. END:VEVENT BEGIN:VEVENT DTSTART:20140718T140000 DTEND:20140718T153000 DTSTAMP:20140717T150000Z UID:ce0a87b874ee96002560e5959d101cd0@cgp.ibs.re.kr SUMMARY:Mirror symmetry of toric A-model and Laudau-Ginzburg B model II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Special Lecture\n\nAbstract: I will explain (homological) Mirror symmetry where we take toric manifold as a symplectic manifold and a version of singularity theory in the complex side. The talk include some of (hopeful most of) the following topic.A summary of Lagrangian Floer homology. How we include open closed and closed open map to it. How we can calculate them in case of toric manifold. How we use rigid analytic family version to construct mirror functor. Application of cardy relation to study Lagrangian Floer theory on toric manifolds. How we can work out equivariant version of virtual fundamental chain technique. Cyclic homology of Floer complex and its relation to open closed map. END:VEVENT BEGIN:VEVENT DTSTART:20140722T140000 DTEND:20140722T153000 DTSTAMP:20140721T150000Z UID:267381fa88df59007e9c16f1822d767e@cgp.ibs.re.kr SUMMARY:Mirror symmetry of toric A-model and Laudau-Ginzburg B model III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Special Lecture\n\nAbstract: I will explain (homological) Mirror symmetry where we take toric manifold as a symplectic manifold and a version of singularity theory in the complex side. The talk include some of (hopeful most of) the following topic.A summary of Lagrangian Floer homology. How we include open closed and closed open map to it. How we can calculate them in case of toric manifold. How we use rigid analytic family version to construct mirror functor. Application of cardy relation to study Lagrangian Floer theory on toric manifolds. How we can work out equivariant version of virtual fundamental chain technique. Cyclic homology of Floer complex and its relation to open closed map. END:VEVENT BEGIN:VEVENT DTSTART:20140724T140000 DTEND:20140724T153000 DTSTAMP:20140723T150000Z UID:75443c5c0df4c69603cc055ece18f5dc@cgp.ibs.re.kr SUMMARY:Mirror symmetry of toric A-model and Laudau-Ginzburg B model IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Special Lecture\n\nAbstract: I will explain (homological) Mirror symmetry where we take toric manifold as a symplectic manifold and a version of singularity theory in the complex side. The talk include some of (hopeful most of) the following topic.A summary of Lagrangian Floer homology. How we include open closed and closed open map to it. How we can calculate them in case of toric manifold. How we use rigid analytic family version to construct mirror functor. Application of cardy relation to study Lagrangian Floer theory on toric manifolds. How we can work out equivariant version of virtual fundamental chain technique. Cyclic homology of Floer complex and its relation to open closed map. END:VEVENT BEGIN:VEVENT DTSTART:20140711T140000 DTEND:20140711T153000 DTSTAMP:20140710T150000Z UID:617532b3904f8a4793af05bfc268d2d7@cgp.ibs.re.kr SUMMARY:Learning seminar on basics of Arnold's Theory of Lagrangian singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Special Lecture\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140707T140000 DTEND:20140707T163000 DTSTAMP:20140706T150000Z UID:93b4ef49e99cb9acfa45c27997c31416@cgp.ibs.re.kr SUMMARY:Spectral theory of hyperbolic surfaces: arithmetic surfaces and Selberg's eigenvalue conjecture LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Junehyuk Jung (KAIST)\n\nEvent: PMI Intensive Lecture series in Number Theory\n\nAbstract: Selberg's eigenvalue conjecture predicts that the lowest nonzero eigenvalue of Laplacian on arithmetic (hyperbolic) surfaces is greater than or equal to 1/4. This is equivalent to the statement that every automorphic representation of GL_2 (principal series representations, in particular) is tempered at archimedean places, hence is a special case of Generalized Ramanujan Conjecture. In this series of lectures, I will first go over spectral theory of Laplacian on hyperbolic surfaces, and introduce Kuznetsov trace formula. When the surface is arithmetic, I'll explain how one can prove the first non-trivial bound \geq 3/16 due to Selberg, using the trace formula and Weil's bound for Kloosterman sums. In the end, to emphasize the role of arithmeticity in Selberg's eigenvalue conjecture, I'm going to construct (non-arithmetic) hyperbolic surfaces which have arbitrarily small first nonzero eigenvalues. END:VEVENT BEGIN:VEVENT DTSTART:20140708T140000 DTEND:20140708T163000 DTSTAMP:20140707T150000Z UID:416c664139b99ebd11851914d2110eb3@cgp.ibs.re.kr SUMMARY:Spectral theory of hyperbolic surfaces: arithmetic surfaces and Selberg's eigenvalue conjecture LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Junehyuk Jung (KAIST)\n\nEvent: PMI Intensive Lecture series in Number Theory\n\nAbstract: Selberg's eigenvalue conjecture predicts that the lowest nonzero eigenvalue of Laplacian on arithmetic (hyperbolic) surfaces is greater than or equal to 1/4. This is equivalent to the statement that every automorphic representation of GL_2 (principal series representations, in particular) is tempered at archimedean places, hence is a special case of Generalized Ramanujan Conjecture. In this series of lectures, I will first go over spectral theory of Laplacian on hyperbolic surfaces, and introduce Kuznetsov trace formula. When the surface is arithmetic, I'll explain how one can prove the first non-trivial bound \geq 3/16 due to Selberg, using the trace formula and Weil's bound for Kloosterman sums. In the end, to emphasize the role of arithmeticity in Selberg's eigenvalue conjecture, I'm going to construct (non-arithmetic) hyperbolic surfaces which have arbitrarily small first nonzero eigenvalues. END:VEVENT BEGIN:VEVENT DTSTART:20140709T140000 DTEND:20140709T163000 DTSTAMP:20140708T150000Z UID:feaed083ea3a7d05399c57b0e0edff59@cgp.ibs.re.kr SUMMARY:Spectral theory of hyperbolic surfaces: arithmetic surfaces and Selberg's eigenvalue conjecture LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Junehyuk Jung (KAIST)\n\nEvent: PMI Intensive Lecture series in Number Theory\n\nAbstract: Selberg's eigenvalue conjecture predicts that the lowest nonzero eigenvalue of Laplacian on arithmetic (hyperbolic) surfaces is greater than or equal to 1/4. This is equivalent to the statement that every automorphic representation of GL_2 (principal series representations, in particular) is tempered at archimedean places, hence is a special case of Generalized Ramanujan Conjecture. In this series of lectures, I will first go over spectral theory of Laplacian on hyperbolic surfaces, and introduce Kuznetsov trace formula. When the surface is arithmetic, I'll explain how one can prove the first non-trivial bound \geq 3/16 due to Selberg, using the trace formula and Weil's bound for Kloosterman sums. In the end, to emphasize the role of arithmeticity in Selberg's eigenvalue conjecture, I'm going to construct (non-arithmetic) hyperbolic surfaces which have arbitrarily small first nonzero eigenvalues. END:VEVENT BEGIN:VEVENT DTSTART:20140708T110000 DTEND:20140708T120000 DTSTAMP:20140707T150000Z UID:d83b4e6350093da35aae87799e677327@cgp.ibs.re.kr SUMMARY:On the least prime primitive root LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: JunSoo Ha (Stanford University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: Primitive roots are one of the most classic object in number theory.A challenging problem on primitive roots is to establish a uniform bound on the size of the least primitive root and the least prime primitive root. In this talk, I will discuss on some historic and related results and describe my recent result on the uniform bound on prime primitive root. END:VEVENT BEGIN:VEVENT DTSTART:20140709T110000 DTEND:20140709T120000 DTSTAMP:20140708T150000Z UID:86507038616a38acd71777cc0ae9eff4@cgp.ibs.re.kr SUMMARY:Almost primes in thin orbits LOCATION:Math. Bldg. #312 DESCRIPTION:Speaker: Hee Oh (Yale University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: We will discuss uniform spectral gap results for the congruence family of thin hyperbolic groups and their applications to affine sieves in linear orbits of thin hyperbolic groups. END:VEVENT BEGIN:VEVENT DTSTART:20140807T100000 DTEND:20140807T110000 DTSTAMP:20140806T150000Z UID:d0505dbd41abeaa3d9f3b1808fc5da94@cgp.ibs.re.kr SUMMARY:Family Floer cohomology and mirror symmetry LOCATION:POSCO International Center DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: One can associate to a Lagrangian torus fibration on a symplectic manifold X a rigid analytic space Y whose points are the unitary local systems on the fibres. Assuming that there are no singular fibres, I will explain how family Floer cohomology gives rise to a functor which assigns to an (unobstructed) Lagrangian in X an object in a (twisted) derived category of Y, and that this functor is faithful. END:VEVENT BEGIN:VEVENT DTSTART:20140807T140000 DTEND:20140807T150000 DTSTAMP:20140806T150000Z UID:45bb9d077ebfd8b19741bab98c006006@cgp.ibs.re.kr SUMMARY:SYZ mirror symmetry and exotic Lagrangian tori LOCATION:POSCO International Center DESCRIPTION:Speaker: Denis Auroux\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Using CP^2 as our main example and source of evidence, we will explain some conjectural connections between wall-crossing in SYZ mirror symmetry, toric degenerations, and monotone Lagrangian tori. The less conjectural part of the talk is based on Renato Vianna's thesis work (arXiv: 1305.7512). END:VEVENT BEGIN:VEVENT DTSTART:20140807T164500 DTEND:20140807T174500 DTSTAMP:20140806T150000Z UID:34fca348cac839e58e41999a15304882@cgp.ibs.re.kr SUMMARY:Witten deformation and scattering diagrams LOCATION:POSCO International Center DESCRIPTION:Speaker: Kwokwai Chan\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Given a Calabi-Yau manifold X equipped with a special Lagrangian torus fibration, we introduce a DGLA via Witten deformation, which is expected to govern the quantum deformations of symplectic structures on X. The Maurer-Cartan equation can be solved explicitly, and under the SYZ transform (i.e. Fourier transform) the leading order terms of the solutions reproduce the scattering diagrams which appear in the Gross-Siebert program. This is based on joint work in progress with Conan Leung and Ziming Ma. END:VEVENT BEGIN:VEVENT DTSTART:20140808T104500 DTEND:20140808T114500 DTSTAMP:20140807T150000Z UID:6f177ec3c8f62a3139c5f2eabcce8d5d@cgp.ibs.re.kr SUMMARY:Localized mirror functors from Fukaya category to matrix factorization category LOCATION:POSCO International Center DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: This is a continuation of the talk by Siu-Cheong Lau. We give more detailed explanation of the geometric construction of localized mirror functors: Given an weakly unobstructed Lagrangian torus or a Lagrangian immersion L, we define a localized Floer potential W(L). We discuss a geometric way to define an A-infinity functor from Fukaya category to the matrix factorization category of W(L). This is done by considering L as a reference, and by using Fukaya category operations to define the functor. In particular, we find a way to identify Lagrangian Floer complex directly as a matrix factorization of the function W(L). We discuss its application to homological mirror symmetry of orbifold projective lines, and toric Fano manifolds, This is a joint work with Hansol Hong, and Siu-Cheong Lau. END:VEVENT BEGIN:VEVENT DTSTART:20140804T100000 DTEND:20140804T110000 DTSTAMP:20140803T150000Z UID:34f53d42bd9d2dd4dce7674479bca0c8@cgp.ibs.re.kr SUMMARY:Cluster algebras and Mirror Symmetry LOCATION:POSCO International Center DESCRIPTION:Speaker: Mark Gross\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: I will talk about recent work with Hacking, Keel and Kontsevich applying ideas developed in the context of mirror symmetry for log Calabi-Yau varieties to the theory of cluster algebras. In particular, the techniques introduced allow simple proofs of significant conjectures in cluster algebras, including the positivity of the Laurent phenomenon in the geometric type case (proved by Schiffler and Lee in the skew-symmetric case). END:VEVENT BEGIN:VEVENT DTSTART:20140805T100000 DTEND:20140805T110000 DTSTAMP:20140804T150000Z UID:4b0a29ef389af163b4fbbc180eb91bf2@cgp.ibs.re.kr SUMMARY:Categorical base loci and Multiplier Ideal Sheaves LOCATION:POSCO International Center DESCRIPTION:Speaker: Ludmil Katzarkov\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140805T153000 DTEND:20140805T163000 DTSTAMP:20140804T150000Z UID:3af4463c55180f376578e7493b93659d@cgp.ibs.re.kr SUMMARY:Mirrors to weighted flips and blow-ups LOCATION:POSCO International Center DESCRIPTION:Speaker: Gabriel Kerr\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Any toric DM stack has a minimal model sequence consisting of weighted flips, blow-ups and projective bundle projections. It is known that any such sequence introduces a semi-orthogonal decomposition of the derived category of coherent sheaves on the stack. In “Symplectomorphism group relations and degenerations of Landau-Ginzburg models”, a joint work with C. Diemer and L. Katzarkov, a decomposition of the mirror Landau-Ginzburg model was defined. It was conjectured that there is a quasi-equivalence between the A and B modelcategories that respects these decompositions. In this talk I will discuss this conjecture and sketch a partial proof. END:VEVENT BEGIN:VEVENT DTSTART:20140804T164500 DTEND:20140804T174500 DTSTAMP:20140803T150000Z UID:b97c609fdb2b5d1f8a95aab622a8fa57@cgp.ibs.re.kr SUMMARY:Generalized SYZ and homological mirror symmetry LOCATION:POSCO International Center DESCRIPTION:Speaker: Siu-Cheong Lau\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Homological mirror symmetry conjecture asserts an equivalence between the derived Fukaya category and the derived category of coherent sheaves of the mirror. The conjecture has been verified in several interesting cases by computing and comparing generators and relations of the categories. However the computations do not explain why we should expect homological mirror symmetry. We attempt to answer this question by introducing a construction of mirror Landau-Ginzburg model analogous to SYZ, and an A-infinity functor from the Fukaya category to the category of matrix factorizations of the mirror. This is a joint work with Cheol-Hyun Cho and Hansol Hong. END:VEVENT BEGIN:VEVENT DTSTART:20140807T153000 DTEND:20140807T163000 DTSTAMP:20140806T150000Z UID:b65e6dfe78ebab2965592dc47dea3549@cgp.ibs.re.kr SUMMARY:The K that worked by itself LOCATION:POSCO International Center DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Renumbering of marked points on moduli spaces of stable maps induces the action of permutation groups on sheaf cohomology of suitable vector bundles. I will talk about K-theoretic Gromov-Witten invariants which are cognizant of this information, and their applicationsto local GW-invariants, those of complete intersections, to fixed point localization, q-hypergeometric functions, and mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20140807T111500 DTEND:20140807T121500 DTSTAMP:20140806T150000Z UID:e3636f0304b0cf1f960b4859818d1df4@cgp.ibs.re.kr SUMMARY:Categorical localization and the wrapped Fukaya category LOCATION:POSCO International Center DESCRIPTION:Speaker: Paul Seidel\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: I will explain recent work (jointly with Abouzaid) which explains the relation between the Fukaya category of a Lefschetz fibration and the wrapped Fukaya category of its total space. END:VEVENT BEGIN:VEVENT DTSTART:20140808T120000 DTEND:20140808T130000 DTSTAMP:20140807T150000Z UID:2e817bf986b4f4ffb7f7fe7e38f06905@cgp.ibs.re.kr SUMMARY:Toward A-model wall crossing in the large complex structure limit LOCATION:POSCO International Center DESCRIPTION:Speaker: Bernd Siebert\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140804T140000 DTEND:20140804T150000 DTSTAMP:20140803T150000Z UID:a3e1d6e16eca8ceef343ade24f36bdfe@cgp.ibs.re.kr SUMMARY:Generation of Fukaya category and potential function LOCATION:POSCO International Center DESCRIPTION:Speaker: Hiroshi Ohta\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: I will talk about generation criteria for Fukaya category of a closed symplectic manifold and discuss some applications to the case of toric manifolds. This is based on my joint work with M. Abouzaid, K. Fukaya, Y.-G. Oh, K. Ono. END:VEVENT BEGIN:VEVENT DTSTART:20140804T153000 DTEND:20140804T163000 DTSTAMP:20140803T150000Z UID:7228713b0981b29fcd9ae95d6c3f6417@cgp.ibs.re.kr SUMMARY:Lagrangian torus fibrations on Grassmannians and potential function LOCATION:POSCO International Center DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: We discuss a joint work with Yuichi Nohara on potential functions of Lagrangian torus fibers of completely integrable systems on the Grassmannian of 2-planes in an n-space associated with triangulations of an n-gon. We also discuss the coordinate change between different triangulations, and Floer cohomologies of some of non-torus fibers. END:VEVENT BEGIN:VEVENT DTSTART:20140805T111500 DTEND:20140805T121500 DTSTAMP:20140804T150000Z UID:49389775e7a44788cfa62cd08eae5068@cgp.ibs.re.kr SUMMARY:Triangulated surfaces in triangulated categories LOCATION:POSCO International Center DESCRIPTION:Speaker: Tobias Dyckerhoff\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: We explain how the theory of cyclic 2-Segal spaces can be used to implement a 2-dimensional instance of Kontsevich's proposal on defining a variant of the Fukaya category of a Stein manifold in terms of a singular Lagrangian spine. As a main result, we associate to a marked oriented surface S a differential Z/2-graded category F(S) which is acted upon by the mapping class group and can be computed as a categorified state sum with respect to any triangulation of S. We further prove a Mayer-Vietoris theorem which allows for the calculation of motivic A^1-homotopy invariants, such as periodic cyclic homology, of F(S). This talk is based on joint work with Mikhail Kapranov. END:VEVENT BEGIN:VEVENT DTSTART:20140805T140000 DTEND:20140805T150000 DTSTAMP:20140804T150000Z UID:2adf9f1a5188d4217ea4db9af218ef25@cgp.ibs.re.kr SUMMARY:Mirror symmetry for exceptional unimodular singularities LOCATION:POSCO International Center DESCRIPTION:Speaker: Changzheng Li\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: In this talk, we will discuss the LG-LG mirror symmetry conjecture. We will talk about the Saito-Givental theory of weighted homogeneous singularities on the Landau-Ginzburg B-side, and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on the Landau-Ginzburg A-side. On the B-side, we develop a perturbative method to compute the genus-zero correlation functions associated to Saito's primitive forms. It is applied to the exceptional unimodular singularities, and we show that the numerical invariants match the FJRW invariants on the A-side. This establishes the first examples of LG-LG mirror symmetry for weighted homogeneous polynomials of central charge greater than one which contain negative degree deformation parameters. This is my joint work with Si Li, Kyoji Saito and Yefeng Shen. END:VEVENT BEGIN:VEVENT DTSTART:20140805T164500 DTEND:20140805T174500 DTSTAMP:20140804T150000Z UID:f7a5b07e62cfa1500ea37cf0be00fda7@cgp.ibs.re.kr SUMMARY:Lagrangian Cobordisms and Fukaya Categories LOCATION:POSCO International Center DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: Given an exact symplectic manifold with some extra decorations, one can construct two categories whose objects are (exact, decorated) Lagrangians: The Fukaya category, and a category whose morphisms are cobordisms. Both can be triangulated, and there is even a functor between them respecting their triangulated structures. In this talk we discuss some work-in-progress drawing parallels between the two categories, and if time allows, we will discuss the relation of our work with that of Biran-Cornea, or discuss possible applications to the Nearby Lagrangian Conjecture and Heegard-Floer invariants for 2-, 3-, and 4-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20140808T093000 DTEND:20140808T103000 DTSTAMP:20140807T150000Z UID:42c7201b92371499a0c0f2a010c6ec60@cgp.ibs.re.kr SUMMARY:Lagrangians associated to minimal model transitions LOCATION:POSCO International Center DESCRIPTION:Speaker: Christopher Woodward\n\nEvent: Homological mirror symmetry and symplectic topology (ICM-2014 Satellite Conference)\n\nAbstract: The Fukaya category is conjectured to be non-empty for compact symplectic manifolds. One way of producing Lagrangians with non-trivial Floer homology is via transitions in the minimal model program (flips and blow-ups). In the toric case, this is essentially a re-interpretation of work of Fukaya-Oh-Ohta-Ono. END:VEVENT BEGIN:VEVENT DTSTART:20140721T140000 DTEND:20140721T153000 DTSTAMP:20140720T150000Z UID:04423cf4eb90f10148c55a32437cc1ae@cgp.ibs.re.kr SUMMARY:On the equivalence of the definitions of volume of representations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungwoon Kim\n\nEvent: Seminar 2014\n\nAbstract: Let G be a rank 1 simple Lie group and M be a connected oriented aspherical tame manifold. Assume that each end of M has amenable fundamental group. There are several definitions of volume of representations of the fundamental group of M into G. We prove that all definitions so far are equivalent. In particular, when M is a finite-volume hyperbolic n-manifold of dimension at least 4.We show that the volume of representations is constant on the connected components of the SO(n,1)-representation variety of the fundamental group of M.This result gives a new proof for the local rigidity theorem of hyperbolic lattices. If time permits, we will discuss the 3-dimensional case and some applications. END:VEVENT BEGIN:VEVENT DTSTART:20140714T160000 DTEND:20140714T180000 DTSTAMP:20140713T150000Z UID:48a1d63dd12821d675d40c739c308134@cgp.ibs.re.kr SUMMARY:Parallelism of shape operator on real hypersurfaces in complex two-plane Grassmannians LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Hyeonjin Lee (POSTECH)\n\nEvent: GAIA Seminar\n\nAbstract: In this talk, we want to introduce a notion of the Reeb parallel shape operator with respect to the Levi-Civita connection (or the generalized Tanaka-Webster connection) of a real hypersurface in and give some characterizations for model spaces related to the parallelism of shape operator. END:VEVENT BEGIN:VEVENT DTSTART:20140716T160000 DTEND:20140716T180000 DTSTAMP:20140715T150000Z UID:e5e85d031f8348b51d5dd80314b3cc32@cgp.ibs.re.kr SUMMARY:Almost-Kahler anti-self-dual metrics LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Inyoung Kim (POSTECH)\n\nEvent: GAIA Seminar\n\nAbstract: We show the existence of strictly almost-Kahler anti-self -dual metrics on certain 4-manifolds by deforming a scalar-flat Kahler metric. We prove any almost-Kahler anti-self-dual 4-manifold has a non-trivial Seiberg-Witten invariant. Using this, we show almost-Kahler anti-self-dual metrics do not exist on certain other 4-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20140723T140000 DTEND:20140723T150000 DTSTAMP:20140722T150000Z UID:cff5f6d055a130bc2f81edce4e5dd95d@cgp.ibs.re.kr SUMMARY:Multiple zeta values and periods of modular forms I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Koji Tasaka (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: The multiple zeta values (abbreviated MZVs) are multivariate generalisations of the values of the Riemann zeta function at positive integers. These real number are known to be related with number theory, knot theory, quantum field theory, arithmetic geometry and so on. Our interest in the study of MZVs is a connection with the theory of elliptic modular forms (or their period polynomials), which was first discovered by Don Zagier in the case of depth 2. Our goal of this talk is to explain a result of Gangl, Kaneko and Zagier that the relations among periods of cusp forms produce that of double zeta values. END:VEVENT BEGIN:VEVENT DTSTART:20140714T140000 DTEND:20140714T153000 DTSTAMP:20140713T150000Z UID:027c9ba73ad96aafedaf058f218322c3@cgp.ibs.re.kr SUMMARY:Learning seminar on basics of Arnold's Theory of Lagrangian singularities II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Special Lecture\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140715T140000 DTEND:20140715T153000 DTSTAMP:20140714T150000Z UID:f8c3257f507405bdf0079753401c9d46@cgp.ibs.re.kr SUMMARY:Learning seminar on basics of Arnold's Theory of Lagrangian singularities III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Special Lecture\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140730T140000 DTEND:20140730T153000 DTSTAMP:20140729T150000Z UID:5826c6d9c54be7339cf987a4ef8bb439@cgp.ibs.re.kr SUMMARY:Compactness of gauged Witten equation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Guangbo Xu\n\nEvent: Seminar 2014\n\nAbstract: Recently Fan-Jarvis-Ruan constructed a mathematical theory of the Landau-Ginzburg A-model, which is based on the analysis of the Witten equation associated with a quasi-homogeneous polynomial. In this talk I will discuss a gauged version of the Witten equation, which was also due to Witten, in his formulation of the gauged linear $\sigma$-model. I will discuss some analytical issue, especially the compactness of the moduli space when we have to perturb the equation. If time permits, I will give a formal definition of the correlation function. This is a joint work with Gang Tian. END:VEVENT BEGIN:VEVENT DTSTART:20140721T160000 DTEND:20140721T180000 DTSTAMP:20140720T150000Z UID:42f47e76f88f18a69efae2d3c4b8ea23@cgp.ibs.re.kr SUMMARY:Learning seminar on basics of Arnold's Theory of Lagrangian singularities IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Special Lecture\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20140801T153000 DTEND:20140801T170000 DTSTAMP:20140731T150000Z UID:0e1b2a01246202b54d58b04360afb8d3@cgp.ibs.re.kr SUMMARY:On Fano manifolds with nef tangent bundle LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Luis Solá Conde\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: As a extension of Mori's characterization of the projective space in terms of the positivity of its tangent bundle, it is a natural question to ask whether the only Fano manifolds with nef tangent bundle are rational homogeneous spaces. In this talk we will review some partial results in this direction, obtained in collaboration with Munoz, Occhetta, Watanabe and Wisniewski. END:VEVENT BEGIN:VEVENT DTSTART:20140722T160000 DTEND:20140722T170000 DTSTAMP:20140721T150000Z UID:0bafa31ceface8bb0b49320714dd5f4c@cgp.ibs.re.kr SUMMARY:A uniform construction of smooth integral models and a recipe for computing local densities of any forms over any local fields LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sungmun Cho (University of Toronto)\n\nEvent: PMI Hwarang Program Seminar\n\nAbstract: In this talk I will explain a simple and uniform construction of smooth integral models associated to quadratic, symplectic, (anti-) hermitian, (anti-) quaternionic hermitian lattices defined over any local field. As one major application, this construction gives a new, simple and effective recipe for computing local densities of the above lattices. Local densities are local factors of the celebrated Smith-Minkowski-Siegel mass formula and the mass formula is an essential tool for the classification of lattices. END:VEVENT BEGIN:VEVENT DTSTART:20140724T150000 DTEND:20140724T170000 DTSTAMP:20140723T150000Z UID:c77fe9755f7fc328bcc1dae6523064d3@cgp.ibs.re.kr SUMMARY:On the regularity of Boltzmann equation in convex domains LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Chanwoo Kim (University of Wisconsin–Madison)\n\nEvent: PMI PDE Seminar\n\nAbstract: Consider the Boltzmann equation in a strictly convex domain with the specular boundary condition. With the aid of a distance function toward the grazing set, we construct weighted C^1 solutions away from the grazing set for all boundary conditions. END:VEVENT BEGIN:VEVENT DTSTART:20140827T150000 DTEND:20140827T180000 DTSTAMP:20140826T150000Z UID:ba99a812b014775a2c223c3eaf3a42ce@cgp.ibs.re.kr SUMMARY:Geometric Langlands from $N=4$ gauge theory II (informal discussion) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Philsang Yoo\n\nEvent: Seminar 2014\n\nAbstract: Geometric Langlands conjecture arises as geometric analogue of the Langlands program in number theory. From a completely different direction, Kapustin-Witten found a physical theory which led to a version of the geometric Langlands correspondence. One of our goals is to rigorously analyze the physical theory using derived algebraic geometry and to obtain the up-to-date version of the conjecture, which was not possible from the original investigation of Kapustin-Witten.The first part of the talk will be a gentle introduction to the geometric Langlands conjecture for anyone interested in the subject. We will start the second part by reviewing some of Kapustin-Witten's main ideas and then provide some hints for how one could have conjectured the geometric Langlands correspondence purely out of physics, without knowing any number theory. No knowledge of number theory or physics is assumed. The main results are based on a joint work in progress with Chris Elliott. END:VEVENT BEGIN:VEVENT DTSTART:20140923T160000 DTEND:20140923T180000 DTSTAMP:20140922T150000Z UID:85ab87bb31674c2c260dfbf6b3789cfd@cgp.ibs.re.kr SUMMARY:Tensor product of A-infinity algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Lino Jose Campos Amorim\n\nEvent: Seminar 2014\n\nAbstract: A-infinity algebras are a generalization of dg-algebras that occur naturally in symplectic geometry. Unlike the case of dg-algebras there is no canonical way to define the tensor product of two A-infinity algebras. In this talk we will discuss two different approaches to this problem. Each approach can be used to generalize the construction of the tensor product to A-infinity algebras with extra structure, namely a cyclic or filtered structure. We will also describe two applications of these constructions: a Kunneth formula in Lagrangian Floer theory and a formula for the cup product on the cohomology of the moduli space of Riemann surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20140901T170000 DTEND:20140901T180000 DTSTAMP:20140831T150000Z UID:e2aca3f72e997735676e689021116a57@cgp.ibs.re.kr SUMMARY:Constructive string field theory of open-closed topological B-type strings LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Quantum Monday 2014\n\nAbstract: In mathematics, String Theory gives interesting invariants, a way to make classicaltheories ‘quantum’. The most provocative example is Mirror Symmetry, which atgenus zero relates quantum cohomology of symplectic manifolds with an (extended)deformation theory of complex manifolds. It currently comes in two versions, open (orhomological) and closed (or classical). Numerous technical tools have emerged inunderstanding this beautiful correspondence, but a rigorous unified perspective ismissing. I propose that such a unified perspective should be provided by open-closedtopological string field theory. END:VEVENT BEGIN:VEVENT DTSTART:20140915T160000 DTEND:20140915T180000 DTSTAMP:20140914T150000Z UID:0c0df2fe7c69efaa4394378ae22a77eb@cgp.ibs.re.kr SUMMARY:An introduction to Heegaard Floer homology I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyungbae Park\n\nEvent: Seminar 2014\n\nAbstract: Heegaard Floer homology, introduced by Ozsvath and Szabo early 2000, has provided a powerful set of invariants for most of the objects in low-dimensional topology and geometry. The Floer homology invariant was originally defined for closed oriented three-manifolds and has been quickly developed to invariants for smooth four-manifolds, knots, three-manifolds with boundary and more. The goal of the seminar is to introduce the relatively new theory to non-experts in the relating fields and discuss how it can be applied to solve problems in their own interests. To achieve it, in the first talk of the seminar, we review the definitions of the set of invariants through concrete examples and introduce main results of the theory. END:VEVENT BEGIN:VEVENT DTSTART:20140916T160000 DTEND:20140916T180000 DTSTAMP:20140915T150000Z UID:7fd022f88235db96a5621ab916bfd00b@cgp.ibs.re.kr SUMMARY:An introduction to Heegaard Floer homology II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyungbae Park\n\nEvent: Seminar 2014\n\nAbstract: In the second talk, we mainly focus on the properties and computational techniques of the Heegaard Floer invariants for three-manifolds and knots. For the three manifolds invariant, we review the Kunneth-type formulas, the surgery formulas and the surgery exact sequences. Regarding the knot invariant, we demonstrate explicit computations of it for some classes of knots. We also discuss algorithmic aspects of the theory. END:VEVENT BEGIN:VEVENT DTSTART:20140912T155000 DTEND:20140912T180000 DTSTAMP:20140911T150000Z UID:85145807289cfdc5c4ccae4d89c3b090@cgp.ibs.re.kr SUMMARY:Cheeger-Gromov universal bounds and topology of 3-manifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jae Choon Cha\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: Using deep analytic methods, Cheeger and Gromov proved that there is a universal bound of the L2 rho invariants of a smooth manifold. I will introduce a new topological approach to understand their universal bound, focusing on the ideas and methods we develop and employ from geometric topology, global analysis, functional analysis, group theory, and controlled homological algebra. Applications include a proof of the existence of a universal bound for topological manifolds, and new relationships of the Cheeger-Gromov invariants and topology of 3-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20140915T200000 DTEND:20140915T220000 DTSTAMP:20140914T150000Z UID:9b525a88b4eda1b4561a949b02599783@cgp.ibs.re.kr SUMMARY:Peak functions and Invariant metrics LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Kang Tae Kim\n\nEvent: GAIA Seminar\n\nAbstract: I will present (1) a method of creating the holomorphic peak functions for broad classes of unbounded domains, (2) a method of obtaining the completeness of the invariant metrics, such as Caratheodory, Kobayashi and Bergman metrics, and (3) some open problems. The first two are from a collaboration with Taeyong Ahn and Herve' Gaussier. END:VEVENT BEGIN:VEVENT DTSTART:20140918T163000 DTEND:20140918T173000 DTSTAMP:20140917T150000Z UID:6b87644b1c1ff796c917981e7d4aa983@cgp.ibs.re.kr SUMMARY:A revisit to Siegel's theorem on cubic equations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: T-Seminar\n\nAbstract: Siegel proved, in 1929, that there are only finitely many integer solutions for a generic binary cubic equations. His result is ineffective in the sense that it does not provide an algorithm to determine the complete set of solutions. Later, Baker obtained an upper bound for the size of hypothetical solutions, which in particular produces the desired algorithm. However, the upper bounds so far obtained by generalisations of Baker's method are so large, rendering the algorithm practically inefficient. In this talk, I will sketch a new method to determine the complete set of solutions, as well as plenty of numerical examples. The new methods depends on the theory of elliptic curves, especially the modularity of elliptic curves defined over the rational numbers. If time permits, I will discuss higher dimensional generalisations of the new method. END:VEVENT BEGIN:VEVENT DTSTART:20140919T150000 DTEND:20140919T170000 DTSTAMP:20140918T150000Z UID:a023243d98928674102c7ff7dd23c502@cgp.ibs.re.kr SUMMARY:Wave breaking and global existence for the generalized periodic two-component Hunter- Saxton system LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byungsoo Moon(PMI, POSTECH)\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: In this talk, we study the wave-breaking phenomena and global existence for the generalized two-component Hunter-Saxton system in the periodic setting. We first establish local well-posedness for the generalized two-component Hunter-Saxton system. We obtain a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions. END:VEVENT BEGIN:VEVENT DTSTART:20140922T200000 DTEND:20140922T220000 DTSTAMP:20140921T150000Z UID:3fe32f037d320667755b980d3c469cec@cgp.ibs.re.kr SUMMARY:Infinitesimal CR automorphisms and stability groups of infinite type models in C2. LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Ninh van Thu\n\nEvent: GAIA Seminar\n\nAbstract: In this talk, we are going to give explicit descriptions for stability groups of real rigid hypersurfaces of infinite type in C2. The decompositions of infinitesimal CR automorphisms are also given. This is a joint work with prof. Atsushi Hayashimoto. END:VEVENT BEGIN:VEVENT DTSTART:20140926T155000 DTEND:20140926T180000 DTSTAMP:20140925T150000Z UID:9a2baac4d17d249919f557d3c8455ed9@cgp.ibs.re.kr SUMMARY:Inference for stochastic processes via estimating functions: Recent review LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sun Young Hwang(Sookmyung Women's University)\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: Abstract: Various estimation methods in time series and stochastic processes are reviewed in a unified framework of estimating functions. In particular, maximum likelihood and quasi-likelihood are discussed in the context of asymptotic optimality within certain estimating functions. Both ergodic and non-ergodic processes are considered, and recent developments are presented. To illustrate the main results, diverse examples are shown including GARCH processes, bifurcating autoregression (BAR), explosive autoregression, conditionally linear processes, and branching Markov processes. END:VEVENT BEGIN:VEVENT DTSTART:20140917T160000 DTEND:20140917T180000 DTSTAMP:20140916T150000Z UID:241912cce353cfe0299f918f734db02c@cgp.ibs.re.kr SUMMARY:Separability of quantum states via algebraic geometry LOCATION:POSTECH DESCRIPTION:Speaker: Joohan Na (KIAS)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Quantum entanglement is now considered as the main resource for quantum information and quantum computation. Distinguishing entangled states from separable ones is a fundametal problem in quantum entanglement theory, but it is so hard, especially known to be an NP-hard problem. In order to determine if a given state is separable or not, it is natural to look at the ranges of the state and its partial transposes by the PPT criterion and the range criterion. In this talk, we explain how to investigate the conditions appeared in the range criterion making use of methods in algebraic geometry and topology. END:VEVENT BEGIN:VEVENT DTSTART:20140925T160000 DTEND:20140925T180000 DTSTAMP:20140924T150000Z UID:4130ff17aa1fc12b37387c28c902f7d4@cgp.ibs.re.kr SUMMARY:Primitive forms via polyvector fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Changzheng Li\n\nEvent: CGP Seminar 2014\n\nAbstract: The theory of primitive forms was introduced by Kyoji Saito in early 1980s, which was first known in singularity theory and has attracted much attention in mirror symmetry recently. In this talk, we will introduce a differential geometric approach to primitive forms, using compactly supported polyvector fields. We will also introduce a perturbative way to calculate the primitive forms, and show some computational examples. This is my joint work with Si Li and Kyoji Saito. END:VEVENT BEGIN:VEVENT DTSTART:20141002T160000 DTEND:20141002T180000 DTSTAMP:20141001T150000Z UID:cc831867944b4d9fe45db9a34628cb0c@cgp.ibs.re.kr SUMMARY:Descent on general diophantine equations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: CGP Seminar 2014\n\nAbstract: We present a strategy to attack diophantine equations. It is a simultaneous generalisation of the descent for elliptic curves, and the Frey curve trick for Fermat's Last Theorem. We will mainly focus on its application to concrete equations such as binary quartics and ternary quintics. In particular, we will prove a finiteness result for certain binary quartic equations, and provide a number of numerical examples of it. END:VEVENT BEGIN:VEVENT DTSTART:20140925T163000 DTEND:20140925T173000 DTSTAMP:20140924T150000Z UID:5a55e29801df90bbcf470d0316d9af89@cgp.ibs.re.kr SUMMARY:The generalized two-component Hunter-Saxton system LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byungsoo Moon\n\nEvent: T-Seminar\n\nAbstract: In the last decades three integrable one-dimensional (with respect to the spatial variable) nonlinear equations rose to prominence in mathematical physics: the Camassa-Holm (CH), the Degasperis-Procesi (DP) and the Hunter-Saxton (HS) equation. Of these, CH and HS are formally linked ( the latter being the short-wave limit of the rst) but this does not mean that they present the same features. In recent years the quest of two-dimensional generalizations was successfully pursued, with considerable success for CH and DP, and to a lesser extent for HS. This gap is in some sense filled by the paper " Wave breaking and global existence for the generalized periodic two-component Hunter-Saxton system” [B. Moon and Y. Liu, J. Dierential Equations 253 (2012) 319-355]. In this T-seminar, I will focus on the motivation, history and background, few results of our model equation, and the some future work. Even if you are brand new to grad school, you are welcome to just come and listen. You'll get to see some of the different areas that are researched here. END:VEVENT BEGIN:VEVENT DTSTART:20140929T200000 DTEND:20140929T220000 DTSTAMP:20140928T150000Z UID:ca9a0111e13c7e35dd7b0760f5a7cd8a@cgp.ibs.re.kr SUMMARY:Quasi-circular domains and origin-preserving automorphisms LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Atsushi Yamamori\n\nEvent: GAIA Seminar\n\nAbstract: It is known by Kaup that all origin-preserving automorphisms of quasi-circular domains must be polynomial mappings. In our previous work, we considered quasi-circular domains in $mathbb C^2$ and proved that such automorphisms must be linear under certain circumstances. In this talk, we generalize the result for higher dimensional cases. END:VEVENT BEGIN:VEVENT DTSTART:20140924T134500 DTEND:20140924T150000 DTSTAMP:20140923T150000Z UID:61741df8364133c03d05bc1c4f220ac5@cgp.ibs.re.kr SUMMARY:Coding Theory of Association Schemes Ⅰ LOCATION:Math. Bldg. #208 DESCRIPTION:Speaker: Hyonju Yu\n\nEvent: Coding Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141010T150000 DTEND:20141010T170000 DTSTAMP:20141009T150000Z UID:3b7c6a8e489a1b192fecb0bd1de00530@cgp.ibs.re.kr SUMMARY:Vortex patches of Serfati LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hantaek Bae (Ulsan National Institute of Science and Technology)\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: In 1993, two proofs of the persistence of regularity of the boundary of a classical vortex patch for the 2D Euler equations were published, one by Chemin and the other by Bertozzi-Constantin. Chemin, in fact, proved a more general result, showing that vorticity initially having discontinuities only in directions normal to a family of vector fields continue to be so characterized by the time-evolved vector fields. A different, four-page 'elementary' proof of the regularity of a vortex patch boundary was published in 1994 by Ph. Serfati, employing only one vector field to describe the discontinuities in the initial data. In this talk, we discuss Serfati's proof along with a natural extension of it to a family of vector fields that reproduces the 1995 result of Chemin. END:VEVENT BEGIN:VEVENT DTSTART:20141017T171000 DTEND:20141017T180000 DTSTAMP:20141016T150000Z UID:df21f48d7ed55799c132dfa334aff71c@cgp.ibs.re.kr SUMMARY:Part II : A fast direct solver for quasi-periodic scattering problems with material junction points LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: June-Yub Lee (Ewha Womans University)\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: A number of problems in computational physics require the solution of the Helmholtz equation. The interaction of acoustic or electromagnetic waves with structured, periodic materials is often complicated by the fact that the scattering geometry involves domains where multiple media meet at a single point.We present a robust integral equation method for the calculation of two-dimensional scattering problems in the presence of triple-points, that is problems involving multiple materials meeting at a single point. Our approach involves both the modification of a standard integral representation [V. Rokhlin (1983)] and the use of adaptive refinement at geometric singularities [L. Greengard and J.-Y. Lee (2012)]. The GMRES iterative solver equipped with Fast Multipole Method (FMM) for the second kind integral equation is an optimal algorithm for a single right-hand-side in the sense that it is a linear-time complexity algorithm with a reasonably small constant. However, a direct numerical method is more efficient algorithm for multiple right-hand-sides. Our fast direct solver is based on a the interpolative decomposition (ID) that is more useful and produces a near-optimal representation for multilevel compression of the linear system of equations [K. L. Ho and L. Greengard (2012)]. We demonstrate the performance of the scheme with several numerical examples END:VEVENT BEGIN:VEVENT DTSTART:20141103T160000 DTEND:20141103T180000 DTSTAMP:20141102T150000Z UID:67b293cb8c497ad35d4ccd26c8f22537@cgp.ibs.re.kr SUMMARY:Model category structures on coalgebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Quantum Monday 2014\n\nAbstract: There are two common approaches to putting weak equivalences on categories of differential graded coalgebras. The first, going back to Quillen, involves using coalgebras as a model for a dual category of algebras. The second, which models the derived category of coalgebras, uses quasi-isomorphisms as weak equivalences. In joint work with Joey Hirsh, we unify these two ideas, realizing them as the extreme values of a poset of model category structures on dg coalgebras over a cooperad which satisfies mild conditions. END:VEVENT BEGIN:VEVENT DTSTART:20141010T133000 DTEND:20141010T150000 DTSTAMP:20141009T150000Z UID:039de1cca4e4eb9562ec1505524a27a1@cgp.ibs.re.kr SUMMARY:Syzygy bound on the cubic strand of a projective variety and 3-linear resolutions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kangjin Han\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: Let X be any projective variety in P^N over an algebraically closed fieldK. Suppose that X is nondegenerate, i.e. not contained in any hyperplane of P^N. Few years ago, K. Han and S. Kwak developed a technique to compare syzygies under projections, as applications they proved sharp upper bounds on the ranks of higher linear syzygies, and characterized the extremal and next-to-extremal cases.In this talk, we report generalizations of these results, which are on-going with S. Kwak and J. Ahn. First, let us consider any variety X such that the defining ideal I_X has no generators of degree less than 3. Since I_X has no generators of degree ≤ 2, so the first non-vanishing strand of the resolution comes from linear syzygies of minimal generators of degree 3. We consider a basic degree bound and sharp bounds for generators and syzygies in this cubic strand. Further, the extremal cases will be discussed in the end. END:VEVENT BEGIN:VEVENT DTSTART:20141013T200000 DTEND:20141013T220000 DTSTAMP:20141012T150000Z UID:16c7b0f515be959789bb5f52ab8bd06c@cgp.ibs.re.kr SUMMARY:Representative maps and connections LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Sungmin Yoo(POSTECH)\n\nEvent: GAIA Seminar\n\nAbstract: The Bergman kernel function gives rise not only to the Bergman metric but also to some special holomorphic coordinate system which is called the Bergman representative map. This map appears to be quite similar to inverse of exponential map of Riemannian geometry. In this talk, I would demonstrate a construction of a holomorphic connection on the holomorphic tangent bundle of a subdomain of a given complex manifold, whose parallel curve gives rise to the inverse of the Bergman representative map. This overlaps largely to the work of S. Webster. I will also discuss some further results if time permits. END:VEVENT BEGIN:VEVENT DTSTART:20141016T163000 DTEND:20141016T173000 DTSTAMP:20141015T150000Z UID:d0315198b1c6e0e3e730341d2519daa0@cgp.ibs.re.kr SUMMARY:Isomorphism classes of association schemes induced by Hadamard matrices LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyonju Yu\n\nEvent: T-Seminar\n\nAbstract: Every Hadamard matrix H of order n > 1 induces a graph with 4n vertices, called the Hadamard graph Γ(H) of H. Since Γ(H) is a distance-regular graph with diameter 4, it induces a 4-class association scheme (Ω, S) of order 4n. In this article we deal with fission schemes of (Ω, S) under certain conditions, and for such a fission scheme we estimate the number of isomorphism classes with the same intersection numbers as the fission scheme. END:VEVENT BEGIN:VEVENT DTSTART:20141027T200000 DTEND:20141027T220000 DTSTAMP:20141026T150000Z UID:71e33b6e48520969762d75580a13d6db@cgp.ibs.re.kr SUMMARY:Brody Curves and Generalized Henon Mappings LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Taeyong Ahn\n\nEvent: GAIA Seminar\n\nAbstract: In this talk, we introduce the concept of Brody curves and generalized Henon mapping. We consider two sets related to generalized Henon mappings: the set of non-escaping points and the set of escaping points. The foliation about these two sets is well known. We briefly review this foliation and finally prove that the leaves of the set of escaping points are all injective Brody and that there exists an injective Brody curve in the set of non-escaping points. Our method is basically modifying the Brody reparametrization lemma. END:VEVENT BEGIN:VEVENT DTSTART:20141028T170000 DTEND:20141028T190000 DTSTAMP:20141027T150000Z UID:36d1f2d1a148f8732bf53d64699526d9@cgp.ibs.re.kr SUMMARY:Rigid character groups, Lubin-Tate theory, and (phi,Gamma)-modules Ⅰ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Peter Schneider (University of Münster)\n\nEvent: PMI Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141030T170000 DTEND:20141030T190000 DTSTAMP:20141029T150000Z UID:b0dd5c04b0aff66351bd9e2d6b0ab0ed@cgp.ibs.re.kr SUMMARY:Rigid character groups, Lubin-Tate theory, and (phi,Gamma)-modulesⅡ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Peter Schneider (University of Münster)\n\nEvent: PMI Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141031T155000 DTEND:20141031T180000 DTSTAMP:20141030T150000Z UID:81817271e2b556f418f3ad10bd603551@cgp.ibs.re.kr SUMMARY:Fully Nonlinear Partial Differential Equations and its Applications LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ki-Ahm Lee (Seoul National University)\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: In this talk, we will discuss fully nonlinear partial differential equations and its applications in physics, engineering, economic and different area of mathematics. We will review recent progresses and challenges in this area. END:VEVENT BEGIN:VEVENT DTSTART:20141111T140000 DTEND:20141111T150000 DTSTAMP:20141110T150000Z UID:a5d90f2851322c8677668257be6343eb@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141018T094500 DTEND:20141018T104500 DTSTAMP:20141017T150000Z UID:1e41055cfb3cb5db7d5ee52c15d68a91@cgp.ibs.re.kr SUMMARY:자연에서 배우는 수학 LOCATION:Outside POSTECH DESCRIPTION:Speaker: Seung-Yeal Ha\n\nEvent: 제2회 IBS 기하학 수리물리 연구단 수학 문화 강연\n\nAbstract: 산속에 매미들은 왜 같은 리듬을 가지고 우는 것일까? 반딧불이는 왜 같은 진동수를 가지고 빛을 주기적으로 내는 것일까?, 새들은 왜 무리를 지어서 날아 다닐까? 등과 같은 질문들은 여러분들이 아마도 한번쯤은 생각해 보았을 것입니다. 이러한 문제들에 대해서 20 세기 초 프랑스 수학자인 포앙카레는 “자연은 우리에게 문제를 제공할 뿐만 아니라, 해답도 제시한다” 고 말했습니다. 만일 여러 대의 무인 항공기나 무인 로봇들을 무리지어서 부여된 임무를 수행하게 하기 위해서 어떤 통제 알고리즘을 만들어야 할까 ? 이런 질문은 공학의 제어 이론에서 중요한 연구 주제입니다. 최근에 자연 생태계의 동물 집단들의 그룹 역동성을 모방한 많은 제어 알고리즘들이 사용되고 있습니다. 본 강연에서는 새 떼나, 물고기 떼, 반디불이 떼들의 집단 역동성에 숨어 있는 수학을 제시하고, 이러한 수학의 공학문제에의 잠재적 응용 가능성에 대하여 이야기 하고자 합니다. END:VEVENT BEGIN:VEVENT DTSTART:20141018T110000 DTEND:20141018T120000 DTSTAMP:20141017T150000Z UID:015af7c1cdf14bbf82d4097638cfe44d@cgp.ibs.re.kr SUMMARY:이론물리학자가 수학을 만날 때... LOCATION:Outside POSTECH DESCRIPTION:Speaker: Seunghwan Kim\n\nEvent: 제2회 IBS 기하학 수리물리 연구단 수학 문화 강연\n\nAbstract: 물리학은 물질, 힘 그리고 운동에 대한 근원적이고도 체계적인 이해를 추구한다. 현대 물리학 이론에 의하면 자연에는 4 가지 종류의 힘이 있으며, 이 힘과 운동을 기술하는 근본 언어는 수학이다. 이 강연에서는 한 이론 물리학자가 과학의 엣지를 추구하는 과정에서 단진자, 카오스, 그리고 뇌로 연구의 프론티어를 확장하며 경험한 기묘하고 복잡한 리듬의 수학적 이해에 대해서 이야기하고자 한다. END:VEVENT BEGIN:VEVENT DTSTART:20141202T140000 DTEND:20141202T153000 DTSTAMP:20141201T150000Z UID:0f547af6e416c661fcd80f6e1ca2130d@cgp.ibs.re.kr SUMMARY:Flexibility of affine cones and total coordinate spaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Alexander Perepechko\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: Let X be an affine algebraic variety of dimension 2 defined over an algebraically closedfield K of characteristic zero, and denote by SAutX AutX the subgroup generated by the1-parameter unipotent subgroups, i.e. actions of the additive group Ga = Ga(K). A varietyX is called flexible if the tangent space to X at an arbitrary regular point x 2 X is generatedby tangent vectors to orbits of Ga-actions. This is equivalent to the infinite transitivity of theaction of SAutX on the regular locus X reg X, see [1]. We use the construction from [3] that provides a correspondence between open cylindricsubsets on a projective variety Y and regular Ga-actions on the affine cone over Y . We willsketch the proofs of flexibility of the following families:1. affine cones over del Pezzo surfaces of degree 4;2. affine cones over secant varieties of Veronese–Segre varieties;3. total coordinate spaces of smooth projective T-varieties of complexity 1.References[1] I.V. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, and M. Zaidenberg, Flexiblevarieties and automorphism groups, Duke Math. J. 162 (2013), no. 4, 767–823.[2] I.V. Arzhantsev, A. Perepechko, and H. S¨uß, Infinite transitivity on universal torsors, theJournal of the LMS, .[3] T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, Group actions on affine cones, MontrealCentre de Recherches Math´ematiques, CRM Proceedings and Lecture Notes 54 (2011), 123–163.[4] A.Yu. Perepechko. Flexibility of affine cones END:VEVENT BEGIN:VEVENT DTSTART:20141121T133000 DTEND:20141121T150000 DTSTAMP:20141120T150000Z UID:d1c38ac5483acdc376c306f342dd13b1@cgp.ibs.re.kr SUMMARY:On toric log Fano varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Florin Ambro\n\nEvent: Algebraic Geometry Seminar 2014\n\nAbstract: I will discus a combinatorial formula for the alpha-invariant of a polarized toric log variety. For toric log Fano varieties, I will give a sharp lower bound for the alpha-invariant, in terms of the global minimal log discrepancy. END:VEVENT BEGIN:VEVENT DTSTART:20141107T150000 DTEND:20141107T170000 DTSTAMP:20141106T150000Z UID:f7a7c2c3565ca17e8ea6839f2b8e64d1@cgp.ibs.re.kr SUMMARY:STABILITY, INSTABILITY, AND BIFURCATION IN ELECTRIFIED THIN FILMS LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngmin Oh\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141127T160000 DTEND:20141127T180000 DTSTAMP:20141126T150000Z UID:c3d8f785bdb3abef2a80061571659f60@cgp.ibs.re.kr SUMMARY:The rational cohomology ring of unordered configurations on the torus LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: CGP Seminar 2014\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20141216T160000 DTEND:20141216T180000 DTSTAMP:20141215T150000Z UID:ebc4b11e907c12fe5aa912afbe69f50b@cgp.ibs.re.kr SUMMARY:Legendrian Graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Danielle O'Donnol\n\nEvent: Seminar 2014\n\nAbstract: A Legendrian graph is an embedding of a graph G in a contact 3-manifold which is everywhere tangent to the contact structure. Central results in contact geometry use Legendrian graphs in their proofs. Together with Elena Pavelescu, I am studying Legendrian graphs in their own right. I will discuss some of our recent results in this area. END:VEVENT BEGIN:VEVENT DTSTART:20141218T160000 DTEND:20141218T180000 DTSTAMP:20141217T150000Z UID:407c851e6d2440257a4401cf8598b9cd@cgp.ibs.re.kr SUMMARY:Combinatorial spatial graph Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Danielle O'Donnol\n\nEvent: CGP Seminar 2014\n\nAbstract: A spatial graph is an embedding, $f$, of a graph $G$ into $S^3$. For each transverse disk spatial graph, $f(G),$ we define a combinatorial invariant $HFG^-(f(G))$ which is a bi-graded module over a polynomial ring. The gradings live in $\mathbb{Z}$ and $H_1(S^3\smallsetminus f(G))$. This invariant is a generalization of combinatorial link Floer homology defined by Manolescu, Ozsvath, Sarkar (MOS) for links in $S^3$. To do this, we have generalized grid diagrams and grid moves. Following MOS, our invariant is the homology of a chain complex that counts certain rectangles in the grid. Although the chain complex depends on the choice of grid, the homology depends only on the embedding. Unlike many homology theories, our theory is not the categorification of an existing polynomial invariant. Thus taking the generalized Euler characteristic gives another new invariant, an Alexander polynomial for balanced spatial graphs. This is joint work with Shelly Harvey (Rice University). END:VEVENT BEGIN:VEVENT DTSTART:20141114T155000 DTEND:20141114T180000 DTSTAMP:20141113T150000Z UID:2fdd93a0e6ab694b613a05ce5a100f43@cgp.ibs.re.kr SUMMARY:Lines, conics and twisted cubics in Fano varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Young-Hoon Kiem (Seoul National University)\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: One of the fundamental ideas in algebraic geometry is that rational curves play a key role. They tell us whether a given variety can be further simplified or not. They can give us enumerative invariants and formulate mirror symmetry. They can also provide important examples of varieties. In this talk I will discuss explicit examples of moduli spaces of rational curves, in particular lines, conics and twisted cubics in Fano varieties and their birational geometry. END:VEVENT BEGIN:VEVENT DTSTART:20141105T130000 DTEND:20141105T140000 DTSTAMP:20141104T150000Z UID:858d32a4c7d1b0363875835cd32ba0fc@cgp.ibs.re.kr SUMMARY:Spectral data for complex Higgs bundles Ⅲ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Laura Schaposnik (University of Illinois at Urbana-Champaign)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: By looking at real Higgs bundles as fixed points of certain involution on the moduli spaces of complex Higgs bundles, one is able to obtain define spectral data, leading to geometric interpretations of the moduli spaces. We shall dedicate this lecture to the study of spectral data for real Higgs bundles, in particular, showing how one gets a finite covering of the Hitchin base for split real forms, and how in other cases the fibres are non-abelian spaces. END:VEVENT BEGIN:VEVENT DTSTART:20141106T153000 DTEND:20141106T163000 DTSTAMP:20141105T150000Z UID:eafb7b31345fc4fedc120d19b661cf1e@cgp.ibs.re.kr SUMMARY:Spectral data for complex Higgs bundles Ⅳ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Laura Schaposnik (University of Illinois at Urbana-Champaign)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: By looking at real Higgs bundles as fixed points of certain involution on the moduli spaces of complex Higgs bundles, one is able to obtain define spectral data, leading to geometric interpretations of the moduli spaces. We shall dedicate this lecture to the study of spectral data for real Higgs bundles, in particular, showing how one gets a finite covering of the Hitchin base for split real forms, and how in other cases the fibres are non-abelian spaces. END:VEVENT BEGIN:VEVENT DTSTART:20141106T163000 DTEND:20141106T173000 DTSTAMP:20141105T150000Z UID:3460899c1e459a6decb8b55474f605ac@cgp.ibs.re.kr SUMMARY:Linear relation among multiple zeta values LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Koji Tasaka\n\nEvent: T-Seminar\n\nAbstract: The aim of this talk is to introduce the multiple zeta value and its linear relations. Their generalisations will be also discussed. END:VEVENT BEGIN:VEVENT DTSTART:20141107T140000 DTEND:20141107T150000 DTSTAMP:20141106T150000Z UID:4460c0b74bf4f1cade8e1bc7240afe02@cgp.ibs.re.kr SUMMARY:On the geometry of the moduli spaces of one-dimensional sheaves LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Mario Maican\n\nEvent: GAIA Seminar\n\nAbstract: We will classify semi-stable sheaves supported on plane curves of low degree and give applications to the geometry of their moduli spaces. END:VEVENT BEGIN:VEVENT DTSTART:20141103T160000 DTEND:20141103T170000 DTSTAMP:20141102T150000Z UID:367ab047af0f4f6a4c5ca2ee871961c0@cgp.ibs.re.kr SUMMARY:An introduction to Higgs bundles I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Laura Schaposnik (University of Illinois at Urbana-Champaign)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: We shall introduce classical Higgs bundles and their moduli space from a geometric and Lie theoretic point of view, motivating their study through representation theory. Then, we will extend these concepts to Higgs bundles whose structure group are complex Lie groups, as well as real forms, and finalize by introducing the Hitchin fibration of the moduli space of Higgs bundles. END:VEVENT BEGIN:VEVENT DTSTART:20141103T200000 DTEND:20141103T220000 DTSTAMP:20141102T150000Z UID:3d12930fb9e453a6952a6f7911b60ee3@cgp.ibs.re.kr SUMMARY:GENERALIZED PARALLELISM OF THE STRUCTURE JACOBI OPERATOR ON REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Hyunjin Lee\n\nEvent: GAIA Seminar\n\nAbstract: For any (1,1)-type tensor T defined on a real hypersurface M in complex two-plane Grassmannians G_2(C^(m+2)) we can consider two kinds of derivatives, namely, covariant and Lie derivatives. Using the relation between these two derivatives with respect to the structure Jacobi operator, R_{\xi}, we classify real hypersurfaces in G_2(C^(m+2)). END:VEVENT BEGIN:VEVENT DTSTART:20141104T153000 DTEND:20141104T163000 DTSTAMP:20141103T150000Z UID:4fd609c3bf57bcc2e5b35039f3f9e404@cgp.ibs.re.kr SUMMARY:Spectral data for complex Higgs bundles II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Laura Schaposnik (University of Illinois at Urbana-Champaign)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Spectral data has been used for many years to study Higgs bundles whose structure groups are complex Lie groups. During the talk we shall recall these constructions for Higgs bundles whose structure groups are classical complex Lie groups, and mention how Langlands duality can be seen through this description of the fibres of the Hitchin fibration as abelian varieties. END:VEVENT BEGIN:VEVENT DTSTART:20141110T200000 DTEND:20141110T220000 DTSTAMP:20141109T150000Z UID:895a8363633fafce8f315ef0cd1fe846@cgp.ibs.re.kr SUMMARY:On the polarized Bergman metric and the estimates of Bergman curvatures LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Liyou Zhang\n\nEvent: GAIA Seminar\n\nAbstract: In this presentation, we will talk about the polarized Bergman metric and its applications to the Bergman curvature estimates on bounded domains in C^n. If time permits, we will mention some recent study on the strongly pseudoconvex domains with constant Bergman curvatures. END:VEVENT BEGIN:VEVENT DTSTART:20141110T150000 DTEND:20141110T170000 DTSTAMP:20141109T150000Z UID:6f903242b6dd2d1ef40b8305bc1dc89b@cgp.ibs.re.kr SUMMARY:Structure of algebraic groups 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Michel Brion (Institut Fourier)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: The theory of algebraic groups has chiefly been developed along two distinct directions: linear (or, equivalently, affine) algebraic groups, and abelian varieties (complete, connected algebraic groups). This is made possible by a fundamental theorem of Chevalley: any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected linear algebraic group, and these are unique.In these lectures, we first expose the above theorem and related structure results about connected algebraic groups that are neither affine nor complete. The class of anti-affine algebraic groups (those having only constant global regular functions) features prominently in these developments. We then present applications to some questions of algebraic geometry: the classification of complete homogeneous varieties, and the structure of connected automorphism groups of complete varieties.Prerequisites: notions of algebraic geometry over an algebraically closed field. Some familiarity with linear algebraic groups will be useful, but not necessary. END:VEVENT BEGIN:VEVENT DTSTART:20141111T150000 DTEND:20141111T170000 DTSTAMP:20141110T150000Z UID:44d5b9bf766759e5edf9ad98cd6d22ab@cgp.ibs.re.kr SUMMARY:Structure of algebraic groups 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Michel Brion (Institut Fourier)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: The theory of algebraic groups has chiefly been developed along two distinct directions: linear (or, equivalently, affine) algebraic groups, and abelian varieties (complete, connected algebraic groups). This is made possible by a fundamental theorem of Chevalley: any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected linear algebraic group, and these are unique.In these lectures, we first expose the above theorem and related structure results about connected algebraic groups that are neither affine nor complete. The class of anti-affine algebraic groups (those having only constant global regular functions) features prominently in these developments. We then present applications to some questions of algebraic geometry: the classification of complete homogeneous varieties, and the structure of connected automorphism groups of complete varieties.Prerequisites: notions of algebraic geometry over an algebraically closed field. Some familiarity with linear algebraic groups will be useful, but not necessary. END:VEVENT BEGIN:VEVENT DTSTART:20141112T130000 DTEND:20141112T150000 DTSTAMP:20141111T150000Z UID:f5d5b41a8e6907432cb8d0859c1a4f0c@cgp.ibs.re.kr SUMMARY:Structure of algebraic groups 3 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Michel Brion (Institut Fourier)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: The theory of algebraic groups has chiefly been developed along two distinct directions: linear (or, equivalently, affine) algebraic groups, and abelian varieties (complete, connected algebraic groups). This is made possible by a fundamental theorem of Chevalley: any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected linear algebraic group, and these are unique.In these lectures, we first expose the above theorem and related structure results about connected algebraic groups that are neither affine nor complete. The class of anti-affine algebraic groups (those having only constant global regular functions) features prominently in these developments. We then present applications to some questions of algebraic geometry: the classification of complete homogeneous varieties, and the structure of connected automorphism groups of complete varieties.Prerequisites: notions of algebraic geometry over an algebraically closed field. Some familiarity with linear algebraic groups will be useful, but not necessary. END:VEVENT BEGIN:VEVENT DTSTART:20141113T153000 DTEND:20141113T163000 DTSTAMP:20141112T150000Z UID:d1431a85546f38bbe8e0029146d08e17@cgp.ibs.re.kr SUMMARY:Structure of algebraic groups 4 (Special colloquium) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Michel Brion (Institut Fourier)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: The theory of algebraic groups has chiefly been developed along two distinct directions: linear (or, equivalently, affine) algebraic groups, and abelian varieties (complete, connected algebraic groups). This is made possible by a fundamental theorem of Chevalley: any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected linear algebraic group, and these are unique.In these lectures, we first expose the above theorem and related structure results about connected algebraic groups that are neither affine nor complete. The class of anti-affine algebraic groups (those having only constant global regular functions) features prominently in these developments. We then present applications to some questions of algebraic geometry: the classification of complete homogeneous varieties, and the structure of connected automorphism groups of complete varieties.Prerequisites: notions of algebraic geometry over an algebraically closed field. Some familiarity with linear algebraic groups will be useful, but not necessary. END:VEVENT BEGIN:VEVENT DTSTART:20141124T160000 DTEND:20141124T180000 DTSTAMP:20141123T150000Z UID:1a7e1ea62c063a32a32570bba2b5cd3b@cgp.ibs.re.kr SUMMARY:Motivic structures in non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Motivic structures in non-commutative geometry\n\nAbstract: I am going to explain briefly how de Rham cohomology works in char p and over $Z_p$, and introduce the natural additional structure it possesses, so-called "filtered Dieudonne module" structure. Prerequisite are just some basic familiarity with smooth algebraic varieties; I will not use any advanced algebraic geometry at all. END:VEVENT BEGIN:VEVENT DTSTART:20141126T160000 DTEND:20141126T180000 DTSTAMP:20141125T150000Z UID:0aea6d4778c76e8222d557b7b9e106e8@cgp.ibs.re.kr SUMMARY:Motivic structures in non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Motivic structures in non-commutative geometry\n\nAbstract: I will recall the basic formalism of cyclic homology, with emphasis on A. Connes' cyclic category $\Lambda$. Prerequisites for this lecture and the rest of them are just basic homological algebra. END:VEVENT BEGIN:VEVENT DTSTART:20141201T160000 DTEND:20141201T180000 DTSTAMP:20141130T150000Z UID:4dc2dc647acce0722ef7d71079b80938@cgp.ibs.re.kr SUMMARY:Motivic structures in non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Motivic structures in non-commutative geometry\n\nAbstract: I will give an overview of the theory of Mackey functors for a finite or profinite group $G$ (for applications, one need the cyclic group $Z$, but the general theory is not significantly different). END:VEVENT BEGIN:VEVENT DTSTART:20141203T160000 DTEND:20141203T180000 DTSTAMP:20141202T150000Z UID:be96f3417e66661a22a95f97dac591bf@cgp.ibs.re.kr SUMMARY:Motivic structures in non-commutative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Motivic structures in non-commutative geometry\n\nAbstract: I will explain how to combine $Z$-Mackey functors and cyclic modules into a single category of "cyclotomic Mackey functors". This category turns out to be equivalent to the category of "cyclotomic complexes", and this is in turn equivalent to filtered Dieudonne modules. This equivalence is themain goal of the lectures. END:VEVENT BEGIN:VEVENT DTSTART:20141117T170000 DTEND:20141117T190000 DTSTAMP:20141116T150000Z UID:c253446b9e9ec67cbcad53990676d24d@cgp.ibs.re.kr SUMMARY:Heisenberg-picture quantum field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Theo Johnson-Freyd\n\nEvent: Quantum Monday 2014\n\nAbstract: The usual Atiyah--Segal axioms describe quantum field theory in terms of a ``Schrodinger picture'' of physics. I will argue that instead a ``Heisenberg picture'' is needed, and describe a small modification of those axioms that accommodates this. As an example, I will describe a skein-theoretic version of quantum Chern-Simons theory as a ``fully extended oriented Heisenberg-picture tqft''. It has the feature that it does not require the ``level'' to be quantized. It provides in particular a tqft packaging of skein theory, and my hope is that it will shed light on open conjectures in quantum topology. Bits of my talk will be based on joint work with M. Brandenburg, A. Chirvasitu, and C. Scheimbauer. END:VEVENT BEGIN:VEVENT DTSTART:20141118T140000 DTEND:20141118T150000 DTSTAMP:20141117T150000Z UID:4ec49437e0e3d4c2b81b3dc7d6ef26a9@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141120T163000 DTEND:20141120T173000 DTSTAMP:20141119T150000Z UID:38dba9968a10a4eb3bc1c359d97d5e5b@cgp.ibs.re.kr SUMMARY:PARALLELISM FOR THE TENSOR OF TYPE (1,1) ON REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyunjin Lee\n\nEvent: T-Seminar\n\nAbstract: A main objective in submanifold geometry is the classica-tion of homogeneous hypersurfaces. Homogeneous hypersurfaces arise as principal orbits of cohomogeneity one actions, and so their classication is equivalent to the classication of cohomogeneity one actions up to or-bit equivalence. Actually, the classication of cohomogeneity one actions in irreducible simply connected Riemannian symmetric spaces of noncom- pact type was obtained by J. Berndt and Y.J. Suh (for complex two-plane Grassmannian G2(Cm+2) = SU(m + 2)=S(U(2)U(m)), [?]). From this, J. Berndt and Y.J. Suh [?] classied real hypersurfaces with isometric Reebow in G2(Cm+2), m 3. It can be described as a tube over a totally geodesic G2(Cm+1) = SU(m + 1)=S(U(2)U(m END:VEVENT BEGIN:VEVENT DTSTART:20141121T150000 DTEND:20141121T160000 DTSTAMP:20141120T150000Z UID:f1b17106fee0c051952a514c468e8d23@cgp.ibs.re.kr SUMMARY:On Multi-dimensional Steady Subsonic Flows Determined by Physical Boundary Conditions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Shangkun Weng\n\nEvent: POSTECH PDEs Seminar\n\nAbstract: This talk will concern an inflow-outflow problem for steady subsonic gas flows in a nozzle with finite length, aiming at finding physically acceptable boundary conditions on upstream and downstream. Firstly, we characterize a set of physically acceptable boundary conditions to ensure the existence of subsonic flows in 2-D finite long nozzles, both the irrotational and full Euler flows are considered. Secondly, we develop a new formulation for 3-D Euler system and discover a new conserved quantity and a system of new conservation laws and obtain the existence of subsonic Euler flows in a rectangular cylinder with physical boundary conditions. END:VEVENT BEGIN:VEVENT DTSTART:20141128T130000 DTEND:20141128T140000 DTSTAMP:20141127T150000Z UID:4d83ca6230533271b314910558ce6206@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141205T130000 DTEND:20141205T140000 DTSTAMP:20141204T150000Z UID:f53fa29db52a29b9825939b0b7bc6588@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20141201T200000 DTEND:20141201T220000 DTSTAMP:20141130T150000Z UID:a7f6faba178b31e2c61593aece9f182f@cgp.ibs.re.kr SUMMARY:Hilbert-Mumford Theorem and its applications LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Dao Phuong Bac\n\nEvent: GAIA Seminar\n\nAbstract: Let $G$ be a reductive group acting linearly on the vector space $V$ via representation $\rho: G \mtn \GL(V)$ defined over an algebraically closed field $k$, and let $v \in V$ be a semistable point, i.e., $0 \notin \overline{G.v}$. Hilbert-Mumford Theorem (1965) characterized an useful criterion for semistable points, namely, there exists a cocharacter $\lambda \in X_{*}(G)$ such that $\lim_{\al \to 0} \lambda(\al).v=0$. The studying of semistable points is motivated by the determining of quotient of an algebraic variety under the action of reductive groups. Furthermore, in 1978, G. Kempf and G. Rousseau(independently) improved this remarkable result by showing that there exists a so-called optimal cocharacter $\lambda_{v}$ satisfying $\lim_{\al \to 0}\lambda_{v}(\al).v \in \overline{G.v} \setminus (G.v)$ and $\lambda_{v}$ takes $v$ outside $G.v$ fastest in some sense. This allows us to deal with many problems of geometric invariant theory over perfect (but non-algebraically closed) base fields. In this talk, we present some refinements and applications of these results for rationality problem of orbits. END:VEVENT BEGIN:VEVENT DTSTART:20141208T200000 DTEND:20141208T220000 DTSTAMP:20141207T150000Z UID:f7668b9d5bc3c257ea55636074fab668@cgp.ibs.re.kr SUMMARY:COMPARISON OF THE BERGMAN AND KAHLER-EINSTEINMETRICS ON A CERTAIN UNBOUNDED DOMAIN LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: HYESEON KIM\n\nEvent: GAIA Seminar\n\nAbstract: It is well-known that the Caratheodory metric and the Kobayashi metric squeeze all pseudo-differential metrics on complex manifolds satisfying the Schwarz lemma with respect to holomorphic mappings and coinciding with the Poincare metric on the unit disc. By contrast, the Bergman metric does not admit the Schwarz lemma. For this reason, one can ask whether the Bergman metric is compared with some invariant metrics. In this talk we shall expound the comparison between the Bergman and Kahler-Einstein metrics on an unbounded strongly pseudoconvex domain with non-compact automorphism group. END:VEVENT BEGIN:VEVENT DTSTART:20141202T160000 DTEND:20141202T170000 DTSTAMP:20141201T150000Z UID:c986d6c98c5dc2e6550327d7d9595b51@cgp.ibs.re.kr SUMMARY:Derived categories of some fake quadrics LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kyoung-Seog Lee (Korea Institute for Advanced Study)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: We will discuss the construction of derived category of an abelian category and the notion of semiorthogonal decompostion and exceptional collection. Then we will discuss how to construct special semiorthogonal decompositions on derived categories of some fake quadrics constructed by Bauer, Catanese, Grunewald. END:VEVENT BEGIN:VEVENT DTSTART:20141212T155000 DTEND:20141212T180000 DTSTAMP:20141211T150000Z UID:dcc667c4990331dfe21f43c891034d66@cgp.ibs.re.kr SUMMARY:Regularized determinant for Riemann surface with punctures LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jinsung Park (Korea Institute for Advanced Study)\n\nEvent: Fall 2014 POSTECH Math Colloquium\n\nAbstract: The regularized determinant of Laplacian is a spectral invariant encoding geometric data of the underlying Riemannian manifold. The regularized determinant plays important roles in several contexts, for instance, the Quillen metric on determinant line bundles and loop series expansion of the partition function in conformal field theory. In this talk, I will explain the basics of the regularized determinant of the Laplacian for hyperbolic Riemann surface with punctures and some relationship of the regularized determinant and the classical Liouville action functional for sphere with punctures. END:VEVENT BEGIN:VEVENT DTSTART:20150105T150000 DTEND:20150105T170000 DTSTAMP:20150104T150000Z UID:482b6814c677a57f468c5f71247f1dee@cgp.ibs.re.kr SUMMARY:p-adic multiple zeta values LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hidekazu Furusho (Naogya University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: I will explain a construction of p-adic analogue of multiple zeta value and then show its various fundamental properties. END:VEVENT BEGIN:VEVENT DTSTART:20150106T160000 DTEND:20150106T170000 DTSTAMP:20150105T150000Z UID:3334a1677e32d80e33aaa552ba4d07f8@cgp.ibs.re.kr SUMMARY:Hyperbolic 3-manifolds of bounded volume and trace field degree. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: BoGwang Jeon\n\nEvent: Seminar 2015\n\nAbstract: In this talk, I present my recent proof of the conjecture that there are only a finte number of hyperbolic 3-manifolds of bounded volume and trace field degree. END:VEVENT BEGIN:VEVENT DTSTART:20150108T160000 DTEND:20150108T180000 DTSTAMP:20150107T150000Z UID:7c16787c699e9816f660c865de5651fc@cgp.ibs.re.kr SUMMARY:Homotopy probability theory: examples and applications LOCATION:CGP Main Hall DESCRIPTION:Speaker: John Terilla\n\nEvent: CGP Seminar 2015\n\nAbstract: New examples and applications of homotopy probability theory will be introduced and discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150224T160000 DTEND:20150224T173000 DTSTAMP:20150223T150000Z UID:f31732fb7cff2af43fe6d35603301ee3@cgp.ibs.re.kr SUMMARY:Jordan property of groups of birational self-maps LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: A group $\Gamma$ is said to be Jordan if for any finite subgroup G of $\Gamma$ there is an abelian subgroup whose index in G is bounded by a constant that depends only on $\Gamma$. We investigate which algebraic varieties have groups of birational selfmaps satisfying the Jordan property. The talk is based on joint work with Constantin Shramov. END:VEVENT BEGIN:VEVENT DTSTART:20150129T160000 DTEND:20150129T180000 DTSTAMP:20150128T150000Z UID:68de128497e9c0410f41050cc6541c71@cgp.ibs.re.kr SUMMARY:Field theories and elliptic cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Daniel Berwick-Evans\n\nEvent: CGP Seminar 2015\n\nAbstract: Connections between elliptic cohomology and 2-dimensional quantum field theory have led to beautiful---and often unexpected---mathematics. For example, Witten's description of a Dirac operator on loop space prompted Ando, Hopkins, Rezk, and Strickland to construct the string orientation for the universal elliptic cohomology theory of topological modular forms. I will describe some recent advances in understanding the depth of this connection between physics and topology. END:VEVENT BEGIN:VEVENT DTSTART:20150302T170000 DTEND:20150302T190000 DTSTAMP:20150301T150000Z UID:d2bb8413f9fe9509772529ed8152c5ed@cgp.ibs.re.kr SUMMARY:Rational homology of configuration spaces via factorization homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benjamin Knudsen\n\nEvent: Quantum Monday 2015\n\nAbstract: The study of configuration spaces is particularly tractable over a field of characteristic zero, and there has been great success over the years in producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and descriptive results such as homological stability. I will discuss recent work of mine that identifies the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces. Time allowing, I will also touch on work in progress concerning cup products for configuration spaces. END:VEVENT BEGIN:VEVENT DTSTART:20150312T160000 DTEND:20150312T165000 DTSTAMP:20150311T150000Z UID:7de156131a35c9b87afdf28f78fe4d58@cgp.ibs.re.kr SUMMARY:Embedding problems of Artin groups into mapping class groups LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong Jin Song\n\nEvent: CGP Seminar 2015\n\nAbstract: Braid groups can be embedded in mapping class groups of surfaces in various ways, mainly because there is a braid relation between two adjacent Dehn twists. The classical Harer conjecture is about the homology triviality of the obvious embedding. In the proof of this conjecture, the categorical delooping plays a key role. Both braid groups and mapping class groups have braided monoidal category structures which gives rise to double loop space structures. The homology homomorphism induced by the Harer embedding is supposed to be trivial if it preserves Kudo-Araki-Dyer-Lashof operation. In order to show this we construct two monoidal 2-categories and functors between them which give rise to two double loop spaces and a double loop space map. This is an important example of categorical delooping technique.There are various interesting embeddings of braid groups into mapping class groups and many of them are homologically trivial. We may extend this to the case of Artin groups. Most interesting Artin groups are exotic type (E_6, E_7, E_8) Artin groups. Waynryb showed that there is no geometric embedding of exotic type Artin groups into mapping class groups. We now may raise a natural question. What about the existence of nongeometric embedding? This problem is still open. It now seems that it is very hard to find an example of such an embedding. If the answer is negative, it should imply an important secret in the structure of mapping class groups.On the other hand, the categorical delooping technique that was used in the proof of Harer conjecture can be interpreted and generalized in the case of embedding of Artin groups in terms of higher category theory or higher operad theory. END:VEVENT BEGIN:VEVENT DTSTART:20150205T160000 DTEND:20150205T180000 DTSTAMP:20150204T150000Z UID:48e3547f6de882fdf81bd7e1d2974fb6@cgp.ibs.re.kr SUMMARY:On smooth isolated curves in general complete intersection Calabi-Yau threefolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Xun Yu\n\nEvent: CGP Seminar 2015\n\nAbstract: Let Y be a Calabi-Yau threefold. Then the expected dimension of the deformation space of a locally complete intersection curve in Y is zero. However, for a given pair (d,g) it is hard to show the existence of a curve of degree d and genus g on Y and even when the existence is shown, it is very hard to prove that the curve is rigid in Y. Recently Knutsen finds a powerful method to show existence of smooth isolated curves in complete intersection Calai-Yau threefolds (CICY). In this talk, I will first recall Knutsen's method and then explain how to use a variant of it to construct new examples of smooth isolated curves in general CICY. Some related conjectures will be mentioned. If time permits, I will also talk about some non-existence results in the quintic case. END:VEVENT BEGIN:VEVENT DTSTART:20150212T160000 DTEND:20150212T180000 DTSTAMP:20150211T150000Z UID:bf97dc87605982611d73c0fd07d60f97@cgp.ibs.re.kr SUMMARY:Mathematical Challenges in the Fluid Mechanics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dongho Chae\n\nEvent: CGP Seminar 2015\n\nAbstract: The question of global regularity/finite time singulality in the Navier-Stokes and/or the Euler quations in $R^3$ is one the most challenging open problems in mathematics. In this talk I will present an introduction to the problem and some of the recent partial results for the Euler equations. END:VEVENT BEGIN:VEVENT DTSTART:20150130T160000 DTEND:20150130T170000 DTSTAMP:20150129T150000Z UID:695a1dc9544ed9366072a416b92b6e09@cgp.ibs.re.kr SUMMARY:I. Geometric modular representation theory LOCATION:Math. Bldg. #208 DESCRIPTION:Speaker: Anthony Henderson (University of Sydney)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Representation theory is one of the oldest areas of algebra, but many basic questions in it are still unanswered. This is especially true in the modular case, where one considers vector spaces over a field k of positive characteristic; typically, complications arise for particular small values of the characteristic. For example, from a vector space V one can construct the symmetric square S^2(V), which is one easy example of a representation of the group GL(V). One would like to say that this representation is irreducible, but that statement is not always true: if k has characteristic 2, there is a nontrivial invariant subspace. Even for GL(V), we do not know the dimensions of all irreducible representations in all characteristics.In this talk, I will introduce some of the main ideas of geometric modular representation theory, a more recent approach which is making progress on some of these old problems. Essentially, the strategy is to re-formulate everything in terms of homology of various topological spaces, where k appears only as the field of coefficients and the spaces themselves are independent of k; thus, the modular anomalies in representation theory arise because homology with modular coefficients is detecting something about the topology that rational coefficients do not. END:VEVENT BEGIN:VEVENT DTSTART:20150202T160000 DTEND:20150202T170000 DTSTAMP:20150201T150000Z UID:e5b84902c81f3444c8dc67b01704413d@cgp.ibs.re.kr SUMMARY:II. The Springer correspondence LOCATION:Math. Bldg. #208 DESCRIPTION:Speaker: Anthony Henderson (University of Sydney)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Here the representations are of a Weyl group (finite crystallographic reflection group), and the geometry is of the nilpotent cone in a simple Lie algebra and its desingularization. END:VEVENT BEGIN:VEVENT DTSTART:20150203T160000 DTEND:20150203T170000 DTSTAMP:20150202T150000Z UID:fec35e99a070552af723d5851be66ac4@cgp.ibs.re.kr SUMMARY:Ⅲ. Character sheaves LOCATION:Math. Bldg. #208 DESCRIPTION:Speaker: Anthony Henderson (University of Sydney)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Here the representations are of a matrix group over a finite field, and the geometry is of the corresponding algebraic group and its conjugacy classes. END:VEVENT BEGIN:VEVENT DTSTART:20150204T160000 DTEND:20150204T170000 DTSTAMP:20150203T150000Z UID:d85dca16847846158f9833124f59e741@cgp.ibs.re.kr SUMMARY:Ⅳ. The geometric Satake equivalence LOCATION:Math. Bldg. #208 DESCRIPTION:Speaker: Anthony Henderson (University of Sydney)\n\nEvent: GAIA Special Lecture Series\n\nAbstract: Here the representations are of an algebraic group, and the geometry is of the affine Grassmannian of the dual group. END:VEVENT BEGIN:VEVENT DTSTART:20150210T140000 DTEND:20150210T150000 DTSTAMP:20150209T150000Z UID:ca01a0ee4ef34cc5f25be1c598ee1db0@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150402T160000 DTEND:20150402T180000 DTSTAMP:20150401T150000Z UID:313cfb9f96dfccd08e400f5e8e8b2517@cgp.ibs.re.kr SUMMARY:Local Poincaré duality & deformation quantization LOCATION:CGP Main Hall DESCRIPTION:Speaker: Theo Johnson-Freyd\n\nEvent: CGP Seminar 2015\n\nAbstract: Poincaré duality implies, among other things, that the de Rham cohomology of a compact oriented manifold is a commutative Frobenius algebra. Then a version of "local Poincaré duality " would be a "homotopy commutative Frobenius algebra" structure on the de Rham complex satisfying some locality conditions. It turns out that there are at least two inequivalent notions of "homotopy commutative Frobenius algebra", depending on whether you work at "tree level" or at "all loop order" in a certain "Feynman" diagrammatics. This choice affects whether local Poincaré duality y is or is not canonical. The "all loop order" version of local Poincaré duality is closely related to Kontsevich-type problems in deformation quantization. In particular, "all loop order" local Poincaré duality on $S^1$ is obstructed; the obstruction answers the question of which Poisson structures admit universal deformation quantizations that do not require taking traces. END:VEVENT BEGIN:VEVENT DTSTART:20150304T140000 DTEND:20150304T160000 DTSTAMP:20150303T150000Z UID:deb6310cbf863b050bc1671930e923cd@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150311T140000 DTEND:20150311T160000 DTSTAMP:20150310T150000Z UID:ab7ea02b3138eccf52eb1a8b870d8ed9@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150318T140000 DTEND:20150318T160000 DTSTAMP:20150317T150000Z UID:aaf7b3a88889e1f14ce8db33d3672091@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150401T140000 DTEND:20150401T160000 DTSTAMP:20150331T150000Z UID:83da3d3231e4fa44d09222fde14badee@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150408T140000 DTEND:20150408T160000 DTSTAMP:20150407T150000Z UID:b5b061edc7a75f049f6d1842c7754041@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150415T140000 DTEND:20150415T160000 DTSTAMP:20150414T150000Z UID:8b70b7874dd7144862e5dc787cee9ea1@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the descriptioin of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150513T140000 DTEND:20150513T160000 DTSTAMP:20150512T150000Z UID:d1f95ec214fb555762a51a007dc1aeb6@cgp.ibs.re.kr SUMMARY:Fukaya category and toric geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Fukaya category and toric geometry\n\nAbstract: The main purpose of this lecture series is to explainsome homological algebra of A-infty category, and thenthe result of Abouzaid-Fukaya-Oh-Ohta-Ono on the description of Fukaya categoryof toric manifolds and its relevant homological mirror symmetry.Since I myself is not an expert on homological algebra, I willspend much time on the algebra part. The pace of lecturesis supposed to be slow and so graduate students are encouraged toattend. END:VEVENT BEGIN:VEVENT DTSTART:20150224T140000 DTEND:20150224T150000 DTSTAMP:20150223T150000Z UID:ff0562fe302b2229b138e382cfff0201@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150310T140000 DTEND:20150310T150000 DTSTAMP:20150309T150000Z UID:c84646184d1cf2709cc67e19b756033b@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150317T140000 DTEND:20150317T150000 DTSTAMP:20150316T150000Z UID:a8b5912e8c568393c63dbc10eaefacfe@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150324T140000 DTEND:20150324T150000 DTSTAMP:20150323T150000Z UID:d626239f1746df526e1a3d7a32617222@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150428T140000 DTEND:20150428T150000 DTSTAMP:20150427T150000Z UID:ef8cd386c57adae1c5d3672ebe2c59b6@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150512T140000 DTEND:20150512T150000 DTSTAMP:20150511T150000Z UID:aca8b17193ed822e2b74bbf2e3ff33b3@cgp.ibs.re.kr SUMMARY:Working Group in Mirror Symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Working Group in Mirror Symmetry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150305T160000 DTEND:20150305T180000 DTSTAMP:20150304T150000Z UID:499478f5a64434f3d714664c6a1b2c5c@cgp.ibs.re.kr SUMMARY:Symplectic embeddings in dimension greater than four LOCATION:CGP Main Hall DESCRIPTION:Speaker: Richard Hind\n\nEvent: Special Lecture\n\nAbstract: A basic problem in quantitative symplectic geometry is the embedding problem, and embeddings of ellipsoids seem the simplest to study. The problem of deciding when one 4-dimensional ellipsoid embeds into another has been reduced to combinatorics by work of McDuff, applying holomorphic curves and Seiberg-Witten theory. In higher dimensions much less is known. I will describe two ways to construct embeddings of higher dimensional ellipsoids. The first method is a process of stabilizing 4-dimensional embeddings. In joint work with Buse we showed that this construction suffices to establish packing stability for rational symplectic manifolds. The second method comes from iterating the symplectic folding map. We will see that this reproduces catalyst embeddings of Guth, and can be used to rule out higher order symplectic capacities. END:VEVENT BEGIN:VEVENT DTSTART:20150306T160000 DTEND:20150306T180000 DTSTAMP:20150305T150000Z UID:5631d844fea402b8ba33ee341f0d6a7a@cgp.ibs.re.kr SUMMARY:Obstructions to symplectic embeddings LOCATION:CGP Main Hall DESCRIPTION:Speaker: Richard Hind\n\nEvent: Special Lecture\n\nAbstract: In dimension 4 the Embedded Contact Homology capacities of Hutchings give a complete set of obstructions to ellipsoid embeddings. In higher dimensions, to date there is no analogue of ECH. Obstructions come from the Ekeland-Hofer capacities and the volume constraint, but we will see that these are not a complete set. I will describe work with Kerman which produces stronger obstructions to certain embeddings. These show that the iterated folding maps are often optimal. Similar obstructions developed with Cristofaro-Gardiner show that in other cases stabilizations of 4-dimensional embeddings are optimal. END:VEVENT BEGIN:VEVENT DTSTART:20150309T160000 DTEND:20150309T180000 DTSTAMP:20150308T150000Z UID:d1c3b9d1b1e87efca6907aa8060a71ac@cgp.ibs.re.kr SUMMARY:Isotopies of embeddings LOCATION:CGP Main Hall DESCRIPTION:Speaker: Richard Hind\n\nEvent: Special Lecture\n\nAbstract: Once we know that a symplectic embedding exists, it is natural to investigate the topology of the space of embeddings. The embeddings of a convex domain into Euclidean space retract onto the linear symplectic group. However it is possible to get sharp bounds on the minimal size of an ambient ball in which isotopies from a given embedding to an inclusion can be performed. This leads to examples of nonisotopic polydisk embeddings into ellipsoids. It is an open question whether ellipsoid embeddings are ever nonisotopic; we show at least that our nonisotopic polydisks cannot be extended to an ellipsoid. END:VEVENT BEGIN:VEVENT DTSTART:20150224T103000 DTEND:20150224T113000 DTSTAMP:20150223T150000Z UID:94c7f378ca0eba07252d80f5a11aa664@cgp.ibs.re.kr SUMMARY:On the geometry of the moduli space of one-dimensional sheaves on Fano varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kiryong Chung\n\nEvent: Seminar 2015\n\nAbstract: After the construction of the moduli space $\mathbf{M}_X(P(m))$ of pure sheaves on a smooth projective variety $X$ with fixed Hilbert polynomial P(m), many algebraic geometers have been investigated about geometric structure of the space $\mathbf{M}_X(P(m))$. If the sheaves are supported on curves in $X$ (i.e. $P(m)=dm+\chi$ is linear), its structure has been studied in the perspective of the enumerative/birational geometry. In this talk, I will present the geometric properties of the space $\mathbf{M}_X(dm+\chi)$ for the Fano varieties $X$ and low degree $d$. The talk will concentrate on the birational relationship with other moduli spaces (for example, Kontsevich space and Hilbert scheme). Also, I will discuss about the \emph{cohomology ring} structure of the space $\mathbf{M}_{K_{\mathbb{P}^2}}(4m+1)$, which is one of the key step for the BPS-computation of the local $\mathbb{P}^2$. The talk is based on the joint works with Jinwon Choi, Mario Maican, and Han-Bom Moon. END:VEVENT BEGIN:VEVENT DTSTART:20150303T103000 DTEND:20150303T113000 DTSTAMP:20150302T150000Z UID:5516c20cf39408776c9c60ce614d8e91@cgp.ibs.re.kr SUMMARY:Bayer-Macrì decomposition on Bridgeland moduli spaces over surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Wanmin Liu\n\nEvent: Seminar 2015\n\nAbstract: Bayer and Macrì established a determinant line bundle theory on the Bridgeland moduli space over surface, which induced birational geometry of the moduli space via wall-crossing of stability conditions. We find a decomposition of the local Bayer-Macrì map and obtain its image in the Néron–Severi group of the moduli space. The geometric meaning of the decomposition is given. As application, we obtain a precise correspondence between Bridgeland walls and Mori walls. Some toy models on Hilbert scheme of points will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150409T160000 DTEND:20150409T180000 DTSTAMP:20150408T150000Z UID:447311d34895cd08b7394bfb34f827d0@cgp.ibs.re.kr SUMMARY:Lagrangian submanifolds via surgeries LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mei-Lin Yau\n\nEvent: CGP Seminar 2015\n\nAbstract: In this talk we will introduce several types of surgeries that can be applied to produce new Lagrangian submanifolds from a given one under suitable conditions. We will discuss their properties and relate examples of these surgical constructions to some known Lagrangian submanifolds obtained by other methods. Many of these Lagrangian submanifolds have been verified to be smoothly but not Hamiltonian isotopic. This is a work in progress. END:VEVENT BEGIN:VEVENT DTSTART:20150304T160000 DTEND:20150304T180000 DTSTAMP:20150303T150000Z UID:6718666ff77c8e59164f57449594f1eb@cgp.ibs.re.kr SUMMARY:A chapter in Finite Group Theory (I, II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jean-Pierre Serre (College de France)\n\nEvent: Special Lecture series\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20150306T160000 DTEND:20150306T170000 DTSTAMP:20150305T150000Z UID:815d94c34cfd7fdb29d9613808f9a225@cgp.ibs.re.kr SUMMARY:Modular Forms Modulo 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jean-Pierre Serre (College de France)\n\nEvent: Special Lecture series\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20150310T170000 DTEND:20150310T180000 DTSTAMP:20150309T150000Z UID:a84de65e79add2763d3de6df0eacf4af@cgp.ibs.re.kr SUMMARY:Cohomological Invariants and Trace Forms(1) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jean-Pierre Serre (College de France)\n\nEvent: Special Lecture series\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20150312T170000 DTEND:20150312T180000 DTSTAMP:20150311T150000Z UID:030c005f844e2204d9d9b233967112a2@cgp.ibs.re.kr SUMMARY:Cohomological Invariants and Trace Forms(2) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jean-Pierre Serre (College de France)\n\nEvent: Special Lecture series\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20150313T160000 DTEND:20150313T170000 DTSTAMP:20150312T150000Z UID:3b63add00467ce385129fab6b43ec65e@cgp.ibs.re.kr SUMMARY:Linear Representations of Finite Groups: a Review LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jean-Pierre Serre (College de France)\n\nEvent: Special Lecture series\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20150403T153000 DTEND:20150403T163000 DTSTAMP:20150402T150000Z UID:c15726c46bde60ba6d4c01eedab8a01d@cgp.ibs.re.kr SUMMARY:Special birational transformations of type (2, 1) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Baohua Fu\n\nEvent: Seminar 2015\n\nAbstract: A birational transformation $f: P^n\rightarrow Z$, where $Z$ is a nonsingular variety of Picard number 1, is called a special birational transformation of type $(a, b)$ if $f$ is given by a linear system of degree a, its inverse is given by a linear system of degree b and the base locus $S$ $\subset$ $P^n$ of $f$ is irreducible and nonsingular. I'll report a joint work with Jun-Muk Hwang on the classification of special birational transformations of type (2,1). END:VEVENT BEGIN:VEVENT DTSTART:20150311T160000 DTEND:20150311T170000 DTSTAMP:20150310T150000Z UID:2932e23080d9ebd2c61f82aa3d6e23ee@cgp.ibs.re.kr SUMMARY:Packing stability for irrational symplectic 4-manifolds. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Richard Hind\n\nEvent: Geometry & Topology Seminar\n\nAbstract: In joint work with Olga Buse and Emmanuel Opshtein we show that associated to every symplectic 4-manifold $(M, \omega)$ is a positive constant $\lambda$ with the following property. There exists a symplectic embedding of a disjoint union of open balls into $M$ provided each ball has capacity at most $\lambda$ and the total volume of the balls is no more than the volume of $M$.In the rational case (that is, when $[\omega] \in H^2(M, \mathbb Q)$) this builds on work of Biran which relies on Donaldson's construction of symplectic hypersurfaces. In the general case we apply a flexible decomposition of $M$ (up to a subset of volume $0$) into a finite union of ellipsoids and pseudo-balls. END:VEVENT BEGIN:VEVENT DTSTART:20150423T160000 DTEND:20150423T180000 DTSTAMP:20150422T150000Z UID:f0ddb757024253f3b3267541e75055d8@cgp.ibs.re.kr SUMMARY:The cotangent bundle of a Grassmannian LOCATION:CGP Main Hall DESCRIPTION:Speaker: Vijay Ravikumar\n\nEvent: CGP Seminar 2015\n\nAbstract: V. Lakshmibai recently proved that the compactification of the cotangent bundle to the ordinary (type $A$) Grassmannian $X$ is isomorphic to a certain affine Schubert variety in an affine two-step partial flag variety (of type $\tilde{A}$). Moreover, this affine Schubert variety is naturally a fiber bundle over $X$ with fiber also isomorphic to $X$. In this talk we discuss Lakshmibai's original result, along with a generalization to all cominuscule Grassmannians. This talk is related to joint work with V. Lakshmibai and William Slofstra. END:VEVENT BEGIN:VEVENT DTSTART:20150310T110000 DTEND:20150310T120000 DTSTAMP:20150309T150000Z UID:6a33c8e5fdb372a74fe3d5b7aa276786@cgp.ibs.re.kr SUMMARY:How Schur’s Q-functions are applied to geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Takeshi Ikeda\n\nEvent: Seminar 2015\n\nAbstract: In 1911, I. Schur introduced a remarkable family of symmetric polynomials called Q-functions in order to describe the irreducible characters of “projective” representations of the symmetric groups. The same functions are known to represent the Schubert classes for the Lagrangian Grassmannian. I will explain how this result by P. Pragacz can be extended to the torus equivariant K-theory of the maximal isotropic Grassmannian as well as the flag variety of the classical Lie groups. END:VEVENT BEGIN:VEVENT DTSTART:20150323T150000 DTEND:20150323T170000 DTSTAMP:20150322T150000Z UID:c83ab35c5adefb0cc78c32db4091d0df@cgp.ibs.re.kr SUMMARY:Analysis of the leading monomial structure of GL₂(k[x,y]) and its applications LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyuk min Kwon (S-Core)\n\nEvent: Math Seminar\n\nAbstract: In this talk, I will give an analysis of the leading monomial structure of GL₂(k[x,y]). And I will discuss its applications to two dimensional polynomial automorphisms and the realization algorithm for matrices in GL₂(k[x,y]). END:VEVENT BEGIN:VEVENT DTSTART:20150331T160000 DTEND:20150331T170000 DTSTAMP:20150330T150000Z UID:cf5133b2625cf11e2803ae2f52565cd4@cgp.ibs.re.kr SUMMARY:Matrix models and enumerative geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Seminar 2015\n\nAbstract: In my talk I will focus on the connection between matrix models and enumerative geometry. In particular, I will discuss matrix models, which describe the generating functions of intersection numbers on moduli spaces both for open and closed Riemann surfaces, linear Hodge integrals and Hurwitz numbers. All of them are tau-functions of the integrable hierarchies of KP\Toda type so that the integrability plays the key role in this description. Linear (Virasoro\W-constraints) and bilinear (KP\MKP integrable hierarchies) equations follow from the matrix model representation. END:VEVENT BEGIN:VEVENT DTSTART:20150403T110000 DTEND:20150403T120000 DTSTAMP:20150402T150000Z UID:70fe733605a1ee4055a120e7855158e6@cgp.ibs.re.kr SUMMARY:Selberg's orthonormality conjecture and joint universality of L-functions. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yoonbok Lee\n\nEvent: Seminar 2015\n\nAbstract: We introduce a new approach how to use an orthonormality relation of coefficients of Dirichlet series defining given L-functions from the Selberg class to prove joint universality. END:VEVENT BEGIN:VEVENT DTSTART:20150327T140000 DTEND:20150327T153000 DTSTAMP:20150326T150000Z UID:f5752cc8870469c984841b28caf4a3ca@cgp.ibs.re.kr SUMMARY:Some Computable Rank of Polynomials LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngho Woo\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: We will introduce a new notion “e-computablity” of rank of polynomials. This is a generalization of the method to computing rank of monomials developed by Carlini, Catalisano and Geramitta. We verify the strassen additive conjecture for many family of forms. This is a joint work with E.Carlini, M.Catalisano, L.Chiantini and A.Geramitta. END:VEVENT BEGIN:VEVENT DTSTART:20150324T153000 DTEND:20150324T163000 DTSTAMP:20150323T150000Z UID:2031a45bfdbe819adb9c2896565c16fe@cgp.ibs.re.kr SUMMARY:SOME ARITHMETIC ASPECTS OF INVARIANT THEORY LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dao Phuong Bac (Vietnam National University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150327T160000 DTEND:20150327T170000 DTSTAMP:20150326T150000Z UID:8f41084f94a48b026749b20d84556b20@cgp.ibs.re.kr SUMMARY:Statistical Arbitrage and Hedge Funds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seunghwan Lee (Managing Director Head of Singapore Research WorldQuant USA)\n\nEvent: Seminar on Hedge Funds and Math\n\nAbstract: Discussion on Statistical Arbitrage strategies. Quantitative models that generate profit from prediction of the market and their future development is a real challenging problem that needs advanced mathematics, computer science, and other fields. It creates new area of science.This is a special seminar for math people interested in hedge funds and financial engineering. In particular, graduate students interested in career in finance industry are encouraged to attend and meet the speaker, who is a pure math Ph.D. playing a leading role in the industry. END:VEVENT BEGIN:VEVENT DTSTART:20150330T200000 DTEND:20150330T220000 DTSTAMP:20150329T150000Z UID:12ce41b925145eeff909582c36db328d@cgp.ibs.re.kr SUMMARY:Bergman representative map via holomorphic connections LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Sungmin Yoo (POSTECH)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150403T155000 DTEND:20150403T180000 DTSTAMP:20150402T150000Z UID:1b057eedebe3788f33abb5362d50220c@cgp.ibs.re.kr SUMMARY:Webs of algebraic curves LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jun-Muk Hwang (KIAS)\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: A family of algebraic curves covering a projective variety $X$ is called a web of curves on $X$ if it has only finitely many members through a general point of $X$. A web of curves on $X$ induces a web-structure, in the sense of local differential geometry, in a neighborhood of a general point of $X$. We will discuss the relation between the local differential geometry of the web-structure and the global algebraic geometry of $X$. END:VEVENT BEGIN:VEVENT DTSTART:20150403T140000 DTEND:20150403T151500 DTSTAMP:20150402T150000Z UID:bf0a5e36cf107e10fa301c98880bcb3a@cgp.ibs.re.kr SUMMARY:Partitions and Modular forms Ⅰ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck Institute)\n\nEvent: POSTECH Mathematics Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150404T110000 DTEND:20150404T121500 DTSTAMP:20150403T150000Z UID:1e94a8164c69b8ab06acf2edf192d7ad@cgp.ibs.re.kr SUMMARY:Partitions and Modular forms Ⅱ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck Institute)\n\nEvent: POSTECH Mathematics Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150404T140000 DTEND:20150404T151500 DTSTAMP:20150403T150000Z UID:b3321a120925a22eab1a8a12b7d2d5a7@cgp.ibs.re.kr SUMMARY:Partitions and Modular forms III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck Institute)\n\nEvent: POSTECH Mathematics Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150416T160000 DTEND:20150416T180000 DTSTAMP:20150415T150000Z UID:6c16ea169d89fbf8836a940f916bc075@cgp.ibs.re.kr SUMMARY:Quantitative h-principle and $C^0$ symplectic geometry II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Emmanuel Opshtein\n\nEvent: CGP Seminar 2015\n\nAbstract: I will explain a serie of results, obtained in collaboration with Lev Buhovski, which concern the action of symplectic homeomorphisms on smooth submanifolds. We will see that this action exhibits both rigidity and flexibility, depending on the symplectic codimension of the objects they act on. For instance, they can squeeze arbitrarily a codimension 4 symplectic polydisc (flexibility), but they preserve many symplectic invariants of coisotropic sub manifolds (rigidity). I will try to explain in depth our central tool : a new version of the h-principle, which we call quantitative h-principle. END:VEVENT BEGIN:VEVENT DTSTART:20150420T110000 DTEND:20150420T120000 DTSTAMP:20150419T150000Z UID:3ca7dd1eec777a3eefe5785bfc8f9e8f@cgp.ibs.re.kr SUMMARY:On Orbifold Groupoids LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rui Wang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A groupoid is a small category with every morphism is invertible. It has many applications in both orbifold theory and non-commutative geometry. I will focus on the former, i.e., on proper \'etale groupoids (also named orbifold groupoids), for which the most important example is the one associated to an effective orbifold. In my three lectures, I will start with basic related definitions, properties and examples. Then I will introduce my on-going research results (joint with Bohui Chen and Cheng-Yong Du) on this topic. END:VEVENT BEGIN:VEVENT DTSTART:20150421T110000 DTEND:20150421T120000 DTSTAMP:20150420T150000Z UID:1622d50ba08250142cf6cc79a31bbbc0@cgp.ibs.re.kr SUMMARY:On Orbifold Groupoids LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rui Wang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A groupoid is a small category with every morphism is invertible. It has many applications in both orbifold theory and non-commutative geometry. I will focus on the former, i.e., on proper \'etale groupoids (also named orbifold groupoids), for which the most important example is the one associated to an effective orbifold. In my three lectures, I will start with basic related definitions, properties and examples. Then I will introduce my on-going research results (joint with Bohui Chen and Cheng-Yong Du) on this topic. END:VEVENT BEGIN:VEVENT DTSTART:20150424T110000 DTEND:20150424T120000 DTSTAMP:20150423T150000Z UID:2aea2e5040696520919d95e786997084@cgp.ibs.re.kr SUMMARY:On Orbifold Groupoids LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rui Wang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A groupoid is a small category with every morphism is invertible. It has many applications in both orbifold theory and non-commutative geometry. I will focus on the former, i.e., on proper \'etale groupoids (also named orbifold groupoids), for which the most important example is the one associated to an effective orbifold. In my three lectures, I will start with basic related definitions, properties and examples. Then I will introduce my on-going research results (joint with Bohui Chen and Cheng-Yong Du) on this topic. END:VEVENT BEGIN:VEVENT DTSTART:20150406T200000 DTEND:20150406T220000 DTSTAMP:20150405T150000Z UID:aff6ea4569317581075377b291bc65e6@cgp.ibs.re.kr SUMMARY:Variations of Ricci-flat metrics on Calabi- Yau manifolds LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Youngjun Choi (Korea Institute for Advanced Study)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: A Calabi-Yau manifold is a compact K¨ahler manifold whose first Chern class vanishes. A celebrated theorem due to Yau implies that there exists a unique K¨ahler-Einstein metric, i.e., Ricci-flat K¨ahler metric on each K¨ahler class.In this talk, we discuss about the basic properties and the constructions of K¨ahler-Einstein metric. And we also discuss about the variations of Ricci-flat Kahler metrics on Calabi-Yau manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20150407T153000 DTEND:20150407T164500 DTSTAMP:20150406T150000Z UID:ab750e35b73baecbfdce5c22ed037ffd@cgp.ibs.re.kr SUMMARY:Partitions and Modular forms Ⅳ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck Institute)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150413T200000 DTEND:20150413T220000 DTSTAMP:20150412T150000Z UID:a8dde6a90ae740e251cb1ee81e01639a@cgp.ibs.re.kr SUMMARY:Integral Kernel Methods in Multidimensional Complex Analysis: From its Origins to Recent Results for Weakly Pseudoconvex Domains LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: R.Michael Range (State University of New York at Albany)\n\nEvent: Special Lecture Series on Complex Analytic Geometry\n\nAbstract: The familiar classical Cauchy kernel has numerous important applications, so it is a central topic in multidimensional complex analysis to study correspond- ing higher dimensional kernels and applications. We shall begin this series of lectures with a quick review of such well known generalizations and results. We will then cover in detail a recent kernel construction that is valid on arbitrary smoothly bounded weaklν (that is, not necessarily strictlν ) pseudoconvex do- mains and that opens the door to significant applications. In that generality it is not possible to construct explicit kernels that are holomorphic in the parameter. Instead, the goal is to preserve some estimates that reflect the complex geom- etry of the boundary and the special role of differentiation with respect to the complex conjugate variables. We will discuss some basic properties of the new kernel and use them to obtain some pointwise a-priori estimates for (0, q) forms that are the analogue of the classical basic estimate on pseudoconvex domains in the L2 theory of the complex Neumann problem. END:VEVENT BEGIN:VEVENT DTSTART:20150414T160000 DTEND:20150414T180000 DTSTAMP:20150413T150000Z UID:4c429efb472d82cf54f9c948e5e26dac@cgp.ibs.re.kr SUMMARY:Integral Kernel Methods in Multidimensional Complex Analysis: From its Origins to Recent Results for Weakly Pseudoconvex Domains LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: R.Michael Range (State University of New York at Albany)\n\nEvent: Special Lecture Series on Complex Analytic Geometry\n\nAbstract: The familiar classical Cauchy kernel has numerous important applications, so it is a central topic in multidimensional complex analysis to study correspond- ing higher dimensional kernels and applications. We shall begin this series of lectures with a quick review of such well known generalizations and results. We will then cover in detail a recent kernel construction that is valid on arbitrary smoothly bounded weaklν (that is, not necessarily strictlν ) pseudoconvex do- mains and that opens the door to significant applications. In that generality it is not possible to construct explicit kernels that are holomorphic in the parameter. Instead, the goal is to preserve some estimates that reflect the complex geom- etry of the boundary and the special role of differentiation with respect to the complex conjugate variables. We will discuss some basic properties of the new kernel and use them to obtain some pointwise a-priori estimates for (0, q) forms that are the analogue of the classical basic estimate on pseudoconvex domains in the L2 theory of the complex Neumann problem. END:VEVENT BEGIN:VEVENT DTSTART:20150414T153000 DTEND:20150414T164500 DTSTAMP:20150413T150000Z UID:1a5768f142501704996436957a97b3b2@cgp.ibs.re.kr SUMMARY:Partitions and Modular forms Ⅴ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck Institute)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150408T170000 DTEND:20150408T180000 DTSTAMP:20150407T150000Z UID:637323034766f6df60c7bbaf495dbb81@cgp.ibs.re.kr SUMMARY:Cylindrical contact homology of subcritical Stein-fillable contact manifolds and more LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Mei-Lin Yau (National Central University)\n\nEvent: Geometry & Topology Seminar\n\nAbstract: In this talk I will consider two examples on which cylindrical contact homology can be defined and explicitly computed, namely subcritical Stein-fillable contact manifolds and a type of contact 3-manifolds associated to positive Dehn twists on a punctured torus. I will focus on the main ideas involved in the computation of their cylindrical contact homologies and discuss the results. This talk is based on my work in cylindrical contact homology. END:VEVENT BEGIN:VEVENT DTSTART:20150417T155000 DTEND:20150417T180000 DTSTAMP:20150416T150000Z UID:de678121035d7779f9bf058ae1bffce7@cgp.ibs.re.kr SUMMARY:Pseudoconvexity: What is it, and why is it central to Complex Analysis? LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: R. Michael Range (Albany University)\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: Pseudoconvexity is a most important concept in multidimensional complex analysis that has emerged in the early part of the 20th century. It has been central to signiÖcant developments since then, and it continues to present chal- lenges and mysteries to todayís researchers. We brieáy discuss its historical roots, highlight some geometric interpretations that illustrate the similarities and di§erences to standard Euclidean convexity, and review some of the prin- cipal results obtained over several decades. At the end we take a brief look at some recent research directions and formulate some open problems. This talk is expository and suitable for a general mathematical audience. END:VEVENT BEGIN:VEVENT DTSTART:20150414T160000 DTEND:20150414T180000 DTSTAMP:20150413T150000Z UID:f6981ebc20a582f2100e47de77f20b26@cgp.ibs.re.kr SUMMARY:Quantitative h-principle and $C^0$ symplectic geometry I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Emmanuel Opshtein\n\nEvent: Seminar 2015\n\nAbstract: I will explain a serie of results, obtained in collaboration with Lev Buhovski, which concern the action of symplectic homeomorphisms on smooth submanifolds. We will see that this action exhibits both rigidity and flexibility, depending on the symplectic codimension of the objects they act on. For instance, they can squeeze arbitrarily a codimension 4 symplectic polydisc (flexibility), but they preserve many symplectic invariants of coisotropic sub manifolds (rigidity). I will try to explain in depth our central tool : a new version of the h-principle, which we call quantitative h-principle. END:VEVENT BEGIN:VEVENT DTSTART:20150507T140000 DTEND:20150507T153000 DTSTAMP:20150506T150000Z UID:96f5caf506301f146fc00d153061c4c7@cgp.ibs.re.kr SUMMARY:Persistent homology and Floer theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Michael Usher\n\nEvent: CGP Seminar 2015\n\nAbstract: I will explain joint work with Jun Zhang which shows how to associate persistent-homology-type barcodes to the chain complexes that appear in Floer theory; when the complex is defined over the Novikov ring this requires rather different constructions than are traditional in persistent homology. Assuming field coefficients, our barcodes give complete invariants of the complex, and satisfy a stability theorem that unifies and extends standard results about the continuity of filtered Floer-theoretic invariants. A rather precise robustness statement for Hamiltonian fixed points follows as a quick corollary. END:VEVENT BEGIN:VEVENT DTSTART:20150504T160000 DTEND:20150504T180000 DTSTAMP:20150503T150000Z UID:1ff70048c0ea50bd03a35e4bf73a3145@cgp.ibs.re.kr SUMMARY:Infinitely many monotone Lagrangian Tori in CP$^2$ I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Renato Vianna\n\nEvent: Infinitely many monotone Lagrangian Tori in CP$^2$\n\nAbstract: In previous work, we constructed an exotic monotone Lagrangian torus inCP$^2$ (not Hamiltonian isotopic to the known Clifford and Chekanov tori) usingtechniques motivated by mirror symmetry. We named it T(1,4,25) because, whenfollowing a degeneration of CP$^2$ to the weighted projective space CP(1,4,25), itdegenerates to the central fiber of the moment map for the standard torus actionon CP(1,4,25). Related to each degeneration from CP$^2$ toCP(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple - a$^2$ + b$^2$ + c$^2$ = 3abc - thereis a monotone Lagrangian torus, which we call T(a$^2$,b$^2$,c$^2$). We employtechniques from symplectic field theory to prove[Theorem] The monotone Lagrangian tori T(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple,are mutually not Hamiltonian isotopic to each other.In the lecture 1, we will start with an introduction and history of the problem regarding monotone Lagrangian tori. Then we describe the tool we use to distinguish monotone Lagrangian tori and define the superpotential. after, we begin to work with an example studied by Denis Auroux that will serve us as the main model to explain wall-crossing and almost toric fibrations. We will then explain wall-crossing formulas and, time permitting, we will explain wall-crossing from a tropical geometry view point. END:VEVENT BEGIN:VEVENT DTSTART:20150424T140000 DTEND:20150424T153000 DTSTAMP:20150423T150000Z UID:b804da028d3189f03309fe8d019b173b@cgp.ibs.re.kr SUMMARY:Ciliberto's conjecture for factorial threefold hypersurfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kyusik Hong\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: Ciliberto's conjecture says that a nodal hypersurface of degree d in $P^4$ is factorial if it has at most $2(d-1)(d-2)$ nodes and contains neither 2-plane nor quadric surfaces. In this talk, I will survey the related results and present some recent works. END:VEVENT BEGIN:VEVENT DTSTART:20150421T173000 DTEND:20150421T183000 DTSTAMP:20150420T150000Z UID:e9b3c3d8fee67ae82820602adc944726@cgp.ibs.re.kr SUMMARY:Modular forms, 3rd order ordinary differential equations and affine vertex operator algebras LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kiyokazu Nagatomo (Osaka University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150422T150000 DTEND:20150422T160000 DTSTAMP:20150421T150000Z UID:9adceb2a4271ce6b507b644254eed1c4@cgp.ibs.re.kr SUMMARY:RAAGs in Diffeos LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sang-hyun Kim (Seoul National University)\n\nEvent: Geometry & Topology Seminar\n\nAbstract: A right-angled Artin group (RAAG) often admits a natural homomorphism into diffeomorphism groups of manifolds, using the fact that two diffeomorphisms with disjoint supports commute. It is a nontrivial task to reinforce this map to become an embedding. We show that an arbitrary RAAG embeds, by a quasi-isometry, into a pure braid group and also into the area-preserving diffeomorphism groups of the disk and of the sphere. We also show that every RAAG embeds into the real line smooth diffeomorphism group. This gives a rich source of embeddings from fundamental groups of manifolds into various diffeomorphism groups. (Joint work with Thomas Koberda, and partly with Hyungryul Baik) END:VEVENT BEGIN:VEVENT DTSTART:20150507T160000 DTEND:20150507T180000 DTSTAMP:20150506T150000Z UID:88d0024a9a7a7ed345951bc5d86340d3@cgp.ibs.re.kr SUMMARY:Infinitely many monotone Lagrangian Tori in CP$^2$ II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Renato Vianna\n\nEvent: Infinitely many monotone Lagrangian Tori in CP$^2$\n\nAbstract: In previous work, we constructed an exotic monotone Lagrangian torus inCP$^2$ (not Hamiltonian isotopic to the known Clifford and Chekanov tori) usingtechniques motivated by mirror symmetry. We named it T(1,4,25) because, whenfollowing a degeneration of CP$^2$ to the weighted projective space CP(1,4,25), itdegenerates to the central fiber of the moment map for the standard torus actionon CP(1,4,25). Related to each degeneration from CP$^2$ toCP(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple - a$^2$ + b$^2$ + c$^2$ = 3abc - thereis a monotone Lagrangian torus, which we call T(a$^2$,b$^2$,c$^2$). We employtechniques from symplectic field theory to prove[Theorem] The monotone Lagrangian tori T(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple,are mutually not Hamiltonian isotopic to each other.In the lecture 2, we will explain almost toric fibrations and their base diagram. We use it to define the monotone Lagrangian tori T(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple, and, then, give a precise statement of the main theorem. After that, depending on how much we were able to cover in Lecture 1, we will either explain wall-crossing from a tropical geometry view point or give an explictic description of the construction of T(1,4,25). END:VEVENT BEGIN:VEVENT DTSTART:20150508T140000 DTEND:20150508T160000 DTSTAMP:20150507T150000Z UID:2f2b1f876a08228b3413cbaae154f6a0@cgp.ibs.re.kr SUMMARY:Infinitely many monotone Lagrangian Tori in CP$^2$ III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Renato Vianna\n\nEvent: Infinitely many monotone Lagrangian Tori in CP$^2$\n\nAbstract: In previous work, we constructed an exotic monotone Lagrangian torus inCP$^2$ (not Hamiltonian isotopic to the known Clifford and Chekanov tori) usingtechniques motivated by mirror symmetry. We named it T(1,4,25) because, whenfollowing a degeneration of CP$^2$ to the weighted projective space CP(1,4,25), itdegenerates to the central fiber of the moment map for the standard torus actionon CP(1,4,25). Related to each degeneration from CP$^2$ toCP(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple - a$^2$ + b$^2$ + c$^2$ = 3abc - thereis a monotone Lagrangian torus, which we call T(a$^2$,b$^2$,c$^2$). We employtechniques from symplectic field theory to prove[Theorem] The monotone Lagrangian tori T(a$^2$,b$^2$,c$^2$), for (a,b,c) a Markov triple,are mutually not Hamiltonian isotopic to each other.In the lecture 3, we will work towards the proof of the main Theorem. For that we need to explain a technique called neck-streching and a corresponding Gromov type convergence of J-holomorphic discs. Finally, we are able to give a proof of the main theorem. If we still have time, we will discuss the CP$^1$ x CP$^1$ case. END:VEVENT BEGIN:VEVENT DTSTART:20150422T160000 DTEND:20150422T180000 DTSTAMP:20150421T150000Z UID:39c687da5cdc7a0e9ba67bf6f4e24dac@cgp.ibs.re.kr SUMMARY:Mirror symmetry, gamma class and modular forms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck)\n\nEvent: POSTECH Mathematics Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150424T170000 DTEND:20150424T180000 DTSTAMP:20150423T150000Z UID:36223006c5f5e6f28cae311970066f78@cgp.ibs.re.kr SUMMARY:Remarks on asymptotic behaviors of strong solutions to a viscous Boussinesq system LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Shangkun Weng\n\nEvent: PMI PDE Seminar\n\nAbstract: In this talk, we first address the space-time decay properties for higher order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space.s The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions in scaling invariant function spaces. We further investigate the asymptotic profiles and decay properties of these strong solutions. Our results recover and extend the important results in Brandolese and Schonbek (Tran. A. M.S. Vol 364, No.10, 2012, 5057-5090). END:VEVENT BEGIN:VEVENT DTSTART:20150501T155000 DTEND:20150501T164000 DTSTAMP:20150430T150000Z UID:39e69a27f74f47812bb50a14c17531bb@cgp.ibs.re.kr SUMMARY:Part I: The zeta function of Euler and Riemann LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck )\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150501T171000 DTEND:20150501T180000 DTSTAMP:20150430T150000Z UID:3c54bfc43483bdd568f1a38eda69da18@cgp.ibs.re.kr SUMMARY:PART II: Multiple zeta values: from Euler to string theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck)\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150502T100000 DTEND:20150502T170000 DTSTAMP:20150501T150000Z UID:88ce6dc332c28d396e921b6b54b5ad18@cgp.ibs.re.kr SUMMARY:Differential equations and Periods of modular forms LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Don Bernard Zagier (Max Planck)\n\nEvent: One day workshop\n\nAbstract: May 2(Sat) 10:00-11:00/ 11:30-12:30/ 14:30-15:30/ 16:00-17:00 END:VEVENT BEGIN:VEVENT DTSTART:20150508T093000 DTEND:20150508T154000 DTSTAMP:20150507T150000Z UID:cb089fc1e01bb7a1bcbe9246efa105fa@cgp.ibs.re.kr SUMMARY:2015 PMI Workshop LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: PMI\n\nEvent: 2015 PMI Workshop\n\nAbstract: Speakers:Jae Choon ChaJinseok ChoYun Sung ChoiYoungJu ChoieHyun Kwang KimByungsoo MoonJeehoon ParkLusheng WangShangkun WengHyonju Yu END:VEVENT BEGIN:VEVENT DTSTART:20150512T150000 DTEND:20150512T163000 DTSTAMP:20150511T150000Z UID:be0256fb515d574bdd9d7df37d842d5c@cgp.ibs.re.kr SUMMARY:Batalin-Vilkovisky algebra and formal Frobenius manifold structure for possibly singular Calabi-Yau projective hypersurfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dokyoung Kim (POSTECH)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: We explain how to attach a Batalin-Vilkovisky(BV) algebra to a possibly singular Calabi-Yau projective hypersurface and how to put the Hodge theoretic informations on such a BV algebra. Moreover, using the Grobner basis theory in super-commutative setting, we provide an explicit algorithm to compute the period integrals of a formal deformation of possibly singular Calabi-Yau projective hypersurfaces via L infinity homotopy theory. Also we briefly introduce the Frobenius manifold structure on the cohomology of such a hypersurface. This is a joint work with Jeehoon Park. END:VEVENT BEGIN:VEVENT DTSTART:20150603T170000 DTEND:20150603T180000 DTSTAMP:20150602T150000Z UID:7ca10080f35ea9501e1e57df30c1c893@cgp.ibs.re.kr SUMMARY:Rigidity theorems of hypersurfaces with free boundary in a wedge in a space form LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Juncheol Pyo (Pusan National University)\n\nEvent: Geometry & Topology Seminar\n\nAbstract: A geodesic sphere in a space form is characterized in various ways. Among all hypersurfaces of a given volume bounding a domain in a space form, a geodesic sphere has the least area, that is, it is the boundary of an isoperimetric domain in a space form. In this talk, we present some rigidity results about compact hyper surfaces with free boundary in a wedge in a space form. First, we prove that every compact immersed stable constant mean curvature hypersurface with free boundary in a wedge is part of a geodesic sphere centered at a point of the edge of the wedge. Second, we show that the same rigidity result holds for a compact embedded constant higher order mean curvature hypersurface with free boundary in a wedge. Finally, we extend this result to a compact immersed hypersurface with free boundary in a wedge that has the additional property that the ratio of two higher order mean curvatures is constant. END:VEVENT BEGIN:VEVENT DTSTART:20150507T160000 DTEND:20150507T180000 DTSTAMP:20150506T150000Z UID:347f437895b248eed42176c60d4b2835@cgp.ibs.re.kr SUMMARY:From Lagrangian inclusions of real surfaces to approximation of continuous functions LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Rasul Shafikov (Western Ontario University, Canada)\n\nEvent: GAIA Short Seminar Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150511T163000 DTEND:20150511T173000 DTSTAMP:20150510T150000Z UID:09a20d967c863101d3f53dacf868ba9b@cgp.ibs.re.kr SUMMARY:The Selberg trace formula as a Dirichlet series LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Min Lee (University of Bristol)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: We explore an idea of Conrey and Li of presenting the Selberg trace formula for Hecke operators as a Dirichlet series. We enhance their work in a few ways, and present two applications, including an interpretation of the Selberg eigenvalue conjecture in terms of quadratic twists of certain Dirichlet series, and a formula for a sum of complete symmetric square L-functions associated to Maass cusp forms. This is a joint work with Andrew Booker. END:VEVENT BEGIN:VEVENT DTSTART:20150522T140000 DTEND:20150522T153000 DTSTAMP:20150521T150000Z UID:2f92041efda4a36c54968160a9af4a30@cgp.ibs.re.kr SUMMARY:Automorphism groups of smooth quintic threefolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Xun Yu\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: Automorphism groups of algebraic varieties are important invariants. By a result of Matsumura-Monsky, almost all smooth hypersurfaces in projective space have finite automorphism groups. In this talk, I would like to talk about some methods which can be used to compute these finite groups. As an application, I will explain how to use them to classify automorphism groups of smooth quintic threefolds. This is a joint work with Professor Keiji Oguiso. END:VEVENT BEGIN:VEVENT DTSTART:20150612T140000 DTEND:20150612T153000 DTSTAMP:20150611T150000Z UID:189460944ba2ccd3f70d5cf3e7d918db@cgp.ibs.re.kr SUMMARY:Rationally connected non-Fano type varieties. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Igor Krylov\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: Varieties of Fano type behave very well under Log Minimal Model Program. It is also known that all varieties of Fano type are rationally connected. Thus it is interesting to know if in the birational class of any rationally connected variety there is a variety of Fano type. Using techniques of birational rigidity, I will construct examples of rationally connected varieties of dimension $\geqslant 4$ which are not birationally equivalent to varieties of Fano type, thereby answering a question of Cascini and Gongyo. I will also discuss the strategy of dealing with dimension 3 case. END:VEVENT BEGIN:VEVENT DTSTART:20150611T140000 DTEND:20150611T153000 DTSTAMP:20150610T150000Z UID:30b1bfcf2ed36a8a11e41941ad19bfaf@cgp.ibs.re.kr SUMMARY:Cylinders in del Pezzo surfaces. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: For a projective variety X and an ample divisor H on it, an H-polar cylinder in X is an open ruled affine subset whose complement is a support of an effective Q-divisor Q-rationally equivalent to H.This notion links together affine, birational and Kahler geometries. I will show how to prove existence and non-existence of H-polar cylinders in smooth and mildly singular del Pezzo surfaces (for different polarizations).The obstructions comes from log canonical thresholds and Fujita numbers. As an application, I will answer an old question of Zaidenberg and Flenner about additive group actions on the cubic Fermat affine threefold cone. This is a joint work with Jihun Park and Joonyeong Won. END:VEVENT BEGIN:VEVENT DTSTART:20150619T140000 DTEND:20150619T153000 DTSTAMP:20150618T150000Z UID:e8b2ce4afd28f755a1effbe7eb1c277f@cgp.ibs.re.kr SUMMARY:Weakly exceptional quotient singularities LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dmitrijs Sakovics\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: The ADE classification of surface singularities is a very well-known result, whose origin can be traced back to F.Klein (or even Plato). Weakly exceptional singularities are one of the ways of generalising the types D and E of surface singularities to higher dimension. I will describe the quotient singularities of this type and will present some ways of looking for them using both the geometric and the group-theoretic approaches. Then I will derive their classification in low dimensions and some results applicable to them in the higher-dimensional cases. END:VEVENT BEGIN:VEVENT DTSTART:20150518T200000 DTEND:20150518T220000 DTSTAMP:20150517T150000Z UID:eef7495a7299c0e9b7e1a9aef54a6893@cgp.ibs.re.kr SUMMARY:GAIA Seminar on Complex Analytic Geometry LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Nikolay Shcherbina\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150523T110000 DTEND:20150523T173000 DTSTAMP:20150522T150000Z UID:269b768619e31b6d80e559595ffb3840@cgp.ibs.re.kr SUMMARY:The 70th KPPY Combinatorics Seminar LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jack Koolen, Jaeyoung Yang ...\n\nEvent: PMI Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150529T155000 DTEND:20150529T180000 DTSTAMP:20150528T150000Z UID:2e14bc87c92f7585b66960375b7785e1@cgp.ibs.re.kr SUMMARY:Investigation of unconventional superconductivity and magnetism by magnetic force microscopy LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jeehoon Kim\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150526T133000 DTEND:20150526T153000 DTSTAMP:20150525T150000Z UID:5901a244d10f5e9e9f86de65ce0454b3@cgp.ibs.re.kr SUMMARY:Witten‐Morse theory and mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ziming Nikolas Ma\n\nEvent: Seminar 2015\n\nAbstract: Wedge product on deRham complex of a Riemannian manifold $M$ can be pulled back to $H^*(M)$ via explicit homotopy, constructed using Green's operator, to give higher product structures. Fukaya's conjecture suggests that Witten deformation of these higher product structures have semi-classical limits as operators defined by counting gradient flow trees with respect to Morse functions, which generalizes the remarkable Witten deformation of deRham differential. We will describe briefly the proof of Fukaya's conjecture in part I of the talk.In part II, we study fiberwise Fourier transform on the semi-flat limits torus bundles $X_0$ and $\check{X}_0$ over a common base $B_0$ for a for a mirror pair of Calabi-Yau manifold $X$ and $\check{X}$. We prove that the process of solving Maurer-Cartan equation in $L^*_{X_0}$, the Fourier transform of the Kodaira-Spencer dgLa on $\check{X}_0$, has semi-classical limit as the scattering process introduced by Kontsevich-Soibelman, which is known to govern the deformation from $\check{X}_0$ to $\check{X}$. This realizes a key step in Fukaya's program on understanding quantum corrections in symplectic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20150601T110000 DTEND:20150601T120000 DTSTAMP:20150531T150000Z UID:711b46bc4eb7a27c8a510d03e0d70b4a@cgp.ibs.re.kr SUMMARY:On the classification of tight contact structures LOCATION:CGP Main Hall DESCRIPTION:Speaker: Juhyun Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The classification of tight contact structures of 3-manifolds is very important issue inlow dimensional contact topology. In these talk, I will focus on the clssification ofsurface bundles over the circle. I will first explain the case of torus bundles over thecircle using two different methods which was independently intruduced by Giroux andHonda. Then I will introduce a generalized proof for surface bundles over the circlewith a higher genus fiber and arbitrary pseudo-Anosov monodromy without extremalcondition using Honda’s method. END:VEVENT BEGIN:VEVENT DTSTART:20150602T110000 DTEND:20150602T120000 DTSTAMP:20150601T150000Z UID:eeee10afa9c871e7b5a5ecb5dedc1a3a@cgp.ibs.re.kr SUMMARY:On the classification of tight contact structures LOCATION:CGP Main Hall DESCRIPTION:Speaker: Juhyun Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The classification of tight contact structures of 3-manifolds is very important issue inlow dimensional contact topology. In these talk, I will focus on the clssification ofsurface bundles over the circle. I will first explain the case of torus bundles over thecircle using two different methods which was independently intruduced by Giroux andHonda. Then I will introduce a generalized proof for surface bundles over the circlewith a higher genus fiber and arbitrary pseudo-Anosov monodromy without extremalcondition using Honda’s method. END:VEVENT BEGIN:VEVENT DTSTART:20150605T110000 DTEND:20150605T120000 DTSTAMP:20150604T150000Z UID:0a21772fab97c91410e829b0db5657f7@cgp.ibs.re.kr SUMMARY:On the classification of tight contact structures LOCATION:CGP Main Hall DESCRIPTION:Speaker: Juhyun Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The classification of tight contact structures of 3-manifolds is very important issue inlow dimensional contact topology. In these talk, I will focus on the clssification ofsurface bundles over the circle. I will first explain the case of torus bundles over thecircle using two different methods which was independently intruduced by Giroux andHonda. Then I will introduce a generalized proof for surface bundles over the circlewith a higher genus fiber and arbitrary pseudo-Anosov monodromy without extremalcondition using Honda’s method. END:VEVENT BEGIN:VEVENT DTSTART:20150602T153000 DTEND:20150602T163000 DTSTAMP:20150601T150000Z UID:d955028ec27ebcd33eef44ecf10a3cef@cgp.ibs.re.kr SUMMARY:Desingularization of multiple zeta-functions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kohji Matsumoto (Nagoya University)\n\nEvent: PMI Number Theory Seminar\n\nAbstract: We introduce the method of desingularization of multiple zeta-functions of generalized Euler-Zagier type, under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at non-positive integer points. The desingularized multiple zeta-function turns to be entire, and is written by a suitable finite linear combination of usual multiple zeta-functions. It is shown that specific combinations of Bernoulli numbers attain special values of desingularized zeta-function at non-positive integer points.(This is a joint work with H. Furusho, Y. Komori and H. Tsumura.) END:VEVENT BEGIN:VEVENT DTSTART:20150605T155000 DTEND:20150605T180000 DTSTAMP:20150604T150000Z UID:ebe28404fa92d4062a83dbf6ce69c1e3@cgp.ibs.re.kr SUMMARY:Liouvillle type and unique continuation theorems in the fluid mechanics LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: DongHo Chae (Chung-Ang University)\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: Liouville theorems and the unique continuation theorems are among the most remarkableproperties for harmonic functions and for solutions of many elliptic partial differential equations. In this talk we discuss two cases, where we want to prove the these theorems in the fluid mechanics. One is related to the search for singularity of the Navier-Stokes/Euler equations in the self-similar form, and the other case is from a questoin by J. Leray for the stationary solutions of the Navier-Stokes equations having finite Dirichlet integral. END:VEVENT BEGIN:VEVENT DTSTART:20150618T160000 DTEND:20150618T180000 DTSTAMP:20150617T150000Z UID:55674b1858ada6a0bbd834f1eca3e8f4@cgp.ibs.re.kr SUMMARY:Legendrian DGA as Immersed Floer Theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Garrett Alston\n\nEvent: CGP Seminar 2015\n\nAbstract: An embedded Legendrian in a contact manifold of the form P x R can be interpreted as an immersed Lagrangian in P. I will explain how the Floer theory of the immersed Lagrangian contains the information of the Legendrian dga. I will also give some conjectural SFT-type applications to non-compact Lagrangians. END:VEVENT BEGIN:VEVENT DTSTART:20150623T133000 DTEND:20150623T153000 DTSTAMP:20150622T150000Z UID:dda59caff13a22466660a66d81344fe9@cgp.ibs.re.kr SUMMARY:Aspects of B-branes and gauged linear sigma models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mauricio Andres Romo Jorquera\n\nEvent: Seminar 2015\n\nAbstract: I will talk about recent results on transport of B-branes along the moduli space of gauged linear sigma models. On the mathematical side this corresponds to derived equivalences between different limit points of the stringy Kahler moduli of Calabi-Yaus. END:VEVENT BEGIN:VEVENT DTSTART:20150604T160000 DTEND:20150604T180000 DTSTAMP:20150603T150000Z UID:12f8c846ae54ee8a28bcc189fff760fb@cgp.ibs.re.kr SUMMARY:Non-orientable surfaces and S-duality LOCATION:CGP Main Hall DESCRIPTION:Speaker: Siye Wu\n\nEvent: CGP Seminar 2015\n\nAbstract: In this talk, I explain the role of non-orientable surfaces in twisted N=4 supersymmetric Yang-Mills theory in 4 dimensions whose compactification along orientable surfaces yields mirror symmetry and geometric Langlands program as studied by Kapustin and Witten. I relate the discrete electricand magnetic charges of 't Hooft in 4 dimensions to the topology of Hitchin's moduli spaces for orientable and non-orientable surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20150609T153000 DTEND:20150609T163000 DTSTAMP:20150608T150000Z UID:40b0949574743b7ddb478653b7984662@cgp.ibs.re.kr SUMMARY:Deformation of period integrals of projective smooth complete intersections LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yesule Kim\n\nEvent: PMI Number Theory Seminar\n\nAbstract: The period matrices are important invariants for complex manifolds. When X, Y are two smooth projective complete intersection varieties with same degree and dimension, we study an explicit relationship between period matrices of X and Y via homotopy Lie theory. (Such a relationship was first studied by Jae-Suk Park and Jeehoon Park in the case of smooth projective hypersurfaces.) The main idea is to understand the period integrals as a (homotopy type) of a cochain map from the BV(Batalin-Vilkovisky) algebra and use the deformation theory attached to the corresponding DGLA(differential graded Lie algebra.) This is a joint work with Jeehoon Park. END:VEVENT BEGIN:VEVENT DTSTART:20150608T170000 DTEND:20150608T183000 DTSTAMP:20150607T150000Z UID:393c9d77681e9946cd73fb2017ae367d@cgp.ibs.re.kr SUMMARY:Chain level string topology via diffuse intersection I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Quantum Monday 2015\n\nAbstract: In these two talks I'll explain some details about the construction of chain level string topology operations using diffuse intersection. I hope to talk about our combinatorial graph model for the space of operations, an interpolation map that uses Riemannian center of mass techniques, and our construction of a universal Thom class on the space of operations. This work is joint with K. Poirier and N. Rounds. END:VEVENT BEGIN:VEVENT DTSTART:20150609T170000 DTEND:20150609T183000 DTSTAMP:20150608T150000Z UID:8213e0e68a29773480bdabc80c7de99a@cgp.ibs.re.kr SUMMARY:Chain level string topology via diffuse intersection II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Seminar 2015\n\nAbstract: In these two talks I'll explain some details about the construction of chain level string topology operations using diffuse intersection. I hope to talk about our combinatorial graph model for the space of operations, an interpolation map that uses Riemannian center of mass techniques, and our construction of a universal Thom class on the space of operations. This work is joint with K. Poirier and N. Rounds. END:VEVENT BEGIN:VEVENT DTSTART:20150610T140000 DTEND:20150610T151500 DTSTAMP:20150609T150000Z UID:218d7f7267cb858ac0a213942d15f59d@cgp.ibs.re.kr SUMMARY:Cubes, Association schemes and spheres(An overview of Algebraic Combinatorics) LOCATION:Math. Bldg. #402 DESCRIPTION:Speaker: Prof. Hyun Kwang Kim\n\nEvent: POSTECH Mathematics Lecture Series\n\nAbstract: These are course ending bonus lectures to Math 561(Combinatorics I). We start with coding theory which is the study of binary cubes. We investigate binary cubes from plenty of viewpoints and briefly introduce basic concepts in coding theory. We also introduce basic four parameters of a code and inequalities satisfied by these parameters. Next we discuss association schems which are natural generalization of many objects in algebra and combinatorics including finite groups and distance regular graphs. We also introduce linear programming of Delsarte and discuss dualities on association schems. The spheres are of course the most interesting. It is a continuous object while the above two are discrete. We will see that many results from other areas of Mathematics can be used in the study of spherical codes and designs. END:VEVENT BEGIN:VEVENT DTSTART:20150624T160000 DTEND:20150624T180000 DTSTAMP:20150623T150000Z UID:c91c48be17d4a6503e959602148554f2@cgp.ibs.re.kr SUMMARY:Introduction to permutation-equivariant quantum K-theory (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Introduction to permutation-equivariant quantum K-theory\n\nAbstract: By quantum K-theory I mean the counterpart of Gromov-Witten theory where the cohomological intersection numbers in moduli spaces of holomorphic curves are replaced with holomorphic Euler characterisics of interesting vector bundles over such moduli spaces. The theory, which is in many ways parallel to the cohomological one, brings up a number of novel features. In particular, as it tuns out, in order to make the theory successful it is necessary to consider the action of the group of permutations of the marked points, decompose sheaf cohomology of bundles over moduli paces according to representations of the permutation groups, and define "permutation-equivariant" K-theoretic GW-invariants as multiplicities of such representations. One reason why it is necessary is that such information is needed in order to apply in K-theory the computation of GW-invariants using tori actions and fixed point localization. Another reason is that natural q-analogues of toric hyper-geometric functions of cohomological mirror theory, do arise in K-theoretic version of mirror theory, but only when one agrees to incorporate the action of permutation groups. In this connection, the K-theoretic analogue of mirror theory leads to a representation of q-hypergeometric functions by oscillating integrals - just as in cohomological theory - with a novel feature however, that they "oscillate fast" when the parameter q approaches roots of unity, and that the stationary phase asymptotics at different roots of unity behave coherently with each other. Yet another surprising aspect of permutation-equivariant theory surfaces when one compares GW-invariants of a line bundle space with those of the base, or of a complete intersection with those of the ambient space. It turns out that K-theory here is more satisfactory than cohomology theory. This is due to the "bosonic-fermionic" correspondence: the Koszul comlex $\sum (-1)^k \bigwedge^k V$, which is the K-theoretic counterpart of the Euler class, is inverse to the symmetric algebra $S^*(V)$, i.e. the permutation-invariant part of the tensor algebra of $V$. The permutation-equivariant quantum K-theory is a work in progress, and many aspects exist only in the outline, while other are open. For example, the all-genera quantum K-theory of the point target space (that is, the theory of representations of symmetric groups in sheaf cohomology over Deligne-Mumford spaces) in genus 0 can be solved by using the general machinery, in its toy version can be handled by bare hands (using Kapranov's description of $\overline{M}_{0,n}$), and in all genera should conjecturally lead to a finite-difference counterpart of the KdV-hierarchy. In the lectures, I intend to oscillate between these modes: illustrate the "bare hands" approach, introduce the general machinery, and outline open problems. END:VEVENT BEGIN:VEVENT DTSTART:20150703T160000 DTEND:20150703T180000 DTSTAMP:20150702T150000Z UID:810f0be092a64b11b727ad6ce304afc1@cgp.ibs.re.kr SUMMARY:Introduction to permutation-equivariant quantum K-theory (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Introduction to permutation-equivariant quantum K-theory\n\nAbstract: By quantum K-theory I mean the counterpart of Gromov-Witten theory where the cohomological intersection numbers in moduli spaces of holomorphic curves are replaced with holomorphic Euler characterisics of interesting vector bundles over such moduli spaces. The theory, which is in many ways parallel to the cohomological one, brings up a number of novel features. In particular, as it tuns out, in order to make the theory successful it is necessary to consider the action of the group of permutations of the marked points, decompose sheaf cohomology of bundles over moduli paces according to representations of the permutation groups, and define "permutation-equivariant" K-theoretic GW-invariants as multiplicities of such representations. One reason why it is necessary is that such information is needed in order to apply in K-theory the computation of GW-invariants using tori actions and fixed point localization. Another reason is that natural q-analogues of toric hyper-geometric functions of cohomological mirror theory, do arise in K-theoretic version of mirror theory, but only when one agrees to incorporate the action of permutation groups. In this connection, the K-theoretic analogue of mirror theory leads to a representation of q-hypergeometric functions by oscillating integrals - just as in cohomological theory - with a novel feature however, that they "oscillate fast" when the parameter q approaches roots of unity, and that the stationary phase asymptotics at different roots of unity behave coherently with each other. Yet another surprising aspect of permutation-equivariant theory surfaces when one compares GW-invariants of a line bundle space with those of the base, or of a complete intersection with those of the ambient space. It turns out that K-theory here is more satisfactory than cohomology theory. This is due to the "bosonic-fermionic" correspondence: the Koszul comlex $\sum (-1)^k \bigwedge^k V$, which is the K-theoretic counterpart of the Euler class, is inverse to the symmetric algebra $S^*(V)$, i.e. the permutation-invariant part of the tensor algebra of $V$. The permutation-equivariant quantum K-theory is a work in progress, and many aspects exist only in the outline, while other are open. For example, the all-genera quantum K-theory of the point target space (that is, the theory of representations of symmetric groups in sheaf cohomology over Deligne-Mumford spaces) in genus 0 can be solved by using the general machinery, in its toy version can be handled by bare hands (using Kapranov's description of $\overline{M}_{0,n}$), and in all genera should conjecturally lead to a finite-difference counterpart of the KdV-hierarchy. In the lectures, I intend to oscillate between these modes: illustrate the "bare hands" approach, introduce the general machinery, and outline open problems. END:VEVENT BEGIN:VEVENT DTSTART:20150715T160000 DTEND:20150715T180000 DTSTAMP:20150714T150000Z UID:6d58c0923402ba670345c38e26cdfa34@cgp.ibs.re.kr SUMMARY:Introduction to permutation-equivariant quantum K-theory (III) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Introduction to permutation-equivariant quantum K-theory\n\nAbstract: By quantum K-theory I mean the counterpart of Gromov-Witten theory where the cohomological intersection numbers in moduli spaces of holomorphic curves are replaced with holomorphic Euler characterisics of interesting vector bundles over such moduli spaces. The theory, which is in many ways parallel to the cohomological one, brings up a number of novel features. In particular, as it tuns out, in order to make the theory successful it is necessary to consider the action of the group of permutations of the marked points, decompose sheaf cohomology of bundles over moduli paces according to representations of the permutation groups, and define "permutation-equivariant" K-theoretic GW-invariants as multiplicities of such representations. One reason why it is necessary is that such information is needed in order to apply in K-theory the computation of GW-invariants using tori actions and fixed point localization. Another reason is that natural q-analogues of toric hyper-geometric functions of cohomological mirror theory, do arise in K-theoretic version of mirror theory, but only when one agrees to incorporate the action of permutation groups. In this connection, the K-theoretic analogue of mirror theory leads to a representation of q-hypergeometric functions by oscillating integrals - just as in cohomological theory - with a novel feature however, that they "oscillate fast" when the parameter q approaches roots of unity, and that the stationary phase asymptotics at different roots of unity behave coherently with each other. Yet another surprising aspect of permutation-equivariant theory surfaces when one compares GW-invariants of a line bundle space with those of the base, or of a complete intersection with those of the ambient space. It turns out that K-theory here is more satisfactory than cohomology theory. This is due to the "bosonic-fermionic" correspondence: the Koszul comlex $\sum (-1)^k \bigwedge^k V$, which is the K-theoretic counterpart of the Euler class, is inverse to the symmetric algebra $S^*(V)$, i.e. the permutation-invariant part of the tensor algebra of $V$. The permutation-equivariant quantum K-theory is a work in progress, and many aspects exist only in the outline, while other are open. For example, the all-genera quantum K-theory of the point target space (that is, the theory of representations of symmetric groups in sheaf cohomology over Deligne-Mumford spaces) in genus 0 can be solved by using the general machinery, in its toy version can be handled by bare hands (using Kapranov's description of $\overline{M}_{0,n}$), and in all genera should conjecturally lead to a finite-difference counterpart of the KdV-hierarchy. In the lectures, I intend to oscillate between these modes: illustrate the "bare hands" approach, introduce the general machinery, and outline open problems. END:VEVENT BEGIN:VEVENT DTSTART:20150722T160000 DTEND:20150722T180000 DTSTAMP:20150721T150000Z UID:a227255ac5fc6b540060f5e646067a27@cgp.ibs.re.kr SUMMARY:Introduction to permutation-equivariant quantum K-theory (IV) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Introduction to permutation-equivariant quantum K-theory\n\nAbstract: By quantum K-theory I mean the counterpart of Gromov-Witten theory where the cohomological intersection numbers in moduli spaces of holomorphic curves are replaced with holomorphic Euler characterisics of interesting vector bundles over such moduli spaces. The theory, which is in many ways parallel to the cohomological one, brings up a number of novel features. In particular, as it tuns out, in order to make the theory successful it is necessary to consider the action of the group of permutations of the marked points, decompose sheaf cohomology of bundles over moduli paces according to representations of the permutation groups, and define "permutation-equivariant" K-theoretic GW-invariants as multiplicities of such representations. One reason why it is necessary is that such information is needed in order to apply in K-theory the computation of GW-invariants using tori actions and fixed point localization. Another reason is that natural q-analogues of toric hyper-geometric functions of cohomological mirror theory, do arise in K-theoretic version of mirror theory, but only when one agrees to incorporate the action of permutation groups. In this connection, the K-theoretic analogue of mirror theory leads to a representation of q-hypergeometric functions by oscillating integrals - just as in cohomological theory - with a novel feature however, that they "oscillate fast" when the parameter q approaches roots of unity, and that the stationary phase asymptotics at different roots of unity behave coherently with each other. Yet another surprising aspect of permutation-equivariant theory surfaces when one compares GW-invariants of a line bundle space with those of the base, or of a complete intersection with those of the ambient space. It turns out that K-theory here is more satisfactory than cohomology theory. This is due to the "bosonic-fermionic" correspondence: the Koszul comlex $\sum (-1)^k \bigwedge^k V$, which is the K-theoretic counterpart of the Euler class, is inverse to the symmetric algebra $S^*(V)$, i.e. the permutation-invariant part of the tensor algebra of $V$. The permutation-equivariant quantum K-theory is a work in progress, and many aspects exist only in the outline, while other are open. For example, the all-genera quantum K-theory of the point target space (that is, the theory of representations of symmetric groups in sheaf cohomology over Deligne-Mumford spaces) in genus 0 can be solved by using the general machinery, in its toy version can be handled by bare hands (using Kapranov's description of $\overline{M}_{0,n}$), and in all genera should conjecturally lead to a finite-difference counterpart of the KdV-hierarchy. In the lectures, I intend to oscillate between these modes: illustrate the "bare hands" approach, introduce the general machinery, and outline open problems. END:VEVENT BEGIN:VEVENT DTSTART:20150729T160000 DTEND:20150729T180000 DTSTAMP:20150728T150000Z UID:f04dc95667969572497f513354f96e9c@cgp.ibs.re.kr SUMMARY:Introduction to permutation-equivariant quantum K-theory (V) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Introduction to permutation-equivariant quantum K-theory\n\nAbstract: By quantum K-theory I mean the counterpart of Gromov-Witten theory where the cohomological intersection numbers in moduli spaces of holomorphic curves are replaced with holomorphic Euler characterisics of interesting vector bundles over such moduli spaces. The theory, which is in many ways parallel to the cohomological one, brings up a number of novel features. In particular, as it tuns out, in order to make the theory successful it is necessary to consider the action of the group of permutations of the marked points, decompose sheaf cohomology of bundles over moduli paces according to representations of the permutation groups, and define "permutation-equivariant" K-theoretic GW-invariants as multiplicities of such representations. One reason why it is necessary is that such information is needed in order to apply in K-theory the computation of GW-invariants using tori actions and fixed point localization. Another reason is that natural q-analogues of toric hyper-geometric functions of cohomological mirror theory, do arise in K-theoretic version of mirror theory, but only when one agrees to incorporate the action of permutation groups. In this connection, the K-theoretic analogue of mirror theory leads to a representation of q-hypergeometric functions by oscillating integrals - just as in cohomological theory - with a novel feature however, that they "oscillate fast" when the parameter q approaches roots of unity, and that the stationary phase asymptotics at different roots of unity behave coherently with each other. Yet another surprising aspect of permutation-equivariant theory surfaces when one compares GW-invariants of a line bundle space with those of the base, or of a complete intersection with those of the ambient space. It turns out that K-theory here is more satisfactory than cohomology theory. This is due to the "bosonic-fermionic" correspondence: the Koszul comlex $\sum (-1)^k \bigwedge^k V$, which is the K-theoretic counterpart of the Euler class, is inverse to the symmetric algebra $S^*(V)$, i.e. the permutation-invariant part of the tensor algebra of $V$. The permutation-equivariant quantum K-theory is a work in progress, and many aspects exist only in the outline, while other are open. For example, the all-genera quantum K-theory of the point target space (that is, the theory of representations of symmetric groups in sheaf cohomology over Deligne-Mumford spaces) in genus 0 can be solved by using the general machinery, in its toy version can be handled by bare hands (using Kapranov's description of $\overline{M}_{0,n}$), and in all genera should conjecturally lead to a finite-difference counterpart of the KdV-hierarchy. In the lectures, I intend to oscillate between these modes: illustrate the "bare hands" approach, introduce the general machinery, and outline open problems. END:VEVENT BEGIN:VEVENT DTSTART:20150701T160000 DTEND:20150701T164500 DTSTAMP:20150630T150000Z UID:aa7a177599b6e496985ad4e94e52dcb6@cgp.ibs.re.kr SUMMARY:(The 1st talk) Developing simulation codes on super-compute LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kab Seok Kang (Max-Planck-Institut fuer Plasmaphysik)\n\nEvent: High Performance supercomputation :theory and application\n\nAbstract: Numerical simulation is an essential tool to research on various areas. To develop simulation codes, developers consider the model which may be presented by partial differential equations (PDE), its discretizations, and solution methods of resulting systems. In this talk, I will consider the numerical methods for PDE based simulation which are developing and include discretization methods and linear and nonlinear solvers. I will focus on what have to be considered to develop simulation codes on modern high performance computers (super-computer, HPC). Also, I will consider multigrid and domain decomposition methods which are solvers to fit modern HPC END:VEVENT BEGIN:VEVENT DTSTART:20150701T170000 DTEND:20150701T174500 DTSTAMP:20150630T150000Z UID:9523025d5d5d527032abab7f1bcf9ed7@cgp.ibs.re.kr SUMMARY:(The 2nd talk) Modern super-computer, Optimization, and HLST LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kab Seok Kang (Max-Planck-Institut fuer Plasmaphysik)\n\nEvent: High Performance supercomputation :theory and application\n\nAbstract: Optimization the code is an essential part of developing simulation code and related to computer architectures. Current and future computer architectures are multi-core, multi-node, and heterogeneous and code developers have to aware them to develop relevant simulation codes. Due to complexity of the high performance computer (HPC), collaboration of applicationist, mathematician, and computer scientist is essentially needed. In this talk, I will consider architecture of the modern HPC, parallelizations, and optimization issues. As an example of collaboration, I will introduce the HLST team in EUROfusion and their efforts in developing simulation codes for fusion energy. END:VEVENT BEGIN:VEVENT DTSTART:20150702T163000 DTEND:20150702T180000 DTSTAMP:20150701T150000Z UID:80b675719095851dc47ff09ee3ce9abd@cgp.ibs.re.kr SUMMARY:Asymptotic base loci via Okounkov body LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: One can associate the Okounkov body to a pseudoeffective divisor on a smooth projective variety with respect to an admissible flag. Using the Okounkov bodies, I present a way to recover the asymptotic base loci, which play a central role in the study of asymptotic behaviors of divisors. As a byproduct, we obtain new nefness and ampleness criteria of divisors in terms of Okounkov bodies. This is joint work with Sung Rak Choi, Yoonsuk Hyun, and Joonyeong Won. END:VEVENT BEGIN:VEVENT DTSTART:20150706T100000 DTEND:20150706T105000 DTSTAMP:20150705T150000Z UID:1bec9531882d100a244f591a8dc6d5be@cgp.ibs.re.kr SUMMARY:Floer homology for 3 manifolds with boundary I LOCATION:POSTECH DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: There are two versions of Floer homology. One is in symplectic geometry and uses the moduli space of perturbed pseudo-holomorphic curve equation. The other is in gauge theory and uses the moduli spaces of solutions of various kinds of the equations appearing in Gauge theory, typically the ASD equation. When one studies gauge theory of 3 manifolds with boundary times real line it is know that two versions are mixed up. In the case we consider ASD equation in gauge theory side, we need to combine it with the study of holomorphic curves to the moduli space of flat connections on surfaces. Several proposal were made in 1990's by various people, how we do it to obtain Floer homology for 3 manifolds with boundary. In this talk I will explain how we can prove conjectures (plus alpha) which I formulated in 1990's, which is a particular version of such projects. END:VEVENT BEGIN:VEVENT DTSTART:20150706T110000 DTEND:20150706T115000 DTSTAMP:20150705T150000Z UID:a19a19e02a9b39d0d1222d7504f4264b@cgp.ibs.re.kr SUMMARY:The derived Maurer-Cartan locus LOCATION:POSTECH DESCRIPTION:Speaker: Ezra Getzler\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: The derived Maurer-Cartan locus of a differential graded Lie algebra L is the differential graded scheme whose function algebra is the Chevalley-Eilenberg complex of the truncation of L in positive degrees. In this talk, I discuss an alternative realization of the derived Maurer-Cartan locus as a cosimplicial scheme, which is grouplike in the sense of Bousfield and Kan, and hence cofibrant. END:VEVENT BEGIN:VEVENT DTSTART:20150706T140000 DTEND:20150706T145000 DTSTAMP:20150705T150000Z UID:4acf46e4ec441c61e9288866745d0444@cgp.ibs.re.kr SUMMARY:Combinatorial approach fo Fukaya categories of surfaces I LOCATION:POSTECH DESCRIPTION:Speaker: Mikhail Kapranov\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: The Fukaya category of a symplectic manifold is a sophisticated analytic object involving counting instantons (pseudo-holomorphic disks). It was suggested by Kontsevich that for a certain kinds of manifolds one can pass to the instanton-free limit obtaining a more combinatorial but still very meaningful object. In these lectures, based on joint works and projects with T. Dyckerhoff, V. Schechtman and Y. Soibelman, I will explain how this approach can be implemented for punctured surfaces. This is based on homotopy theory of dg-categories which will be reviewed. The approximate division of material is as follows. (1) The two-dimensional symmetry of homological algebra. Surface interpretation of diagrams of exact triangles in triangulated categories. Dg-enhancements of triangulated categories. The Morita model structure on the category of dg-categories. END:VEVENT BEGIN:VEVENT DTSTART:20150706T095000 DTEND:20150706T100000 DTSTAMP:20150705T150000Z UID:ad48c0becf980692aee6df888a6dd8fd@cgp.ibs.re.kr SUMMARY:Opening LOCATION:POSTECH DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150706T153000 DTEND:20150706T162000 DTSTAMP:20150705T150000Z UID:9ee809391a09b2113d1235b2f554e66d@cgp.ibs.re.kr SUMMARY:Index and determinant of n-tuples of commuting operators LOCATION:POSTECH DESCRIPTION:Speaker: Ryszard Nest\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: Suppose that $A = (A_1, ..., A_n)$ is an n-tuple of commuting operators on a Hilbert space $f = (f_1, . . . , f_n)$ and $g$ is an $(n+1)$-tuple of functions holomorphic in a neighbourhood of the (Taylor) spectrum of A. The n-tuple of operators $f(A) = (f_1(A_1, . . . , A_n), . . . , f_n(A_1, . . . , A_n))$ give rise to a complex $K(f(A), H)$, its so called Koszul complex, which is Fredholm whenever $f^{-1}(0)$ does not intersect the essential spectrum of the n-tuple A.Given that f satisfies the above condition, we will give a local formulae for the index of $K(f(A), H)$ and the relative determinant of $g(A)$ acting on $K(f(A), H)$.The index formula is a generalisation of the fact that the winding number of a continuous nowhere zero function f on the unit circle is, in the case when it has a holomorphic extension $\tilde f$ to the interior of the disc, equal to the number of zero’s of $\tilde f$ counted with multiplicity. The explicit local formula for the relative determinant of $g(A)$ gives, in particular, an extension of the Deligne’s formula for the Tate tame symbol to, in general, singular complex curves. This is joint work with Jens Kaad. END:VEVENT BEGIN:VEVENT DTSTART:20150706T163000 DTEND:20150706T172000 DTSTAMP:20150705T150000Z UID:8c8b4ff7b3eb0c2e7057f313dc7f85d5@cgp.ibs.re.kr SUMMARY:Algebraic models of local period maps and Yukawa coupling LOCATION:POSTECH DESCRIPTION:Speaker: Marco Manetti\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: We describe some L-infinity model for the local period map of a compact Kaehler manifold. Application includes the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology; as a byproduct we obtain an interpretation in the framework of (derived) deformation theory of the Yukawa coupling. Joint work with R. Bandiera (Roma). END:VEVENT BEGIN:VEVENT DTSTART:20150707T100000 DTEND:20150707T105000 DTSTAMP:20150706T150000Z UID:084f4e67944dfc56daea04edeeca41ab@cgp.ibs.re.kr SUMMARY:Conformal Bootstrap, Hyperbolic Quantum Geometry and Holography I LOCATION:POSTECH DESCRIPTION:Speaker: Herman Verlinde\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: In these lectures, I will explain the formal structure of 2D conformal field theory and its relation with hyperbolic quantum geometry. I will describe how the CFT correlation functions decompose into holomorphic conformal blocks, and write the conformal bootstrap equations that express crossing symmetry. I will then show that the same formal structure arises from quantizing the Teichmuller space of constant curvature metrics on a Riemann surface with marked points. This formal structure is captured by the special quantum group Uq(SL2). Finally, I will explain why the R-matrix of the quantum group is in fact equal to the exact scattering matrix of point particles near a black hole geometry in 2+1-D anti-de Sitter space time. This match provides a mathematically precise realization of the holographic AdS/CFT dictionary. I will end with an overview of further recent progress and will list some future directions. END:VEVENT BEGIN:VEVENT DTSTART:20150707T110000 DTEND:20150707T115000 DTSTAMP:20150706T150000Z UID:b2888cc7a4dec6633a051513b80dd35e@cgp.ibs.re.kr SUMMARY:Semiorthogonal decompositions of the derived category of W-equivariant sheaves LOCATION:POSTECH DESCRIPTION:Speaker: Alexander Polishchuk\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: In these lectures, I will explain the formal structure of 2D conformal field theory and its relation with hyperbolic quantum geometry. I will describe how the CFT correlation functions decompose into holomorphic conformal blocks, and write the conformal bootstrap equations that express crossing symmetry. I will then show that the same formal structure arises from quantizing the Teichmuller space of constant curvature metrics on a Riemann surface with marked points. This formal structure is captured by the special quantum group Uq(SL2). Finally, I will explain why the R-matrix of the quantum group is in fact equal to the exact scattering matrix of point particles near a black hole geometry in 2+1-D anti-de Sitter space time. This match provides a mathematically precise realization of the holographic AdS/CFT dictionary. I will end with an overview of further recent progress and will list some future directions. END:VEVENT BEGIN:VEVENT DTSTART:20150707T140000 DTEND:20150707T145000 DTSTAMP:20150706T150000Z UID:16d8bdb849a8cd49a1809d5df18b51ed@cgp.ibs.re.kr SUMMARY:Floer homology for 3 manifolds with boundary II LOCATION:POSTECH DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: There are two versions of Floer homology. One is in symplectic geometry and uses the moduli space of perturbed pseudo-holomorphic curve equation. The other is in gauge theory and uses the moduli spaces of solutions of various kinds of the equations appearing in Gauge theory, typically the ASD equation. When one studies gauge theory of 3 manifolds with boundary times real line it is know that two versions are mixed up. In the case we consider ASD equation in gauge theory side, we need to combine it with the study of holomorphic curves to the moduli space of flat connections on surfaces. Several proposal were made in 1990's by various people, how we do it to obtain Floer homology for 3 manifolds with boundary. In this talk I will explain how we can prove conjectures (plus alpha) which I formulated in 1990's, which is a particular version of such projects. END:VEVENT BEGIN:VEVENT DTSTART:20150707T153000 DTEND:20150707T162000 DTSTAMP:20150706T150000Z UID:374cf60bcae93414df57b2d210249d64@cgp.ibs.re.kr SUMMARY:Deforming holomorphic Chern-Simons at large N LOCATION:POSTECH DESCRIPTION:Speaker: Si Li\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: We describe the universal deformation of holomorphic Chern-Simons theory in the large N by Kodaira-Spencer gravity on Calabi-Yau background. We construct its quantization in the BV formalism via deformation theory, which leads to a mathematical realization of B-twisted open-closed string field theory. This is joint work with K. Costello. END:VEVENT BEGIN:VEVENT DTSTART:20150707T163000 DTEND:20150707T172000 DTSTAMP:20150706T150000Z UID:bc84b5c8b4b766975871f8a010127932@cgp.ibs.re.kr SUMMARY:Poster Session LOCATION:CGP Main Hall DESCRIPTION:Speaker: \n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150708T100000 DTEND:20150708T105000 DTSTAMP:20150707T150000Z UID:7ec3d89ec0b30581ddd0c99fbc0b2a33@cgp.ibs.re.kr SUMMARY:Combinatorial approach fo Fukaya categories of surfaces II LOCATION:POSTECH DESCRIPTION:Speaker: Mikhail Kapranov\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: The Fukaya category of a symplectic manifold is a sophisticated analytic object involving counting instantons (pseudo-holomorphic disks). It was suggested by Kontsevich that for a certain kinds of manifolds one can pass to the instanton-free limit obtaining a more combinatorial but still very meaningful object. In these lectures, based on joint works and projects with T. Dyckerhoff, V. Schechtman and Y. Soibelman, I will explain how this approach can be implemented for punctured surfaces. This is based on homotopy theory of dg-categories which will be reviewed. The approximate division of material is as follows. (2) The Waldhausen space and matrix factorizations.The Waldhausen construction in algebraic K-theory. Its extension to (pre)triangulated categories. The cyclic nature of the Waldhausen construction for a 2-periodic category. Interpretation via matrix factorizations. END:VEVENT BEGIN:VEVENT DTSTART:20150708T110000 DTEND:20150708T115000 DTSTAMP:20150707T150000Z UID:c9bc5b72107abcec42cbd447c1a16f6a@cgp.ibs.re.kr SUMMARY:Conformal Bootstrap, Hyperbolic Quantum Geometry and Holography II LOCATION:POSTECH DESCRIPTION:Speaker: Herman Verlinde\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: In these lectures, I will explain the formal structure of 2D conformal field theory and its relation with hyperbolic quantum geometry. I will describe how the CFT correlation functions decompose into holomorphic conformal blocks, and write the conformal bootstrap equations that express crossing symmetry. I will then show that the same formal structure arises from quantizing the Teichmuller space of constant curvature metrics on a Riemann surface with marked points. This formal structure is captured by the special quantum group Uq(SL2). Finally, I will explain why the R-matrix of the quantum group is in fact equal to the exact scattering matrix of point particles near a black hole geometry in 2+1-D anti-de Sitter space time. This match provides a mathematically precise realization of the holographic AdS/CFT dictionary. I will end with an overview of further recent progress and will list some future directions. END:VEVENT BEGIN:VEVENT DTSTART:20150709T100000 DTEND:20150709T105000 DTSTAMP:20150708T150000Z UID:691e54c14a7577a1cd67dab4626d415f@cgp.ibs.re.kr SUMMARY:Floer homology for 3 manifolds with boundary III LOCATION:POSTECH DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: There are two versions of Floer homology. One is in symplectic geometry and uses the moduli space of perturbed pseudo-holomorphic curve equation. The other is in gauge theory and uses the moduli spaces of solutions of various kinds of the equations appearing in Gauge theory, typically the ASD equation. When one studies gauge theory of 3 manifolds with boundary times real line it is know that two versions are mixed up. In the case we consider ASD equation in gauge theory side, we need to combine it with the study of holomorphic curves to the moduli space of flat connections on surfaces. Several proposal were made in 1990's by various people, how we do it to obtain Floer homology for 3 manifolds with boundary. In this talk I will explain how we can prove conjectures (plus alpha) which I formulated in 1990's, which is a particular version of such projects. END:VEVENT BEGIN:VEVENT DTSTART:20150709T110000 DTEND:20150709T115000 DTSTAMP:20150708T150000Z UID:c60a1102d80d34e4c828676bba96c169@cgp.ibs.re.kr SUMMARY:Sheaf of categories and applications LOCATION:POSTECH DESCRIPTION:Speaker: Ludmil Katzarkov\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: We attempt to build a correspondence between of sheaf of categories and nonabelian Hodge theory. END:VEVENT BEGIN:VEVENT DTSTART:20150709T140000 DTEND:20150709T145000 DTSTAMP:20150708T150000Z UID:0f094403a672643cfbffb4bfc0e56402@cgp.ibs.re.kr SUMMARY:Conformal Bootstrap, Hyperbolic Quantum Geometry and Holography III LOCATION:POSTECH DESCRIPTION:Speaker: Herman Verlinde\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: In these lectures, I will explain the formal structure of 2D conformal field theory and its relation with hyperbolic quantum geometry. I will describe how the CFT correlation functions decompose into holomorphic conformal blocks, and write the conformal bootstrap equations that express crossing symmetry. I will then show that the same formal structure arises from quantizing the Teichmuller space of constant curvature metrics on a Riemann surface with marked points. This formal structure is captured by the special quantum group Uq(SL2). Finally, I will explain why the R-matrix of the quantum group is in fact equal to the exact scattering matrix of point particles near a black hole geometry in 2+1-D anti-de Sitter space time. This match provides a mathematically precise realization of the holographic AdS/CFT dictionary. I will end with an overview of further recent progress and will list some future directions. END:VEVENT BEGIN:VEVENT DTSTART:20150709T153000 DTEND:20150709T162000 DTSTAMP:20150708T150000Z UID:62a2bff0ac4143442efa35538bb9d66b@cgp.ibs.re.kr SUMMARY:Algebraic proofs of degenerations of Hodge-de Rham complexes LOCATION:POSTECH DESCRIPTION:Speaker: Andrei Caldararu\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: Algebraic proofs of degenerations of Hodge-de Rham complexes END:VEVENT BEGIN:VEVENT DTSTART:20150709T163000 DTEND:20150709T172000 DTSTAMP:20150708T150000Z UID:a389792c15fb8abe3642c8a47a9e7145@cgp.ibs.re.kr SUMMARY:Round Table Discussion LOCATION:POSTECH DESCRIPTION:Speaker: \n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150710T100000 DTEND:20150710T105000 DTSTAMP:20150709T150000Z UID:2af23014c10e1c1e39fac8d6e84648e9@cgp.ibs.re.kr SUMMARY:Combinatorial approach fo Fukaya categories of surfaces III LOCATION:POSTECH DESCRIPTION:Speaker: Mikhail Kapranov\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: The Fukaya category of a symplectic manifold is a sophisticated analytic object involving counting instantons (pseudo-holomorphic disks). It was suggested by Kontsevich that for a certain kinds of manifolds one can pass to the instanton-free limit obtaining a more combinatorial but still very meaningful object. In these lectures, based on joint works and projects with T. Dyckerhoff, V. Schechtman and Y. Soibelman, I will explain how this approach can be implemented for punctured surfaces. This is based on homotopy theory of dg-categories which will be reviewed. The approximate division of material is as follows. (3) Perverse Schobers (categorified perverse sheaves) as coefficient data for Fukaya categories.Perverse sheaves and their quiver descriptions. Categorification of quiver descriptions. Perverse Schobers on a disk and spherical functors. Perverse Schobers on surfaces in terms of gluing of several spherical functors, Categorification of the sheaf of cohomology with support. END:VEVENT BEGIN:VEVENT DTSTART:20150710T110000 DTEND:20150710T115000 DTSTAMP:20150709T150000Z UID:c61aa3c01cfbde4b4626e37b57894895@cgp.ibs.re.kr SUMMARY:On the Riemann-Hilbert correspondence for irregular holonomic D-modules LOCATION:POSTECH DESCRIPTION:Speaker: Andrea D'Agnolo\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: The problem of describing irregular ordinary differential equations in geometrical terms has been standing for a long time.In a joint work with Masaki Kashiwara, we prove a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular. The construction of our target category is based on the theory of ind-sheaves by Kashiwara-Schapira and is influenced by Tamarkin's work on symplectic geometry. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya.In this talk, I will present the irregular Riemann-Hilbert correspondence and show how Stokes phenomena can be decribed in a purely topological way. END:VEVENT BEGIN:VEVENT DTSTART:20150710T140000 DTEND:20150710T145000 DTSTAMP:20150709T150000Z UID:1abc3cb13ee4e88207bd2cc276742566@cgp.ibs.re.kr SUMMARY:Enriched infinity-categories LOCATION:POSTECH DESCRIPTION:Speaker: Vladimir Hinich\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: We propose a notion of infinity-category enriched over arbitrary (=not necessarily cartesian) monoidal infinity-category with colimits. In case the monoidal structure on the infinity category is cartesian, our definition is equivalent to that based on simplicial objects with Segal-type condition. END:VEVENT BEGIN:VEVENT DTSTART:20150710T153000 DTEND:20150710T162000 DTSTAMP:20150709T150000Z UID:d92b88f0891210cc35e929ba323bca6a@cgp.ibs.re.kr SUMMARY:Categorical Interpretation of flops LOCATION:POSTECH DESCRIPTION:Speaker: Alexey Bondal\n\nEvent: Geometry and Physics XIII - Derived Geometry\n\nAbstract: A homological interpretation of the Minimal Model Program (MMP) in Birational Geometry is based on the idea that MMP is about "minimization" of the derived category of coherent sheaves on a variety, when the variety is minimized inside its birational class. We expect that if variety X allows a divisorial contraction or a flip X → Y, then the derived category of X has a semiorthogonal decomposition and one component of this decomposition is equivalent to the derived category of Y. Minimizing the birational model should have the categorical incarnation in the chopping off semiorthogonal components of the derived category. A minimal model is expected to be a representative in the birational class of a variety whose derived category does not allow semiorthogonal components equivalent to the derived category of a variety birationally equivalent to X.Since the minimal model is not unique in dimension higher than 2, MMP also considers birational transformations, called flops, that link various minimal models. The derived categories are conjectured to be equivalent under flops.We will describe the algebra of various functors related to flops of relative dimension 1. In particular, we give a description of the relevant auto-equivalences in terms of spherical twists and give a categorical description of such flops by means t-structures and torsion pairs. END:VEVENT BEGIN:VEVENT DTSTART:20150812T160000 DTEND:20150812T180000 DTSTAMP:20150811T150000Z UID:b01a9134c5012b3b8d8c68d9e73f5d29@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence and A infinity functor (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence and A infinity functor\n\nAbstract: Wehrheim-Woodward proposed a plan to associate $A_{\infty}$ functor to a Lagrangian correspondence between symplectic manifolds (that is nothing but a Lagrangian submanifold of the product) and realized it in case everlything is monotone and all the Lagrangian submanifolds involved are embedded. Its generalization is now studied by Bottman-Wehrheim. Those works are based on degeneration analysis called strip shrinking and figure eight bubble. Lekili-Lipyanskiy found a way to bypass degeneration analysis in the monotone case + alpha. In this talk I will explain that we can work the project out in complete generality (in the compact case) without using degeneration analysis but using immersed Lagrangian Floer theory of Akaho-Joyce and homological algebra of A infinity category. Relation to open-closed map and to Künneth theorem will also be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150814T160000 DTEND:20150814T180000 DTSTAMP:20150813T150000Z UID:ecae103a3559c49fbbc94453135d5d75@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence and A infinity functor (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence and A infinity functor\n\nAbstract: Wehrheim-Woodward proposed a plan to associate $A_{\infty}$ functor to a Lagrangian correspondence between symplectic manifolds (that is nothing but a Lagrangian submanifold of the product) and realized it in case everlything is monotone and all the Lagrangian submanifolds involved are embedded. Its generalization is now studied by Bottman-Wehrheim. Those works are based on degeneration analysis called strip shrinking and figure eight bubble. Lekili-Lipyanskiy found a way to bypass degeneration analysis in the monotone case + alpha. In this talk I will explain that we can work the project out in complete generality (in the compact case) without using degeneration analysis but using immersed Lagrangian Floer theory of Akaho-Joyce and homological algebra of A infinity category. Relation to open-closed map and to Künneth theorem will also be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150817T160000 DTEND:20150817T180000 DTSTAMP:20150816T150000Z UID:96335ce69afe81d8a5ecafbbb36549f7@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence and A infinity functor (III) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence and A infinity functor\n\nAbstract: Wehrheim-Woodward proposed a plan to associate $A_{\infty}$ functor to a Lagrangian correspondence between symplectic manifolds (that is nothing but a Lagrangian submanifold of the product) and realized it in case everlything is monotone and all the Lagrangian submanifolds involved are embedded. Its generalization is now studied by Bottman-Wehrheim. Those works are based on degeneration analysis called strip shrinking and figure eight bubble. Lekili-Lipyanskiy found a way to bypass degeneration analysis in the monotone case + alpha. In this talk I will explain that we can work the project out in complete generality (in the compact case) without using degeneration analysis but using immersed Lagrangian Floer theory of Akaho-Joyce and homological algebra of A infinity category. Relation to open-closed map and to Künneth theorem will also be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150820T160000 DTEND:20150820T180000 DTSTAMP:20150819T150000Z UID:274793906b959075cf5e31b17e043cfe@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence and A infinity functor (IV) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence and A infinity functor\n\nAbstract: Wehrheim-Woodward proposed a plan to associate $A_{\infty}$ functor to a Lagrangian correspondence between symplectic manifolds (that is nothing but a Lagrangian submanifold of the product) and realized it in case everlything is monotone and all the Lagrangian submanifolds involved are embedded. Its generalization is now studied by Bottman-Wehrheim. Those works are based on degeneration analysis called strip shrinking and figure eight bubble. Lekili-Lipyanskiy found a way to bypass degeneration analysis in the monotone case + alpha. In this talk I will explain that we can work the project out in complete generality (in the compact case) without using degeneration analysis but using immersed Lagrangian Floer theory of Akaho-Joyce and homological algebra of A infinity category. Relation to open-closed map and to Künneth theorem will also be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150804T160000 DTEND:20150804T180000 DTSTAMP:20150803T150000Z UID:41ed05ab728ae97aa557ddd4454f0b65@cgp.ibs.re.kr SUMMARY:Minimal Lagrangian surfaces in $CP^2$ via integrable system methods LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hui Ma\n\nEvent: Seminar 2015\n\nAbstract: The construction of minimal Lagrangian surfaces in the complex projective plane $CP^2$ gained much interest in differential geometry and mathematical physics during the past twenty years. In this talk I will discuss the contributions of integrable system methods, mainly the construction of minimal Lagrangian tori, minimal Lagrangian equivariant surfaces, etc. END:VEVENT BEGIN:VEVENT DTSTART:20150806T160000 DTEND:20150806T180000 DTSTAMP:20150805T150000Z UID:ce792c621621f8c8dd96a4db2af8ea5e@cgp.ibs.re.kr SUMMARY:On Gauss images of isoparametric hypersurfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hui Ma\n\nEvent: CGP Seminar 2015\n\nAbstract: The Gauss image of an isoparametric hypersurface in the unit sphere is a compact minimal Lagrangian submanifold embedded in the complex hyperquadric. In this talk, we will discuss geometric and topological properties of Gauss images. In particular, we will discuss their Hamiltonian stability. The talk is based on the joint work with Professor Y. Ohnita. END:VEVENT BEGIN:VEVENT DTSTART:20150825T155500 DTEND:20150825T164500 DTSTAMP:20150824T150000Z UID:1b03b521de99c77e33e088bbdec5207f@cgp.ibs.re.kr SUMMARY:Reaching ground state at positive temperature. LOCATION:POSTECH DESCRIPTION:Speaker: Renaud Leplaideur\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: The Thermodynamic formalism was imported in Dynamical Systems in the 70's by Sinai, Ruelle and Bowen. Given an observable function $\phi$ called potential, one marks out a measure called equilibrum state by using a variational principle. The maximized quantity is then called the pressure.This may be done for the one-parameter family of potential $\beta.\phi$ where $\beta$ denotes in Statistical Mechanics the inverse of the temperature.Then, if $\beta$ goes to $+\infty$, any accumulation point for the equilibrium state family is a $\phi$-maximizing measure, called ground state in Statistical Mechanics.Moreover, for "good" dynamical systems the pressure function, that is the pressure for $\beta.\phi$, is analytic.In these settings, we say that we have a phase transition if the pressure function stops to be analytic. Although analyticity is rare, we will explain why it is far from obvious to exhibit potentials with phase transition.Then, we shall show a machinery to exhibit potentials with freezing phase transition, which means that there exists a critical $\beta=\beta_c$ such that for every $\beta>\beta_c$ the equilibrium state is a ground state. END:VEVENT BEGIN:VEVENT DTSTART:20150827T130000 DTEND:20150827T135000 DTSTAMP:20150826T150000Z UID:84e9bc956e580e69ffac7fc135a066e7@cgp.ibs.re.kr SUMMARY:Legendrian singular links and singular connected sums LOCATION:POSTECH DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we can define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a kind of tangle replacement. This method provides a way to classify Legendrian singular links.This is a joint work with Y. Bae and S. Kim. END:VEVENT BEGIN:VEVENT DTSTART:20150824T110500 DTEND:20150824T115500 DTSTAMP:20150823T150000Z UID:4b9e14fa43b6ecf8208c1afcb360fed1@cgp.ibs.re.kr SUMMARY:The non-hyperbolicity of irrational invariant curves for conservative twist map. LOCATION:POSTECH DESCRIPTION:Speaker: Marie-Claude Arnaud\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: This is a joint work with Pierre Berger.We will prove that if a loop that is invariant by a $C^{1+\alpha}$ diffeomorphism of a surface carries a hyperbolic measure, then there is a periodic point in the loop. We will deduce different consequences for the essentiel curves that are invariant by a symplectic twist map f of the annulus, as the proof of half-part of the so-called"Greene criterion'', introduced by J.~M.~Greene in 1978: by using the residues of some minimizing periodic orbits, it is possible to detect if there exists an invariant curve with a given (irrational) rotation number for a given symplectic twist map . END:VEVENT BEGIN:VEVENT DTSTART:19700101T090000 DTEND:19700101T090000 DTSTAMP:19700101T000000Z UID:ecbc17323f06f0a791691d11f57bfb86@cgp.ibs.re.kr SUMMARY:Global existence of weak shocks past solid ramps LOCATION:POSTECH DESCRIPTION:Speaker: Myoungjean Bae\n\nEvent: \n\nAbstract: Ludwig Prandtl (1936) first employed the shock polar analysis to show that, when a steady supersonic flow impinges a solid wedge whose angle is less than a critical angle (i.e., the detachment angle), there are two possible configurations: the weak shock solution and the strong shock solution, and conjectured that the weak shock solution is physically admissible since it is the one observed experimentally. The fundamental issue of whether one or both of the strong and the weak shocks are physically admissible has been vigorously debated over several decades and has not yet been settled in a definite manner. In this talk, I address this longstanding open issue and present recent analysis to establish the stability theorem for steady weak shock solutions as the long- time asymptotics of unsteady flows for all the physical parameters up to the detachment angle for potential flow. This talk is based on joint work with Gui-Qiang G. Chen (Univ. of Oxford) and Mikhail Feldman(UW-Madison). END:VEVENT BEGIN:VEVENT DTSTART:20150828T154000 DTEND:20150828T163000 DTSTAMP:20150827T150000Z UID:4ec6149d284eb888d0551e1b341e51e6@cgp.ibs.re.kr SUMMARY:On the self-similar blow-up and the Liouville type results for the Euler equations LOCATION:POSTECH DESCRIPTION:Speaker: Dongho Chae\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: The question of spontaneous apparition of singularity(blow-up)/global regularity in the 3D incompressible Euler equations is among the most outstanding open problems in the partial differential equations. Similar problem for the 3D Navier-Stokes equations is listed on the seven millennium problems by the Clay Mathematics Institute. There are many numerical/physical evidences that if the finite time blow-up happens it is highly probable that it is of the self-similar type. In the case of the 3D Navier-Stokes equations, the question of self-similar blow-up is proposed by J. Leray in 1930,and answered negatively by Necas-Ruzicka-Sverak and Tsai. The crucial tool of their proof is the maximum principle, which is originated fromthe ellipticity nature of the corresponding self-similar equations. In the case of Euler equations, mainly due to the lack of the elliptic structure in the self-similar equations we need to develop new methods. in this talk we review theresult on this problem by myself, and a series of further developments on the subject later by myself and my collaborators until the very recent Liouville type/the unique continuation type results on the time periodic solutions of the self-similar Euler equations. END:VEVENT BEGIN:VEVENT DTSTART:20150827T155500 DTEND:20150827T164500 DTSTAMP:20150826T150000Z UID:71961c22ac954d0b23ac71f03b300323@cgp.ibs.re.kr SUMMARY:Homological mirror functors via counting polygons. LOCATION:POSTECH DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: We explain an elementary construction of a homological mirror symmetry functor, between symplectic geometry (Fukaya category) and complex geometry ( matrix factorization of a function). The formalism that we propose (joint work with H. Hong and S.C. Lau) uses a formal deformation theory of a Lagrangian L in a symplectic manifold. This formalism transforms Lagrangian submanifolds in a symplectic manifold to matrix factorizations of a mirror potential function W(L). We illustrate this in (real) surface examples, by computing matrix factorizations corresponding to curves (which are Lagrangians) in surfaces. If time permits, we will explain a non-commutative generalization of the functor to non-commutative Landau-Ginzburg models. END:VEVENT BEGIN:VEVENT DTSTART:20150824T143500 DTEND:20150824T152500 DTSTAMP:20150823T150000Z UID:aaddae286d06c7fc59d5610eac17c6bd@cgp.ibs.re.kr SUMMARY:Emergence of local flocking states in flocking models LOCATION:POSTECH DESCRIPTION:Speaker: Seung-Yeal Ha\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: In this talk, we present the asymptotic emergence of bi-cluster flocking configurations for flocking models with short-range communication weights for well-prepared initial configurations. For this, we derive a system of differential inequalities for the functionals that mea- sure the local spatial and velocity fluctuations and differences of local spatial and velocity averages. We then derive the upper bound of spatial fluctuations and the lower bound of the difference between local velocity averages. We explicitly present an admissible class of initial configurations leading to the asymptotic emergence of local-flocking configurations. This is a joint work between CAS group (Feimin Huang and Chunyin Jin) and SNU group (Junghee Cho and Dongnam Ko). END:VEVENT BEGIN:VEVENT DTSTART:20150827T170000 DTEND:20150827T175000 DTSTAMP:20150826T150000Z UID:c27383142bc4795c476b84b16a993227@cgp.ibs.re.kr SUMMARY:Toward a dynamical interpretation of Hamiltonian spectral invariants on surfaces. LOCATION:Science Bldg. II #105 DESCRIPTION:Speaker: Vincent Humilière\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Spectral invariants are real numbers associated in a canonical way to Hamiltonian functions on a symplectic manifold. These invariants are extremely useful in symplectic topology, but they remain somewhat mysterious. After introducing them and showing how useful they are, I will talk about some joint work with Frederic Le Roux and Sobhan Seyfaddini where we provide a dynamical interpretation of these invariants for autonomous Hamiltonians on surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20150828T110500 DTEND:20150828T115500 DTSTAMP:20150827T150000Z UID:cb262593047685b653d408fc8b8ec426@cgp.ibs.re.kr SUMMARY:Cartan-Fubini type extension theorems LOCATION:POSTECH DESCRIPTION:Speaker: Jun-Muk Hwang\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Cartan-Fubini type extension theorems give various settings where local structure-preserving maps can be extended to global holomorphic maps. They can be viewed as holomorphic generalizations of Liouville's theorem in conformal geometry. We will give an introductory survey of recent progress on this topic. END:VEVENT BEGIN:VEVENT DTSTART:20150824T100000 DTEND:20150824T105000 DTSTAMP:20150823T150000Z UID:6932dfb8648d62172ad77f12c5d02a8d@cgp.ibs.re.kr SUMMARY:Recent progress on the spectral theory of Neumann-Poincare operator and plasmon resonance LOCATION:POSTECH DESCRIPTION:Speaker: Hyeonbae Kang\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: The Neumann-Poincare (NP) operator is a boundary integral operator naturally arising when solving boundary value problem using layer potentials.Its study goes back to Neumann and Poincare as the name suggests. It was the central object in the theory of singular integral operators in the last century. Recently there is rapidly growing interest in the spectrum of NP operator in relation to resonance on plasmonic materials and cloaking by anomalous localized resonance. In this talk we review recent developments in the spectral theory of NP operator and applications. END:VEVENT BEGIN:VEVENT DTSTART:20150828T100000 DTEND:20150828T105000 DTSTAMP:20150827T150000Z UID:3f6597bed4d90ebc3b52fedf3de97d0f@cgp.ibs.re.kr SUMMARY:A vanishing theorem on fake projective planes with enough automorphisms LOCATION:POSTECH DESCRIPTION:Speaker: JongHae Keum\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X,2L)$ = 0 for all $i$ and for every ample line bundle $L$ with $L^2$ = 1. For every fake projective plane with automorphism group of order 9, we prove the same vanishing for every cubic root (and its twist by a 2-torsion) of the canonical bundle $K$. As an immediate consequence, there are exceptional sequences of length 3 on such fake projective planes. END:VEVENT BEGIN:VEVENT DTSTART:20150825T100000 DTEND:20150825T105000 DTSTAMP:20150824T150000Z UID:59b60a54dbab3d268ac49eef5ad53fb4@cgp.ibs.re.kr SUMMARY:Singularities of plurisubharmonic functions LOCATION:POSTECH DESCRIPTION:Speaker: Dano Kim\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Singularity of a plurisubharmonic(PSH) function can be measured in terms of its Lelong numbers, multiplier ideal sheaves, log-canonical thresholds and higher Lelong numbers. PSH functions can be regarded as 'flexible' objects compared to usual 'rigid' objects such as holomorphic functions. We will survey recent results, problems and examples on such PSH singularity. In particular, we will discuss Demailly approximation of PSH functions and continuity of higher Lelong numbers in the case of toric PSH functions. END:VEVENT BEGIN:VEVENT DTSTART:20150825T170000 DTEND:20150825T175000 DTSTAMP:20150824T150000Z UID:db314d86310e7e3dd0c32776cd6e4c5a@cgp.ibs.re.kr SUMMARY:Spatial heterogeneity and diffusion with non-constant steady states LOCATION:POSTECH DESCRIPTION:Speaker: Yong Jung Kim\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: It is spatial heterogeneity, but not nonlinearity, that gives nonconstant steady states. In this talk we consider diffusion operator which has a spatial heterogeneity arising naturally from biological or physical organisms. The starvation driven diffusion is of such a type. In fact many of biological species increase their dispersal rate at the place where starvation starts. To model such a behavior we need to understand how organisms measure the starvation and respond to it. END:VEVENT BEGIN:VEVENT DTSTART:20150825T143500 DTEND:20150825T152500 DTSTAMP:20150824T150000Z UID:e127a8f9316a02adc10fde6526629b78@cgp.ibs.re.kr SUMMARY:Contact geometry and the restricted three-body problem LOCATION:POSTECH DESCRIPTION:Speaker: Otto van Koert\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: We will give a brief survey of the history of the restricted three-body problem to motivate global surfaces of section, a tool that can be used to discretize a dynamical system. We then describe how techniques from contact geometry, such as holomorphic curves, can be used to construct such global surfaces of section. On the practical side, we will also go into some numerical results to visualize the return maps and the dynamics. END:VEVENT BEGIN:VEVENT DTSTART:20150827T100000 DTEND:20150827T105000 DTSTAMP:20150826T150000Z UID:e68135262576cf38ee2935811fa14f48@cgp.ibs.re.kr SUMMARY:Exceptional collections on Dolgachev surfaces associated with degenerations LOCATION:POSTECH DESCRIPTION:Speaker: Yongnam Lee\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Dolgachev surfaces are simply connected minimal elliptic surfaces with p_g=q=0 and of Kodaira dimension 1. These surfaces were constructed by logarithmic transformations of rational elliptic surfaces. Dolgachev surfaces can be also constructed via Q-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities based on the construction by Lee-Park. In this talk, some exceptional bundles and collections on Dolgachev surfaces associated with Q-Gorenstein smoothing will be constructed based on the idea of Hacking. Furthermore, in the case if Dolgachev surfaces were of type (2, 3), we describe the Picard group and present a numerical exceptional collection. This is a joint work with Yonghwa Cho. END:VEVENT BEGIN:VEVENT DTSTART:20150827T110500 DTEND:20150827T115500 DTSTAMP:20150826T150000Z UID:9fef14fe732dcbdd1d014a25ab65d2be@cgp.ibs.re.kr SUMMARY:Intersection forms of Riemannian surfaces LOCATION:POSTECH DESCRIPTION:Speaker: Daniel Massart\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Given a closed, oriented surface M, the algebraic intersection of closedcurves induces a symplectic form $Int(., .)$ on the first homology group of$M$. If $M$ is equipped with a Riemannian metric $g$, the first homology groupof $M$ inherits a norm, called the stable norm. We study the norm of thebilinear form $Int(., .)$, with respect to the stable norm, that is, the quantity$$K(M, g) = \sup_{α,β}\frac{Int(α, β)}{l_g(α)l_g(β)}$$where the supremum is taken over all closed geodesics $α$ and $β$, and $l_g$denotes the length with respect to the metric g. We ask three basic questions:• is it true that for almost every metric g, the supremum $K(M)$ isactually a maximum ?• is it possible to find asymptotic estimates for $K(M, g)$ when $g$ hascurvature $-1$, and goes to infinity in the moduli space ?• does $K(M, g)$ have a minimum when g ranges over the moduli spaceof curvature $-1$ metrics ? END:VEVENT BEGIN:VEVENT DTSTART:20150825T133000 DTEND:20150825T142000 DTSTAMP:20150824T150000Z UID:4091d3fb63fb0c72999f97ae4784d3dd@cgp.ibs.re.kr SUMMARY:Birational rigidity of Fano threefold hypersurfaces LOCATION:POSTECH DESCRIPTION:Speaker: Jihun Park\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: In 1979 Reid discovered the 95 families of K3 surfaces in three dimensional weighted projective spaces. After this, Fletcher, who was a Ph.D. student of Ried, discovered the 95 families of weighted Fano threefold hypersurfaces in his Ph.D. dissertation in 1988. These are quasi-smooth hypersurfaces of degrees $d$ with only terminal singularities in weighted projective spaces $\mathbb{P}(1, a_1, a_2, a_3, a_4)$, where $d=\sum a_i$. All Reid’s 95 families of K3 surfaces arises as anticanonical divisors in Fletcher’s 95 families of Fano threefolds. These Fano threefold hypersurfaces carry many fascinating properties. In my talk, I explain how to verify that all the quasi-smooth Fano threefold hypersurfaces in the 95 families are non-rational, which confirms the conjecture of Corti, Pukhlikov and Reid. Since the entire proof is very long and adopts various methods, I will focus on one or two interesting families out of the 95 families. END:VEVENT BEGIN:VEVENT DTSTART:20150828T133000 DTEND:20150828T142000 DTSTAMP:20150827T150000Z UID:999adb7b5e38d0badc129baa49cb4f95@cgp.ibs.re.kr SUMMARY:FABER-KRAHN INEQUALITIES IN SHARP QUANTITATIVE FORM LOCATION:POSTECH DESCRIPTION:Speaker: Guido de Philippis\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: In this talk we present a sharp quantitative improvement of the celebrated FaberKrahninequality. The latter asserts that balls uniquely minimize the first eigenvalueof the Dirichlet-Laplacian, among sets with given volume. We prove that indeedmore can be said: the difference between the first eigenvalue $\lambda(\Omega)$ of a set $\Omega$ andthat of a ball of the same volume controls the deviation from spherical symmetryof $\Omega$. Moreover, such a control is the sharpest possible. This settles a conjectureby Bhattacharya, Nadirashvili and Weitsman. END:VEVENT BEGIN:VEVENT DTSTART:20150825T110500 DTEND:20150825T115500 DTSTAMP:20150824T150000Z UID:f8c1a8aa07db7e96eca15d3c2cbb2404@cgp.ibs.re.kr SUMMARY:Ergodic Theorems for foliations by Riemann.Surfaces. LOCATION:POSTECH DESCRIPTION:Speaker: Nessim Sibony\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: I will discuss a general ergodic Theorem for Foliations, with singularities, by Riemann Surfaces. In a second part, I will discuss several unique ergodicity results, for foliations by Riemann Surfaces in the complex projective space.The talk is based on joint works with, T.C Dinh, V.A Nguyen and J.E Fornaess. END:VEVENT BEGIN:VEVENT DTSTART:20150828T143500 DTEND:20150828T152500 DTSTAMP:20150827T150000Z UID:a0802a58cd3fef41fd20029b00e3e87f@cgp.ibs.re.kr SUMMARY:A quasi-periodic Frenkel_Kontorova model LOCATION:POSTECH DESCRIPTION:Speaker: Philippe Thieullen\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: A periodic Frenkel-Kontorova model describes configurations of a chain of atoms at the lowest energy in a periodic environment. In a joint work with E. Garibaldi and S. Petite, we extend the Frenkel-Kontorova model to quasi-crystal models. The space of environments is given by a minimal and uniquely ergodic R-flow possessing a transverse flow box of locally constant height. If the external potential is locally transversally constant, we show the existence of calibrated configurations (a stronger notion than minimizing congiguration), that is configurations of a chain of atoms at the lowest energy, for every environments. END:VEVENT BEGIN:VEVENT DTSTART:20150827T143500 DTEND:20150827T152500 DTSTAMP:20150826T150000Z UID:d28a49ff92cb645d9cb675b8626ee0f7@cgp.ibs.re.kr SUMMARY:Symplectic homegenization, towards a non-convex Aubry-Mather theory. LOCATION:POSTECH DESCRIPTION:Speaker: Nicolas Vichery\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: "In this talk, we will review applications of the homogenization of lagrangian spectral invariants in cotangent bundle as studied previously in a joint work with Monzner and Zapolsky. This can be seen as an extension of Viterbo's"symplectic homogenization" process in the cotangent bundle of tori. We will then stress our attention on links with Aubry-Mather theory, especially rotation vector of some invariant measures and subdifferential of the homogenized hamiltonian." END:VEVENT BEGIN:VEVENT DTSTART:20150826T100000 DTEND:20150826T105000 DTSTAMP:20150825T150000Z UID:26c21a5749ee68abe1fcc49e2476faf6@cgp.ibs.re.kr SUMMARY:Weak KAM and Aubry Mather theory for weakly coupled systems of Hamilton-Jacobi equations. LOCATION:POSTECH DESCRIPTION:Speaker: Maxime Zavidovique\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: We will explain what are weakly coupled systems of Hamilton-Jacobi equations and how certain results from classical weak KAM theory persist in this setting. In particular, we will explain what is the Aubry set and how it is characterized in terms of subsolutions. Finally, we will present in some cases a representation formula for the evolutionary equation and discuss its implications. This is based on joint works with Andrea Davini and Antonio Siconolfi. END:VEVENT BEGIN:VEVENT DTSTART:20150826T110500 DTEND:20150826T115500 DTSTAMP:20150825T150000Z UID:ef8e0c823c40b79136da9cfb4252f716@cgp.ibs.re.kr SUMMARY:Moments of orthogonal polynomials and its applications LOCATION:POSTECH DESCRIPTION:Speaker: Jiang Zeng\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: In this talk I will discuss some recent interplays between orthogonal polynomials and combinatorics.According to the theory developped in the 1980's by Flajolet and Viennot many classical combinatorial sequences such as the number of perfect matchings, derangements, and other weighted permutation problems are the moments of classical orthogonoal polynomials. Over the past decade several $q$-analogues of the combinatorial counterparts have been obtained in the $q$-Askey-Wilson scheme. I will explain how to use the method of separation of variables to solve the linearization coefficients problems in the light of recent developpements of their moments.More important is that the separation of variables technique leads naturally to integral representations of combinatorial numbers where the integrand contains a product of one or more types of orthogonal polynomials, which thereby confirms the positivity of such an integral. Finally I will show the recent connection of Carlitz's $q$-Bernoulli numbers to moments of big $q$-Jacobi polynomials, which permits to derive nice factorisations of Hankel determinants of $q$-Bernoulli numbers, and continued fractions for their generating series. END:VEVENT BEGIN:VEVENT DTSTART:20150731T140000 DTEND:20150731T153000 DTSTAMP:20150730T150000Z UID:eacc3e0bb89b203536a2f9539b6d98b0@cgp.ibs.re.kr SUMMARY:Singular Kahler-Einstein metrics of small angles LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jesus Martinez Garcia\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: The existence of a Kahler-Einstein metric on a Fano variety is equivalent to the algebro-geometric concept of K-stability. However K-stability is very difficult to test. For those Fano varieties which are not K-stable, we can define a singular Kahler-Einstein metric known as Kahler-Einstein metric with edge singularities, depending on a parameter in (0,1]. These metrics also have a reformulation in terms of log K-stability. It is well known that a smooth del Pezzo surface admits a Kahler-Einstein metric if and only if it is not the blow-up of the plane in one or two points. However they always admit a Kahler-Einstein edge metric. In this talk, after introducing all these topics, I explain how we can use birational geometry and log canonical thresholds to find Kahler-Einstein edge metrics on all del Pezzo surfaces. This is joint work with Ivan Cheltsov. END:VEVENT BEGIN:VEVENT DTSTART:20150811T160000 DTEND:20150811T180000 DTSTAMP:20150810T150000Z UID:be2a7230ce1fa71029344dbfddf8ec7b@cgp.ibs.re.kr SUMMARY:Semi-global invariants for focus-focus singularities (following Vu Ngoc San) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Wonmo Lee\n\nEvent: Seminar 2015\n\nAbstract: Focus-focus singularities occur frequently on completely integrable Hamiltonian systems.Following V.N. San's paper, I will explain his proof on the semi-global classification, up to symplectic equivalence, of singular Lagrangian foliation given by a completely integrable Hamiltonian system of a symplectic 4-manifold, in a full neighbourhood of a singular leaf of focus-focus type. END:VEVENT BEGIN:VEVENT DTSTART:20150813T160000 DTEND:20150813T180000 DTSTAMP:20150812T150000Z UID:edb2122dced5f0fd676774edee9810d1@cgp.ibs.re.kr SUMMARY:An affine quantum cohomology ring and periodic Toda lattice LOCATION:CGP Main Hall DESCRIPTION:Speaker: Leonardo Constantin Mihalcea\n\nEvent: CGP Seminar 2015\n\nAbstract: A theorem of B. Kim identified the relations of the quantum cohomology ring of the (generalized) flag manifolds with the conserved quantities for the Toda lattice. There were expectations that a similar statement exists, relating a previously undefined quantum cohomology ring for the affine flag manifolds to the periodic Toda lattice. I will show how to construct such a quantum cohomology ring, which deforms the usual quantum cohomology ring and it depends on an additional affine quantum parameter. The construction uses the technique of "curve neighborhoods" of Schubert varieties, which were defined and studied earlier by the speaker in several joint works with A. Buch, P.E. Chaput, and N. Perrin. It turns out that the conserved quantities of the periodic Toda lattice give the ideal of relations in the new ring, at least in Lie types A-D and E6. The current project is joint with Liviu Mare. END:VEVENT BEGIN:VEVENT DTSTART:20150817T100000 DTEND:20150817T103000 DTSTAMP:20150816T150000Z UID:90373b2f03c3f1a32715281e43b3f333@cgp.ibs.re.kr SUMMARY:Circle packing - Graphs, Geometry, Groups from Gauss to Gromov I LOCATION:POSTECH DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150817T113000 DTEND:20150817T120000 DTSTAMP:20150816T150000Z UID:036cf6e4a89e6ed3689e4ea5c6129843@cgp.ibs.re.kr SUMMARY:Along came determinant I LOCATION:POSTECH DESCRIPTION:Speaker: Jaehyouk Lee\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150817T150000 DTEND:20150817T153000 DTSTAMP:20150816T150000Z UID:cec42dee40da0d1f850e8468da59dccf@cgp.ibs.re.kr SUMMARY:Algebraic structures of plane curves and matrix factorizations I LOCATION:POSTECH DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150818T113000 DTEND:20150818T120000 DTSTAMP:20150817T150000Z UID:d1decc2bf0dfc2673d6ae93bff0229f4@cgp.ibs.re.kr SUMMARY:Along came determinant II LOCATION:POSTECH DESCRIPTION:Speaker: Jaehyouk Lee\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150818T100000 DTEND:20150818T103000 DTSTAMP:20150817T150000Z UID:df156e6b1b7590935f5a413fb26877f7@cgp.ibs.re.kr SUMMARY:Circle packing - Graphs, Geometry, Groups from Gauss to Gromov II LOCATION:POSTECH DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150818T150000 DTEND:20150818T153000 DTSTAMP:20150817T150000Z UID:24910713c4dc4c8ccec1e11c5f0523d3@cgp.ibs.re.kr SUMMARY:Algebraic structures of plane curves and matrix factorizations II LOCATION:POSTECH DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150820T113000 DTEND:20150820T120000 DTSTAMP:20150819T150000Z UID:75ba777dd82ff303dbc471a8c75d64bf@cgp.ibs.re.kr SUMMARY:Along came determinant III LOCATION:POSTECH DESCRIPTION:Speaker: Jaehyouk Lee\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150820T100000 DTEND:20150820T103000 DTSTAMP:20150819T150000Z UID:8b76b802f399bce93a597706b0d90572@cgp.ibs.re.kr SUMMARY:Circle packing - Graphs, Geometry, Groups from Gauss to Gromov III LOCATION:POSTECH DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150820T150000 DTEND:20150820T153000 DTSTAMP:20150819T150000Z UID:bd270b48cee45abfe1cc87959dc129d1@cgp.ibs.re.kr SUMMARY:Algebraic structures of plane curves and matrix factorizations III LOCATION:POSTECH DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: 2015 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150824T155500 DTEND:20150824T164500 DTSTAMP:20150823T150000Z UID:c32e143e586b54637e2f3a47a7f2f981@cgp.ibs.re.kr SUMMARY:Global existence of weak shocks past solid ramps LOCATION:POSTECH DESCRIPTION:Speaker: Myoungjean Bae\n\nEvent: Korean French Conference in Mathematics\n\nAbstract: Ludwig Prandtl (1936) first employed the shock polar analysis to show that,when a steady supersonic flow impinges a solid wedge whose angle is less than a critical angle (i.e., the detachment angle), there are two possible configurations: the weak shock solution and the strong shock solution, and conjectured that the weak shock solution is physically admissible since it is the one observed experimentally. The fundamental issue of whether one or both of the strong and the weak shocks are physically admissible has been vigorously debated over several decades and has not yet been settled in a definite manner. In this talk, I address this longstanding open issue and present recent analysis to establish the stability theorem for steady weak shock solutions as the long- time asymptotics of unsteady flows for all the physical parameters up to the detachment angle for potential flow. This talk is based on joint work with Gui-Qiang G. Chen (Univ. of Oxford) and Mikhail Feldman(UW-Madison). END:VEVENT BEGIN:VEVENT DTSTART:20150903T160000 DTEND:20150903T180000 DTSTAMP:20150902T150000Z UID:f5cd6f4227507ca397c8a71152b9d9d2@cgp.ibs.re.kr SUMMARY:Overview of Mane's conjecture LOCATION:CGP Main Hall DESCRIPTION:Speaker: Daniel Massart\n\nEvent: CGP Seminar 2015\n\nAbstract: In the first part of this talk we give motivation for, and statement of, Mane's conjectures in Lagrangian dynamics. In the second part we explain some recent results in two degrees of freedom. END:VEVENT BEGIN:VEVENT DTSTART:20150915T160000 DTEND:20150915T173000 DTSTAMP:20150914T150000Z UID:11a1e6952450b20f33b1d42f6a86397b@cgp.ibs.re.kr SUMMARY:Birational geometry of Fano 3-folds of codimension 2 and 3 LOCATION:CGP Main Hall DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: There are 95, 85 and 70 families of Fano 3-fold embedded in weighted projective spaces as codimension 1, 2 and 3 respectively. Corti-Pukhlikov-Reid and Cheltsov-Park proved that codimension 1 Fano 3-folds are birationally rigid, that is, they are not birational to a Mori fiber space other than themselves. Unlike the codimension 1 case, many Fano 3-folds of codimension greater than 1 is birationally non-rigid. In this talk I will talk about recent results on the study of birational geometry of Fano 3-folds of codimension 2 and 3. END:VEVENT BEGIN:VEVENT DTSTART:20150908T140000 DTEND:20150908T150000 DTSTAMP:20150907T150000Z UID:a0641ef2b8efaf2ef65d3a227f36dd12@cgp.ibs.re.kr SUMMARY:A chain level Batalin-Vilkovisky structure in string topology via de Rham chains LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kei Irie\n\nEvent: CGP Seminar 2015\n\nAbstract: We propose a new chain model of the free loop space of a C^\infty-manfold, and define a chain level refinement of the Chas-Sullivan BV structure on loop space homology. Our construction involves a notion of de Rham chains, which is a hybrid of singular chains and differential forms. Relations to (1)Deligne's conjecture for Hochshild cochains, and (2)(expected) chain level structures in Floer homology of cotangent bundles, will be also discussed. END:VEVENT BEGIN:VEVENT DTSTART:20150910T160000 DTEND:20150910T170000 DTSTAMP:20150909T150000Z UID:df336ec6fcba480752b64779057a2a71@cgp.ibs.re.kr SUMMARY:Dense existence of periodic Reeb orbits and ECH spectral invariants LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kei Irie\n\nEvent: CGP Seminar 2015\n\nAbstract: We prove (1) for any closed contact three-manifold with a C^\infty-generic contact form, the union of periodic Reeb orbits is dense, (2) for any closed surface with a C^\infty-generic Riemannian metric, the union of closed geodesics is dense. A key observation is that, the fact that embedded contact homology (ECH) spectral invariants recover the volume (proved by Cristofaro-Gardiner, Hutchings and Ramos) implies a version of C^\infty-closing lemma. END:VEVENT BEGIN:VEVENT DTSTART:20150916T140000 DTEND:20150916T160000 DTSTAMP:20150915T150000Z UID:361c368b5906af59a4477cb17ee7226d@cgp.ibs.re.kr SUMMARY:Deformation theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Nero Budur\n\nEvent: Intensive Lecture Series by Nero Budur\n\nAbstract: A principle due to Deligne states that every infinitesimal deformation problem over a field of characteristic zero is controlled by a differential graded Lie algebra (DGLA). This principle has been illustrated for example by Goldman-Millson and Simpson to show that some important moduli spaces admit at most quadratic singularities. We illustrate a finer new principle: the infinitesimal deformations with cohomology constraints are controlled by a pair consisting of a DGLA together with a DGL-module. This is joint work with Botong Wang. END:VEVENT BEGIN:VEVENT DTSTART:20150921T140000 DTEND:20150921T160000 DTSTAMP:20150920T150000Z UID:7ea3e21734005f50dd15c52fc19a2845@cgp.ibs.re.kr SUMMARY:Rank one local systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Nero Budur\n\nEvent: Intensive Lecture Series by Nero Budur\n\nAbstract: We give a survey about the state of the art on the structure of the cohomology jump loci of local systems in the rank one case. We present some applications to homotopy type restrictions. We also give the proof of the structure result for smooth quasi-projective complex varieties, due jointly with Botong Wang. END:VEVENT BEGIN:VEVENT DTSTART:20150923T160000 DTEND:20150923T180000 DTSTAMP:20150922T150000Z UID:bcfc8ae38da700a3b776a165d9033e90@cgp.ibs.re.kr SUMMARY:Local systems and singularities LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Nero Budur\n\nEvent: Intensive Lecture Series by Nero Budur\n\nAbstract: The classical Monodromy Theorem states that the eigenvalues of the monodromy on the cohomology of the Milnor fiber of a hypersurface singularity are roots of unity. This follows from example from a classical result of Malgrange and Kashiwara that the roots of the b-function are rational and their exponentials recover the monodromy eigenvalues. In this lecture we will show that these results form but a small facet of a larger picture involving local systems. END:VEVENT BEGIN:VEVENT DTSTART:20150904T155000 DTEND:20150904T180000 DTSTAMP:20150903T150000Z UID:d703e8acc2748147f755449b27ceabf3@cgp.ibs.re.kr SUMMARY:Optimal transport, a natural matching between mass distributions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Young-Heon Kim\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: Optimal transport theory considers matchings between mass distributions, which minimize the average cost of moving a mass from one location to another. It gives a natural and effective way to interpolate different mass distributions, yielding many applications in analysis and geometry, including giving effective methods of showing isoperimetric and Sobolev inequalities. Also, analysis of optimal transport is related to the study of fully nonlinear partial differential equations of Monge-Ampere type. In the first lecture, we explain a few key examples in the theory. In the second lecture, we explain a recent result on the geometric barycenters over the space of probability measures, which is related to optimal transport between (infinitely) many mass distributions. END:VEVENT BEGIN:VEVENT DTSTART:20150907T140000 DTEND:20150907T160000 DTSTAMP:20150906T150000Z UID:d2f86a09f477fb8605a09aab10526462@cgp.ibs.re.kr SUMMARY:Galois Symmetry I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: Quantum Monday 2015\n\nAbstract: In this series of lectures, we will study Galois representations and their roles in the proof of Fermat's Last Theorem (by Wiles). END:VEVENT BEGIN:VEVENT DTSTART:20150914T140000 DTEND:20150914T160000 DTSTAMP:20150913T150000Z UID:9c31b2ce28b02996003dae49ff49370c@cgp.ibs.re.kr SUMMARY:Galois Symmetry II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: Quantum Monday 2015\n\nAbstract: We will review a basic structure of the absolute Galois group of the rational number field, and discuss some basic theorems from representation theory. If time permits, we will briefly studyKummer theory. END:VEVENT BEGIN:VEVENT DTSTART:20150921T190000 DTEND:20150921T210000 DTSTAMP:20150920T150000Z UID:bcb59a102d0c59d152988d266fcaa6e4@cgp.ibs.re.kr SUMMARY:Galois Symmetry III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: Quantum Monday 2015\n\nAbstract: We will introduce Galois cohomology and define Selmer group. If time permits, we will discuss Poitou-Tate duality as well. END:VEVENT BEGIN:VEVENT DTSTART:20150907T160000 DTEND:20150907T180000 DTSTAMP:20150906T150000Z UID:e1e9831f542fbdbb621bd96281bb1f20@cgp.ibs.re.kr SUMMARY:Reducible Galois representations and Eisenstein ideals LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: PMI Number Theory Seminar\n\nAbstract: In this talk, we will discuss the structure of the kernels of Eisenstein primeson modular Jacobians. This work could be regarded as the counterpart of the work of Ribet on irreducible representations. END:VEVENT BEGIN:VEVENT DTSTART:20150909T140000 DTEND:20150909T150000 DTSTAMP:20150908T150000Z UID:e05a0f203daf6b0f86f4c379438e9e98@cgp.ibs.re.kr SUMMARY:Moduli of certain K3 surfaces via GIT LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Motivated by an attempt to solve certain diophantine equations, I will describe the moduli space of certain K3 surfaces using projective equivalence classes of certain geometric configurations in the projective plane.I will focus on two types of configurations: four lines and a point, whose moduli is of dimension two, and two conics and a point, whose moduli is of dimension four. END:VEVENT BEGIN:VEVENT DTSTART:20150911T140000 DTEND:20150911T150000 DTSTAMP:20150910T150000Z UID:5797d42f4ee732ca0332ef220865376d@cgp.ibs.re.kr SUMMARY:Moduli of certain K3 surfaces via GIT LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Motivated by an attempt to solve certain diophantine equations, I will describe the moduli space of certain K3 surfaces using projective equivalence classes of certain geometric configurations in the projective plane.I will focus on two types of configurations: four lines and a point, whose moduli is of dimension two, and two conics and a point, whose moduli is of dimension four. END:VEVENT BEGIN:VEVENT DTSTART:20150915T140000 DTEND:20150915T150000 DTSTAMP:20150914T150000Z UID:a6f7c1c5f938a35a1f2a1f1c250f9ce9@cgp.ibs.re.kr SUMMARY:Moduli of certain K3 surfaces via GIT LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Motivated by an attempt to solve certain diophantine equations, I will describe the moduli space of certain K3 surfaces using projective equivalence classes of certain geometric configurations in the projective plane.I will focus on two types of configurations: four lines and a point, whose moduli is of dimension two, and two conics and a point, whose moduli is of dimension four. END:VEVENT BEGIN:VEVENT DTSTART:20151019T160000 DTEND:20151019T180000 DTSTAMP:20151018T150000Z UID:f3bab5de2e31685d9019f96dc1ee20f1@cgp.ibs.re.kr SUMMARY:Geodesics and Noncommutative Surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jens Hoppe\n\nEvent: APCTP-IBSCGP Seminar\n\nAbstract: Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, I will define discrete curvature, and a noncommutative Gauss-Bonnet theorem. After giving a general introduction to the Poisson-algebraic reformulation for surfaces, as well as explaining a method to associate sequences of finite dimensional matrices to them, I will focus on examples, including noncommutative analogues of minimal surfaces ( that play a central role in one of the promising attempts to unify the known physical interactions ).I will begin/end my talk with a historical survey of geodesics on ellipsoids. END:VEVENT BEGIN:VEVENT DTSTART:20150911T155000 DTEND:20150911T180000 DTSTAMP:20150910T150000Z UID:8f1060ccadc6d9c01610fb462479ee39@cgp.ibs.re.kr SUMMARY:Krull dimension of the power series ring over nonSFT domains LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byung Gyun Kang (POSTECH)\n\nEvent: POSTECH MATH Colloquium\n\nAbstract: We prove that the Krull dimension of the power series ring over a nonSFT domain is at least . Ever since Arnold proved 33 years ago that the Krull dimension of the power series ring over a nonSFT ring is infinite, in fact at least , the Krull dimension of the power series ring over various nonSFT domains has attracted people's attention.It is known by scholars such as B.G.Kang, M.H.Park, Loper, Lucas, P.T.Toan that the Krull dimension of the power series rings is at least over nondiscrete valuation domains and nonNoetherian almost Dedekind domains, and uncountable over nonSFT domains. In this talk we introduce a method, which is valid for all nonSFT domains to set the minimum of the Krull dimension of the power series ring over them at . END:VEVENT BEGIN:VEVENT DTSTART:20150924T160000 DTEND:20150924T180000 DTSTAMP:20150923T150000Z UID:1c6ac7a9265489246db39644bbda5718@cgp.ibs.re.kr SUMMARY:Cyclic homology of a different kind LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: CGP Seminar 2015\n\nAbstract: Periodic cyclic homology $HP_*(A)$ of an associative algebra $A$is a non-commutative generalization of de Rham cohomology -- when $A$ isthe algebra of functions on a smooth algebraic variety $X$, $HP_*(A)$reduces to the de Rham cohomology of $X$. In the very definition of$HP_*(A)$, one needs to take the total complex of a certain bicomplex.There are two ways to do it. One of them gives $0$ in characteristic $0$,so it has been largely ingored. However, about 10 years ago it has beensuggested by Kontsevich that in positive characteristic, taking the"wrong" total complex is not stupid at all and gives an interesting newhomology theory. I am going to give a brief reminder about the classictheory of $HP_*(A)$ and de Rham cohomology, and then show thatKontsevich's suggestion is indeed true -- there is an interesting newhomology theory for algebras and DG algebras that behaves as nicely as$HP_*(A)$, but differs from it at least in some important examples. END:VEVENT BEGIN:VEVENT DTSTART:19700101T200000 DTEND:19700101T220000 DTSTAMP:19700101T000000Z UID:727adb70119758b99a430b15cd940af2@cgp.ibs.re.kr SUMMARY:Effective Actions of the General Indefinite Unitary Groups on Holomorphically Separable Manifolds LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Nagata Yoshikazu\n\nEvent: \n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150922T160000 DTEND:20150922T170000 DTSTAMP:20150921T150000Z UID:2450031c577e0a140cd26d2e1596e083@cgp.ibs.re.kr SUMMARY:Why are quantum invariants interesting? LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jinseok Cho (PMI)\n\nEvent: PMI T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20150921T160000 DTEND:20150921T180000 DTSTAMP:20150920T150000Z UID:ba459130384331ab419fb7b34fa7c90c@cgp.ibs.re.kr SUMMARY:Variation of anticyclotomic Iwasawa invariants in Hida families LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Chan-Ho Kim(KIAS)\n\nEvent: POSTECH PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151002T155000 DTEND:20151002T180000 DTSTAMP:20151001T150000Z UID:ee4c00deb5a2b4e8bfdb06d1812947e1@cgp.ibs.re.kr SUMMARY:I: Counting polygons in the surface and symplectic geometry II: Mirror symmetry, counting polygons and non-commutative geometry LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: 2015 Fall Math Colloquium\n\nAbstract: We explain via several elementary examples (curves, counting polygons) that geometric concept (called a Fukaya category of a symplectic manifold) is systematically related to an algebraic concept (called matrix factorization of a function), which is called mirror symmetry.This canonical functor is constructed using formal deformation theory of a Lagrangian submanifold which is a joint work with H. Hong and S.C. Lau.This formalism also has a non-commutative generalization. END:VEVENT BEGIN:VEVENT DTSTART:20151005T140000 DTEND:20151005T160000 DTSTAMP:20151004T150000Z UID:55e996d6cf43172a53e24a7ad4dfd14a@cgp.ibs.re.kr SUMMARY:Galois symmetry IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: Quantum Monday 2015\n\nAbstract: We will introduce Galois deformation theory. END:VEVENT BEGIN:VEVENT DTSTART:20151006T160000 DTEND:20151006T170000 DTSTAMP:20151005T150000Z UID:266ee80d60bbf7adbc0949ab920e0c63@cgp.ibs.re.kr SUMMARY:Grid diagrams for singular knots LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byung Hee An\n\nEvent: PMI T-Seminar\n\nAbstract: A grid diagram is a link diagram of vertical strands and the samenumber of horizontal strands with the properties that at everycrossing the vertical strand crosses over the horizontal strand and notwo horizontal segments are co-linear and no two vertical segments areco-linear.It is known that every knot admits a grid diagram, and moreover, so dothe relatives such as Legendrian knots, transverse knots, closures ofbraids, as well.Indeed, Ng and D. Thurston in 2009 showed that all these knot theoriescan be obtained from the set of grid diagrams up to appropriate setsof moves, respectively.In this talk, we consider the generalization of this result to singular knots. END:VEVENT BEGIN:VEVENT DTSTART:20151012T140000 DTEND:20151012T160000 DTSTAMP:20151011T150000Z UID:f01e077941c6b8d0bf60c3eb61cd7f02@cgp.ibs.re.kr SUMMARY:Galois Symmetry V LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: Quantum Monday 2015\n\nAbstract: We will study the local shape of Galois representations attached to elliptic curves and modular forms. END:VEVENT BEGIN:VEVENT DTSTART:20151019T140000 DTEND:20151019T153000 DTSTAMP:20151018T150000Z UID:b63df81a23b5cfac13eb9854a27922cd@cgp.ibs.re.kr SUMMARY:Chern-Simons theory and its relation to 3-dimensional N=2 supersymmetric conformal field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hee-Joong Chung\n\nEvent: Quantum Monday 2015\n\nAbstract: I will review several aspects of Chern-Simons theory from a physics vantage point, including knot polynomial, A-polynomial, and quantization. Then I will discuss 3d-3d relation between complex Chern-Simons theory and 3-dimensional N=2 supersymmetric conformal field theory where all flat connections in Chern-Simons theory are taken into account. END:VEVENT BEGIN:VEVENT DTSTART:19700101T090000 DTEND:19700101T090000 DTSTAMP:19700101T000000Z UID:d6ebfff260e616a03263b17525fc71bb@cgp.ibs.re.kr SUMMARY:I: Elliptic curves and theta-congruent numbers, II: Rational curves on quotients of abelian varieties by finite groups LOCATION:CGP Main Hall DESCRIPTION:Speaker: \n\nEvent: Math Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151013T140000 DTEND:20151013T152000 DTSTAMP:20151012T150000Z UID:ca46cb78923158b8a3b34365a103911c@cgp.ibs.re.kr SUMMARY:Topological extension of Calabi invariants and its application LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Tuesday\n\nAbstract: In this talk, I will explain how we can extend the classical Calabi homomorphism on the area-preserving diffeomorphism group of two-disc to the group of Hamiltonian homeomorphisms. END:VEVENT BEGIN:VEVENT DTSTART:20151021T140000 DTEND:20151021T160000 DTSTAMP:20151020T150000Z UID:a7d7a2fd391c174883000da8a13b8a45@cgp.ibs.re.kr SUMMARY:Chern-Simons theory and its relation to 3-dimensional N=2 supersymmetric conformal field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hee-Joong Chung\n\nEvent: Quantum Monday 2015\n\nAbstract: I will review several aspects of Chern-Simons theory from a physics vantage point, including knot polynomial, A-polynomial, and quantization. Then I will discuss 3d-3d relation between complex Chern-Simons theory and 3-dimensional N=2 supersymmetric conformal field theory where all flat connections in Chern-Simons theory are taken into account. END:VEVENT BEGIN:VEVENT DTSTART:20151023T140000 DTEND:20151023T160000 DTSTAMP:20151022T150000Z UID:d508c3858bb9e31d07850963fe9b67de@cgp.ibs.re.kr SUMMARY:Chern-Simons theory and its relation to 3-dimensional N=2 supersymmetric conformal field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hee-Joong Chung\n\nEvent: Quantum Monday 2015\n\nAbstract: I will review several aspects of Chern-Simons theory from a physics vantage point, including knot polynomial, A-polynomial, and quantization. Then I will discuss 3d-3d relation between complex Chern-Simons theory and 3-dimensional N=2 supersymmetric conformal field theory where all flat connections in Chern-Simons theory are taken into account. END:VEVENT BEGIN:VEVENT DTSTART:20151103T160000 DTEND:20151103T173000 DTSTAMP:20151102T150000Z UID:4996d28c5b1e5e395d70491bbd9f04cc@cgp.ibs.re.kr SUMMARY:Minimal cubic surfaces over finite fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Andrey Trepalin\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: Let us consider a cubic surface $X$ over a finite field $F_q$. Then the Weyl group $W(E_6)$ acts on $Pic(\overline{X})$. It is well-known that there are five possibilities for the image of the Galois group $Gal(\overline{F}_q / F_q)$ in the Weyl group $W(E_6)$ such that the cubic surface is minimal. For each of these possibilities we explicitely construct examples of minimal cubic surfaces for odd $q$ such that $q = 3k + 1$ and some other cases. END:VEVENT BEGIN:VEVENT DTSTART:20151029T160000 DTEND:20151029T173000 DTSTAMP:20151028T150000Z UID:da0eb5f2142fa40eee84664ac20d705f@cgp.ibs.re.kr SUMMARY:Automorphisims of Fano threefolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: I will survey results describing automorphism groups of smooth Fano threefolds of Picard rank 1. In particular, I will show that the automorphism group may be infinite only if the intermediate Jacobian is trivial. The approach is (mostly) based on an accurate analysis of Hilbert schemes of lines and conics on Fano threefolds. The talk is based on a joint work with A.Kuznetsov and Yu.Prokhorov. END:VEVENT BEGIN:VEVENT DTSTART:20151020T140000 DTEND:20151020T152000 DTSTAMP:20151019T150000Z UID:f8c0f33d166575ba5ebc493b4628b64c@cgp.ibs.re.kr SUMMARY:Introduction to Fukaya category and mirror symmetry I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Symplectic Tuesday\n\nAbstract: In these series of talks, I will give a short introduction to Fukaya category and explain various examples of (homological) mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20151215T100000 DTEND:20151215T120000 DTSTAMP:20151214T150000Z UID:174f1e93e25fe2277885ae3743047e5e@cgp.ibs.re.kr SUMMARY:Knot contact homology - definition and calculation LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: We define knot contact homology and show how to compute it for links in $R^3$ from a braid presentation. END:VEVENT BEGIN:VEVENT DTSTART:20151214T140000 DTEND:20151214T153000 DTSTAMP:20151213T150000Z UID:f0dc785b8507cf4d131ab5b1070adf55@cgp.ibs.re.kr SUMMARY:Asymptotics of quantum invariants. I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Stavros Garoufalidis\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: We will give introductory and up-to-date lectures on asymptotics of quantum invariants. END:VEVENT BEGIN:VEVENT DTSTART:20151214T160000 DTEND:20151214T173000 DTSTAMP:20151213T150000Z UID:1c1b228570ec025da29c0c3d5b0dfbc5@cgp.ibs.re.kr SUMMARY:Volume conjecture as a simple quantization problem: its generalization and categorification I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sergei Gukov\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: The generalized volume conjecture relates holomorphic curves (more generally, holomorphic Lagrangian submanifolds in Hitchin moduli spaces) with quantum group invariants of knots and 3-manifolds. Our goal in these lectures will be to review this relation, based on Chern-Simons gauge theory with complex gauge group, and to see how it explains known facts and predicts new ones. In particular, since many quantum group invariants of knots can be categorified to homological invariants, one may wonder whether the generalized (or quantum) volume conjecture admits a natural categorification. I will argue that the answer to this question is "yes" and introduce a certain deformation of the holomorphic curves that completely describes the "color behavior" of knot homology. This deformation is strong enough to distinguish mutants, and its most interesting properties include relation to knot contact homology and knot Floer homology.Links to lecture notes:http://arxiv.org/pdf/1211.6075.pdf http://arxiv.org/pdf/1211.6075.pdf http://arxiv.org/pdf/1510.01795.pdf END:VEVENT BEGIN:VEVENT DTSTART:20151214T100000 DTEND:20151214T120000 DTSTAMP:20151213T150000Z UID:6343bb0a58b51bc4fc7f12144463d89a@cgp.ibs.re.kr SUMMARY:Quantum Teichmuller theory and TQFT I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Rinat Kashaev\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: I will explain basic elements underlying the quantum Teichmuller theory and its recent extension to a generalized TQFT based on shaped triangulations of three-dimensional pseudo-manifolds. Subjects to be addressed: Penner and ratio coordinates; groupoid of (decorated) ideal triangulations; quantization; tetrahedral symmetries; examples of calculation; a version of the volume conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20151110T160000 DTEND:20151110T173000 DTSTAMP:20151109T150000Z UID:c5457825cb1ee5ee3d16d35e33aa31e1@cgp.ibs.re.kr SUMMARY:Log minimal model program under a positivity condition LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Zhengyu Hu\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: Let $(X,\Delta)$ be a log pair with mild singularities (eg. Kawamata log terminal, log canonical). Assume that either the adjoint divisor $K_{X}+\Delta$ or the boundary divisor $\Delta$ has some certain positivity assumption. Then $(X,\Delta)$ has either a good minimal model or a Mori fiber space (see [BCHM]'s main result and its extensions). In this talk, I will give a brief introduction to log minimal model program (LMMP), and I will discuss on a special LMMP, a special termination and ACC for log canonical thresholds. As an application of these modern techniques, I will also sketch the idea that how to extend the termination of LMMP with scaling on Kawamata log terminal pairs to log canonical pairs under a positivity condition. END:VEVENT BEGIN:VEVENT DTSTART:20151110T140000 DTEND:20151110T152000 DTSTAMP:20151109T150000Z UID:ed998e4a8db4f4ec5af37db28e0daa4f@cgp.ibs.re.kr SUMMARY:A special Lagrangian fibration on a complex Grassmannian of two planes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Changzheng Li\n\nEvent: Symplectic Tuesday\n\nAbstract: In this talk, we will start with a review of mirror symmetry for complex Grassmannians. In the case of complex Grassmannian Gr(2, n) of two planes, we equip Gr(2, n) with a meromorphic volume form which has simple pole along a specified anti-canonical divisor -K. We construct a special Lagrangian fibration on the complement of -K in Gr(2, n). This is my joint work with Kwok Wai Chan and Naichung Conan Leung. END:VEVENT BEGIN:VEVENT DTSTART:20151027T140000 DTEND:20151027T152000 DTSTAMP:20151026T150000Z UID:911b013ef51d3f8a8f508246c45e8d84@cgp.ibs.re.kr SUMMARY:Introduction to Fukaya category and mirror symmetry II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Symplectic Tuesday\n\nAbstract: In these series of talks, I will give a short introduction to Fukaya category and explain various examples of (homological) mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20151102T140000 DTEND:20151102T160000 DTSTAMP:20151101T150000Z UID:041369d437af09013e3d81dc9f977d80@cgp.ibs.re.kr SUMMARY:Feynman periods: numbers and geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Doryn\n\nEvent: Quantum Monday 2015\n\nAbstract: I will speak on the Feynman periods, the values of Feynman integrals in (massless, scalar) phi^4 theory, from the number-theoretical perspective. Then I define a closely related geometrical object, the graph hypersurface. One can try to study the geometry of these hypersurfaces (cohomology, Grothendieck ring, number of rational points over finite fields) and to relate it to the periods. END:VEVENT BEGIN:VEVENT DTSTART:20151124T140000 DTEND:20151124T152000 DTSTAMP:20151123T150000Z UID:b5337c3688577436a38ff1c2bfdecc3b@cgp.ibs.re.kr SUMMARY:Intro to fukaya category and mirror symmetry III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Symplectic Tuesday\n\nAbstract: In these series of talks, I will give a short introduction to Fukaya category and explain various examples of (homological) mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20151127T140000 DTEND:20151127T153000 DTSTAMP:20151126T150000Z UID:78fc9ce57ddff0817a1d9a11d1f93848@cgp.ibs.re.kr SUMMARY:Birational boundedness of singular log Fano threefolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jiang Chen\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: We show that the family of 3-folds of $\epsilon$-Fano type is birationally bounded. END:VEVENT BEGIN:VEVENT DTSTART:20151102T130000 DTEND:20151102T140000 DTSTAMP:20151101T150000Z UID:74a66b13436c2fa720567a22cb48aa36@cgp.ibs.re.kr SUMMARY:Working Group of the string field theory of the B-model LOCATION:CGP Main Hall DESCRIPTION:Speaker: Calin Iuliu Lazaroiu\n\nEvent: Seminar 2015\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151104T170000 DTEND:20151104T181500 DTSTAMP:20151103T150000Z UID:0ea01a1acbcc2915cb5a2f37aa0d064f@cgp.ibs.re.kr SUMMARY:The conjecture of Birch and Swinnerton-Dyer (II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: John Coates (Univ. of Cambridge & POSTECH)\n\nEvent: 2015 POSTECH Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151103T160000 DTEND:20151103T170000 DTSTAMP:20151102T150000Z UID:82d9e6f9a88d43e7adc804b850b475ef@cgp.ibs.re.kr SUMMARY:Legendrian knots and Eliashberg-Chekanov algebra LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151102T140000 DTEND:20151102T160000 DTSTAMP:20151101T150000Z UID:74dd00fd9ea658b039b0c82e1ccae1e3@cgp.ibs.re.kr SUMMARY:Mod $p$ local-global compatibility for $\mathrm{GL}_{3}(\mathbb{Q}_p)$ in the non-ordinary case LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Chol Park (KIAS)\n\nEvent: POSTECH PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151106T155000 DTEND:20151106T180000 DTSTAMP:20151105T150000Z UID:6d2e04baaf4e0778d79521ffff2c1b31@cgp.ibs.re.kr SUMMARY:Mapping Class groups, categorification and loop spaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yongjin Song (Inha Univ.)\n\nEvent: 2015 Fall Math Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151123T140000 DTEND:20151123T160000 DTSTAMP:20151122T150000Z UID:aee22979b21e9be0315c8fdc9d95cda0@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2015\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20151130T140000 DTEND:20151130T160000 DTSTAMP:20151129T150000Z UID:19696f2a3bb96c37eec8ccc9ed9c7c9d@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2015\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20151207T140000 DTEND:20151207T160000 DTSTAMP:20151206T150000Z UID:27de3ab8b3f5025fc6ff76b159469775@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2015\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20151116T102000 DTEND:20151116T110000 DTSTAMP:20151115T150000Z UID:49e0776a8995ebe1f3d83e845f097086@cgp.ibs.re.kr SUMMARY:Comparison of mirror functors of the elliptic curve via LG/CY correspondence LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: We review two different kinds of homological mirror symmetries of elliptic curves. One has been classically known since Polishchuk-Zaslow's work, which has B-model as a derived category, while the other due to Cho-Hong-Lau has the B-model as Landau-Ginzburg theory, namely the category of matrix factorizations. We investigate how they are related via Orlov's LG/CY correspondence theorem. END:VEVENT BEGIN:VEVENT DTSTART:20151116T112000 DTEND:20151116T120000 DTSTAMP:20151115T150000Z UID:ec53557af91a2bb9aff7d317dd408c88@cgp.ibs.re.kr SUMMARY:Tautological rings of moduli spaces of curves LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Mehdi Tavakol\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: The study of intersection theory on moduli spaces of curves was started by Mumford.He established the foundational framework for understanding the geometry of spaces of curves.He also defined the notion of tautological classes on these spaces. Tautological classes have been studied extensively since then.In this talk I will discuss the development of methods for this study since Mumford. END:VEVENT BEGIN:VEVENT DTSTART:20151116T140000 DTEND:20151116T144000 DTSTAMP:20151115T150000Z UID:c8c8025c87e034e083d54e3674f5d512@cgp.ibs.re.kr SUMMARY:Equivariant surgery for circle actions LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: Let $M$ be a $(2n+1)$-dimensional closed manifold equipped with a fixed point free circle action such that there are only finitely many exceptional orbits. In this talk, we present a way of constructing a new closed manifold $\widetilde{M}$ with a free $S^1$-action from $M$ via $S^1$-equivariant surgery technique. As consequences, firstly we presents a new method to obtain resolutions of isolated cyclic quotient singularities. Secondly, we prove that the Chern number $N = \langle c_1(E)^n, [B] \rangle$ of the complex line orbi-bundle $E$ associated to $M$ satisfies $l \cdot N \in \mathbb{Z}$ where $B = M / S^1$ and $l$ is the least common multiple of the orders of the isotropy groups of the element of $M$. Finally, we illustrate several applications of our results in symplectic topology. This is joint work with Byung Hee An. END:VEVENT BEGIN:VEVENT DTSTART:20151116T145000 DTEND:20151116T153000 DTSTAMP:20151115T150000Z UID:653b9e760b96f0c7a44c84fa4516702f@cgp.ibs.re.kr SUMMARY:Liouville type theorems for the steady axially symmetric Navier-Stokes equations LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Shangkun Weng (PMI)\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: In this talk, I will briefly introduce the physical background of the Navier-Stokes equations and also the main mathematical achievements in this field during the past 80 years. Then I will talk about my recent works on the steady axially symmetric Navier-Stokes equations. Some of my works are joint with Prof. Dongho Chae at Chung-Ang University. END:VEVENT BEGIN:VEVENT DTSTART:20151116T160000 DTEND:20151116T164000 DTSTAMP:20151115T150000Z UID:67c6f6bb59880fc3e8b5d4a127a954e2@cgp.ibs.re.kr SUMMARY:Cohomology support loci and forms of degree one LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: Cohomology support loci of rank one local systems of a smooth quasi-projective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group. Tangent spaces of the character variety are (partially) represented by logarithmic 1-forms. We give a relation between cohomology support loci and the natural strata of 1-forms given by the dimension of the vanishing locus. END:VEVENT BEGIN:VEVENT DTSTART:20151116T165000 DTEND:20151116T173000 DTSTAMP:20151115T150000Z UID:a62bd055e07ba99c6d93189f35c3bae6@cgp.ibs.re.kr SUMMARY:Restriction problem and some estimates LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Chuhee Cho (BK21+)\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: In this talk we introduce the restriction problem and some known results.Also we show an improved restriction estimate for hyperbolic surfaces in $\mathbb{R}^3$. END:VEVENT BEGIN:VEVENT DTSTART:20151117T102000 DTEND:20151117T110000 DTSTAMP:20151116T150000Z UID:3f532b480f5d7c04610d3994a47d5a14@cgp.ibs.re.kr SUMMARY:Defining functions for unbounded domains in almost complex manifolds LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Harz Tobias (SRC-GAIA)\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: I will explain that every strictly pseudoconvex domain$\Omega$ in an almost complex manifold $(M,J)$ admits a$J$-plurisubharmonic defining function, which is defined on an openneighborhood of the closure $\bar{\Omega}$, and which is strictly$J$-plurisubharmonic near the boundary $b\Omega$. This is joint workwith N. Shcherbina and G. Tomassini. END:VEVENT BEGIN:VEVENT DTSTART:20151117T112000 DTEND:20151117T120000 DTSTAMP:20151116T150000Z UID:3a2285c6b57650795c17773fd7e1a444@cgp.ibs.re.kr SUMMARY:On combinatorics on spheres LOCATION:Daemyung Resort, Geoje DESCRIPTION:Speaker: Hyonju Yu (PMI)\n\nEvent: 2015 Pohang Mathematics Workshop\n\nAbstract: In this talk, we discuss ``good'' finite subset on the unit sphere.(1.) Coding theorical viewpointFind a subset $X$ of $S^{n-1}$ in which the points are mutuallyseparated as much as possible(1.1) (Tammes problem) for given $X$, make the minimum distance of $X$ as large as possible(1.2) (Packing problem) for given $d$, make $X$ as large as possible under the condition; minimum distance of $X\geq d$(2.) Design theoritical viewpointFind a finite subsets of $S^{n-1}$ which approximates the whole space ex) spherical design, $\ldots$ END:VEVENT BEGIN:VEVENT DTSTART:20151111T170000 DTEND:20151111T181500 DTSTAMP:20151110T150000Z UID:37d7e08fcec968fc1e6e20156017ef07@cgp.ibs.re.kr SUMMARY:The conjecture of Birch and Swinnerton-Dyer (III) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: John Coates (Univ.of Cambridge&POSTECH)\n\nEvent: 2015 POSTECH Lecture Series\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151113T155000 DTEND:20151113T180000 DTSTAMP:20151112T150000Z UID:b95a5b65f84411d1a270725220508fd5@cgp.ibs.re.kr SUMMARY:Primitive automorphisms of projective manifolds of positive entropy LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Keiji Oguiso (Osaka University / University of Tokyo)\n\nEvent: 2015 Fall Math Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151217T160000 DTEND:20151217T173000 DTSTAMP:20151216T150000Z UID:c63f3ca7712883c7905e146253c0fb50@cgp.ibs.re.kr SUMMARY:Chern-Simons theory, open topological strings, and augmentations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: We discuss the relation between Chern-Simons theory in a 3-manifold and Gromov-Witten invariants in its cotangent bundle. In case of $S^3$ one can perform a large N transition for topological strings and relate the Gromov-Witten theory to the corresponding theory in the resolved conifold. We show in this context how the disk potential is related to the augmentation variety of knot contact homology. END:VEVENT BEGIN:VEVENT DTSTART:20151218T140000 DTEND:20151218T153000 DTSTAMP:20151217T150000Z UID:ddcc82ead2e384926b26a7c6e7eade6f@cgp.ibs.re.kr SUMMARY:Knot contact homology and higher genus curves LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: In this last lecture we outline a strategy for calculating higher genus open Gromov-Witten amplitudes from generalizations of knot contact homology in the spirit of rational symplectic field theory. The approach uses linearized knot contact homology at generic points in the augmentation variety. END:VEVENT BEGIN:VEVENT DTSTART:20151216T100000 DTEND:20151216T120000 DTSTAMP:20151215T150000Z UID:33f88cc25bd50a76ad67047d428a0d9e@cgp.ibs.re.kr SUMMARY:Asymptotics of quantum invariants. II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Stavros Garoufalidis\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: We will give introductory and up-to-date lectures on asymptotics of quantum invariants. END:VEVENT BEGIN:VEVENT DTSTART:20151218T100000 DTEND:20151218T113000 DTSTAMP:20151217T150000Z UID:5de381092ee7040d79c9231027dc1cc0@cgp.ibs.re.kr SUMMARY:Asymptotics of quantum invariants. III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Stavros Garoufalidis\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: We will give introductory and up-to-date lectures on asymptotics of quantum invariants. END:VEVENT BEGIN:VEVENT DTSTART:20151215T140000 DTEND:20151215T153000 DTSTAMP:20151214T150000Z UID:1b28ba274cb54f9668f1ba03b3f4269d@cgp.ibs.re.kr SUMMARY:Volume conjecture as a simple quantization problem: its generalization and categorification II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sergei Gukov\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: The generalized volume conjecture relates holomorphic curves (more generally, holomorphic Lagrangian submanifolds in Hitchin moduli spaces) with quantum group invariants of knots and 3-manifolds. Our goal in these lectures will be to review this relation, based on Chern-Simons gauge theory with complex gauge group, and to see how it explains known facts and predicts new ones. In particular, since many quantum group invariants of knots can be categorified to homological invariants, one may wonder whether the generalized (or quantum) volume conjecture admits a natural categorification. I will argue that the answer to this question is "yes" and introduce a certain deformation of the holomorphic curves that completely describes the "color behavior" of knot homology. This deformation is strong enough to distinguish mutants, and its most interesting properties include relation to knot contact homology and knot Floer homology. END:VEVENT BEGIN:VEVENT DTSTART:20151217T100000 DTEND:20151217T120000 DTSTAMP:20151216T150000Z UID:7f46178c4a1316f455f615fe3d33f106@cgp.ibs.re.kr SUMMARY:Volume conjecture as a simple quantization problem: its generalization and categorification III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sergei Gukov\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: The generalized volume conjecture relates holomorphic curves (more generally, holomorphic Lagrangian submanifolds in Hitchin moduli spaces) with quantum group invariants of knots and 3-manifolds. Our goal in these lectures will be to review this relation, based on Chern-Simons gauge theory with complex gauge group, and to see how it explains known facts and predicts new ones. In particular, since many quantum group invariants of knots can be categorified to homological invariants, one may wonder whether the generalized (or quantum) volume conjecture admits a natural categorification. I will argue that the answer to this question is "yes" and introduce a certain deformation of the holomorphic curves that completely describes the "color behavior" of knot homology. This deformation is strong enough to distinguish mutants, and its most interesting properties include relation to knot contact homology and knot Floer homology. END:VEVENT BEGIN:VEVENT DTSTART:20151215T160000 DTEND:20151215T173000 DTSTAMP:20151214T150000Z UID:539451393b100a6d85266efabaaa7a9a@cgp.ibs.re.kr SUMMARY:Quantum Teichmuller theory and TQFT II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Rinat Kashaev\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: I will explain basic elements underlying the quantum Teichmuller theory and its recent extension to a generalized TQFT based on shaped triangulations of three-dimensional pseudo-manifolds. Subjects to be addressed: Penner and ratio coordinates; groupoid of (decorated) ideal triangulations; quantization; tetrahedral symmetries; examples of calculation; a version of the volume conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20151217T140000 DTEND:20151217T153000 DTSTAMP:20151216T150000Z UID:4696ebed5456c36010800ee41ce59d3e@cgp.ibs.re.kr SUMMARY:Quantum Teichmuller theory and TQFT III LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Rinat Kashaev\n\nEvent: Winter School on Volume Conjecture, Chern-Simons Theory and Knot Contact Homology\n\nAbstract: I will explain basic elements underlying the quantum Teichmuller theory and its recent extension to a generalized TQFT based on shaped triangulations of three-dimensional pseudo-manifolds. Subjects to be addressed: Penner and ratio coordinates; groupoid of (decorated) ideal triangulations; quantization; tetrahedral symmetries; examples of calculation; a version of the volume conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20151118T140000 DTEND:20151118T160000 DTSTAMP:20151117T150000Z UID:c85801e4d214f9f81b8070a75bbf2d37@cgp.ibs.re.kr SUMMARY:Algebraic complete integrability of some hamiltonian systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Vasile Brinzanescu\n\nEvent: Seminar 2015\n\nAbstract: We shall present a general case of Hamiltonian systems and we shall give the proof of the algebraic complete integrability for the Bloch-Iserles system. The results are obtained in collaboration with Tudor Ratiu. END:VEVENT BEGIN:VEVENT DTSTART:20151120T140000 DTEND:20151120T160000 DTSTAMP:20151119T150000Z UID:e8192fd757ebecfa55709226f28ff147@cgp.ibs.re.kr SUMMARY:Algebraic complete integrability of some hamiltonian systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Vasile Brinzanescu\n\nEvent: Seminar 2015\n\nAbstract: We shall present a general case of Hamiltonian systems and we shall give the proof of the algebraic complete integrability for the Bloch-Iserles system. The results are obtained in collaboration with Tudor Ratiu. END:VEVENT BEGIN:VEVENT DTSTART:20151116T160000 DTEND:20151116T180000 DTSTAMP:20151115T150000Z UID:b8f84c3f57311765e38ede689bd4f85d@cgp.ibs.re.kr SUMMARY:(Generlised) geometry of stringy correction LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ruben Minasian\n\nEvent: Seminar 2015\n\nAbstract: I will discuss the structure of (some) stringy corrections to effective actions and the role played by three-form H-flux. END:VEVENT BEGIN:VEVENT DTSTART:20151123T170000 DTEND:20151123T180000 DTSTAMP:20151122T150000Z UID:d2ea4abc10f49ee4958e367a2944e1f1@cgp.ibs.re.kr SUMMARY:On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions\n\nAbstract: I will review the mathematical formulation of four-dimensional Supergravity theories, which involves, among other structures, Special Kahler and Quaternionic manifolds. In addition, I will discuss the local classification of its supersymmetric solutions, which amounts to classifying, up to local isometry, four-dimensional Lorentz manifolds equipped with certain parallel spinors. I will conclude with some progress by the author on the resolution of a long-standing problem in String Theory: obtaining the first, analytic, exact black hole solution in String Theory compactified to four dimensions on a Calabi-Yau three-fold. This problem can be reformulated in terms of an elegant "algebraic" equation involving topological data of the CY compactification three-fold. END:VEVENT BEGIN:VEVENT DTSTART:20151124T170000 DTEND:20151124T180000 DTSTAMP:20151123T150000Z UID:6e7959d5303f45a34b6340757616a306@cgp.ibs.re.kr SUMMARY:On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions\n\nAbstract: I will review the mathematical formulation of four-dimensional Supergravity theories, which involves, among other structures, Special Kahler and Quaternionic manifolds. In addition, I will discuss the local classification of its supersymmetric solutions, which amounts to classifying, up to local isometry, four-dimensional Lorentz manifolds equipped with certain parallel spinors. I will conclude with some progress by the author on the resolution of a long-standing problem in String Theory: obtaining the first, analytic, exact black hole solution in String Theory compactified to four dimensions on a Calabi-Yau three-fold. This problem can be reformulated in terms of an elegant "algebraic" equation involving topological data of the CY compactification three-fold. END:VEVENT BEGIN:VEVENT DTSTART:20151125T170000 DTEND:20151125T180000 DTSTAMP:20151124T150000Z UID:4da16e4cfd1477a652cfe9251b2b10fb@cgp.ibs.re.kr SUMMARY:On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions\n\nAbstract: I will review the mathematical formulation of four-dimensional Supergravity theories, which involves, among other structures, Special Kahler and Quaternionic manifolds. In addition, I will discuss the local classification of its supersymmetric solutions, which amounts to classifying, up to local isometry, four-dimensional Lorentz manifolds equipped with certain parallel spinors. I will conclude with some progress by the author on the resolution of a long-standing problem in String Theory: obtaining the first, analytic, exact black hole solution in String Theory compactified to four dimensions on a Calabi-Yau three-fold. This problem can be reformulated in terms of an elegant "algebraic" equation involving topological data of the CY compactification three-fold. END:VEVENT BEGIN:VEVENT DTSTART:20151126T170000 DTEND:20151126T180000 DTSTAMP:20151125T150000Z UID:90d69f6654a09b1b1a5c7468c171b883@cgp.ibs.re.kr SUMMARY:On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions\n\nAbstract: I will review the mathematical formulation of four-dimensional Supergravity theories, which involves, among other structures, Special Kahler and Quaternionic manifolds. In addition, I will discuss the local classification of its supersymmetric solutions, which amounts to classifying, up to local isometry, four-dimensional Lorentz manifolds equipped with certain parallel spinors. I will conclude with some progress by the author on the resolution of a long-standing problem in String Theory: obtaining the first, analytic, exact black hole solution in String Theory compactified to four dimensions on a Calabi-Yau three-fold. This problem can be reformulated in terms of an elegant "algebraic" equation involving topological data of the CY compactification three-fold. END:VEVENT BEGIN:VEVENT DTSTART:20151127T170000 DTEND:20151127T180000 DTSTAMP:20151126T150000Z UID:2cae204312ec17c10dcfc3056d46be71@cgp.ibs.re.kr SUMMARY:On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: On the mathematical formulation of four-dimensional Supergravity and its supersymmetric solutions\n\nAbstract: I will review the mathematical formulation of four-dimensional Supergravity theories, which involves, among other structures, Special Kahler and Quaternionic manifolds. In addition, I will discuss the local classification of its supersymmetric solutions, which amounts to classifying, up to local isometry, four-dimensional Lorentz manifolds equipped with certain parallel spinors. I will conclude with some progress by the author on the resolution of a long-standing problem in String Theory: obtaining the first, analytic, exact black hole solution in String Theory compactified to four dimensions on a Calabi-Yau three-fold. This problem can be reformulated in terms of an elegant "algebraic" equation involving topological data of the CY compactification three-fold. END:VEVENT BEGIN:VEVENT DTSTART:20151126T140000 DTEND:20151126T153000 DTSTAMP:20151125T150000Z UID:8c0da2ff3440d794f12c8f4adfccf691@cgp.ibs.re.kr SUMMARY:The Craw-Ishii Conjecture LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: In this talk, I propose a conjecture on quotient singularities and the moduli spaces of G-constellations. For a finite group G in GL_n, a G-equivariant sheaf F on C^n is called a G-constellation if H^0(F) is isomorphic to the regular representation of G as G-modules. In [Craw and Ishii, Duke 2004], Craw and Ishii proved that for a finite abelian group G in SL_3(C), every projective crepant resolution of C^3/G is isomorphic to the fine moduli space of theta-stable G-constellations for some GIT parameter theta. The (generalised) Craw-Ishii conjecture says that for G in GL_3, every relative (projective) minimal model of C^3/G has a moduli interpretation using G-constellations. In this talk, I prove this conjecture in some cases. END:VEVENT BEGIN:VEVENT DTSTART:20151201T140000 DTEND:20151201T152000 DTSTAMP:20151130T150000Z UID:40d19fe88c75f2805bba9b27f957e41e@cgp.ibs.re.kr SUMMARY:Matrix factorizations of complete intersections LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: Symplectic Tuesday\n\nAbstract: We study the recent work on matrix factorizations of complete intersections due to Eisenbud-Peeva. We try to understand the definition and examples, and discuss how it can play a role in the homological mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20151130T160000 DTEND:20151130T180000 DTSTAMP:20151129T150000Z UID:cafbdecc94cd481c4664257c94b989a6@cgp.ibs.re.kr SUMMARY:On the average number of integral points on elliptic curves LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dohyeong Kim\n\nEvent: POSTECH PMI Number Theory Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151204T155000 DTEND:20151204T180000 DTSTAMP:20151203T150000Z UID:059d7a8da7b9537b5c1c66822bfe32a9@cgp.ibs.re.kr SUMMARY:I: How did I choose my research topics? II: Modeling and analysis for emergent phenomena LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seung Yeal Ha (Seoul National University)\n\nEvent: 2015 Fall Math Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20151209T140000 DTEND:20151209T160000 DTSTAMP:20151208T150000Z UID:eac5a7e0ad17879f453210910cafb06a@cgp.ibs.re.kr SUMMARY:On symplectic ﬁllings of quotient surface singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jongil Park\n\nEvent: Seminar 2015\n\nAbstract: One of active research areas in 4-manifold theory is to cassify symplectic ﬁllings of certain 3-manifolds equipped with a natural contact structure. Among them, people have long studied sym-plectic ﬁllings of the link of a normal complex surface singularity. Note that the link of a normal complex surface singularity carries a canonical contact structure which is also known as the Milnor ﬁllable contact structure.For example, P. Lisca classiﬁed symplectic ﬁllings of cyclic quo-tient singularities whose corresponding link is lens space, and A. Nemethi and P. Popescu-Pampu identiﬁed the correspondence be-tween the symplectic ﬁllings in Lisca’s classiﬁcation and the Milnor ﬁbers for cyclic quotient singularities. Furthermore, M. Bhupal and K. Ono tried to extend these results, so that they classiﬁed all pos-sible symplectic ﬁllings of quotient surface singularities.In a series of two talks, I’d like to review known results and to investigate the correspondence between the symplectic ﬁllings in Bhupal–Ono’s classiﬁcation and the Milnor ﬁbers of quotient surface singularities. This is a joint work with Heesang Park, Dongsoo Shin, and Giancarlo Urz´ua. END:VEVENT BEGIN:VEVENT DTSTART:20151211T160000 DTEND:20151211T180000 DTSTAMP:20151210T150000Z UID:b1b097104a4e8b33d9fc855e022c7bdb@cgp.ibs.re.kr SUMMARY:On symplectic ﬁllings of quotient surface singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jongil Park\n\nEvent: Seminar 2015\n\nAbstract: One of active research areas in 4-manifold theory is to cassify symplectic ﬁllings of certain 3-manifolds equipped with a natural contact structure. Among them, people have long studied sym-plectic ﬁllings of the link of a normal complex surface singularity. Note that the link of a normal complex surface singularity carries a canonical contact structure which is also known as the Milnor ﬁllable contact structure.For example, P. Lisca classiﬁed symplectic ﬁllings of cyclic quo-tient singularities whose corresponding link is lens space, and A. Nemethi and P. Popescu-Pampu identiﬁed the correspondence be-tween the symplectic ﬁllings in Lisca’s classiﬁcation and the Milnor ﬁbers for cyclic quotient singularities. Furthermore, M. Bhupal and K. Ono tried to extend these results, so that they classiﬁed all pos-sible symplectic ﬁllings of quotient surface singularities.In a series of two talks, I’d like to review known results and to investigate the correspondence between the symplectic ﬁllings in Bhupal–Ono’s classiﬁcation and the Milnor ﬁbers of quotient surface singularities. This is a joint work with Heesang Park, Dongsoo Shin, and Giancarlo Urz´ua. END:VEVENT BEGIN:VEVENT DTSTART:20151210T140000 DTEND:20151210T160000 DTSTAMP:20151209T150000Z UID:cf983b1dea615ff600fb7db6db31a942@cgp.ibs.re.kr SUMMARY:A mathematical approach to BPS state counting in orientifold string theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Matthew B. Young\n\nEvent: Seminar 2015\n\nAbstract: The problem of understanding BPS states in Calabi-Yau compactifications of oriented string theory has led to a number of subfields of mathematics, Donaldson-Thomas theory and Gromov-Witten theory being two prime examples.Mathematicians and physicists have by now developed sophisticated techniques to approach this problem. However, if one considers orientifold string theory, a string theory which includes unoriented worldsheets, then our understanding is at a much more basic level. In this talk, after introducing the orientifold construction and explaining why it is of natural interest to mathematicians, I'll describe some recent results about the structure of Donaldson-Thomas theory with orientifolds. In particular, I'll explain a framework which allows one to prove orientifoldversions of wall-crossing formulas and the integrality conjecture of Kontsevich-Soibelman and Joyce-Song. END:VEVENT BEGIN:VEVENT DTSTART:20151221T160000 DTEND:20151221T173000 DTSTAMP:20151220T150000Z UID:7de3525da5d2b0d6c58c6b675a4970a5@cgp.ibs.re.kr SUMMARY:A new cycle-theoretic obstruction to rationality in dimension 4 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Vladimir Guletskii\n\nEvent: Algebraic Geometry Seminar 2015\n\nAbstract: In my talk, I will outline a certain approach to the non-rationality problem of a very general cubic fourfold in 5-dimensional projective space. The approach will be based on a new cycle-theoretic obstruction to rationality, given in terms of integral Chow-groups over non-algebraically closed fields, which behaves well in families provided Ayoub's conservation in dimension 2. Some preliminary but concrete results along this line will be presented too. END:VEVENT BEGIN:VEVENT DTSTART:20151221T140000 DTEND:20151221T160000 DTSTAMP:20151220T150000Z UID:51f5f1ab8ae506fa9494eee0006cea8d@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2015\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20151221T160000 DTEND:20151221T180000 DTSTAMP:20151220T150000Z UID:389799f26a80b083951717871983e00f@cgp.ibs.re.kr SUMMARY:Arithmetic topology on branched covers of 3-manifolds I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Ueki\n\nEvent: Seminar 2015\n\nAbstract: The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings, respectively. The study of these analogies is called arithmetic topology now. In my talks, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology. END:VEVENT BEGIN:VEVENT DTSTART:20151223T160000 DTEND:20151223T180000 DTSTAMP:20151222T150000Z UID:82ef30fac7a96bd6b74464d9a1fa36c3@cgp.ibs.re.kr SUMMARY:Arithmetic topology on branched covers of 3-manifolds II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Ueki\n\nEvent: Seminar 2015\n\nAbstract: The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings, respectively. The study of these analogies is called arithmetic topology now. In my talks, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology. END:VEVENT BEGIN:VEVENT DTSTART:20160106T112000 DTEND:20160106T122000 DTSTAMP:20160105T150000Z UID:49097e02fe25d1a7630e56fb6dad9c23@cgp.ibs.re.kr SUMMARY:Scattering diagrams and deformation of complex structures LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Kwokwai Chan\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Given a Calabi-Yau manifold equipped with a Lagrangian torus fibration, we introduce a DGLA via Witten deformation, which is mirror to the Kodaira-Spencer DGLA that governs deformation of complex structures. We show that semi-classical limits of the corresponding Maurer-Cartan solutions give rise to scattering diagrams which have played a key role in the Gross-Siebert program. This realizes part of Fukaya's program in understanding mirror symmetry via the SYZ approach. This talk is based on joint work with Conan Leung and Ziming Ma. END:VEVENT BEGIN:VEVENT DTSTART:20160109T160000 DTEND:20160109T170000 DTSTAMP:20160108T150000Z UID:719e02c02e2c2a2571dc0f67527d910c@cgp.ibs.re.kr SUMMARY:Categorification of Donaldson-Thomas invariants LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The Donaldson-Thomas invariant is a virtual count of stable sheaves on a Calabi-Yau 3-fold. A categorified DT invariant refers to a cohomology theory or a motivic invariant whose Euler number is the Donaldson-Thomas invariant. A key ingredient in the categorification is a compatible choice of local holomorphic functions whose critical loci give us an open cover of the moduli space of stable sheaves. I will talk about the notion of a critical virtual manifold which codifies the issue of finding the compatible holomorphic functions, and then will discuss various natural structures on a critical virtual manifold such as semi-perfect obstruction theory, DT type invariant, weighted Euler number, perverse sheaves and mixed Hodge modules, as well as the issue of orientability. Next I will show that a moduli space of simple sheaves on a Calabi-Yau 3-fold is a critical virtual manifold by using the holomorphic Chern-Simons functional and gauge theory. Finally I will discuss several categorified DT invariants and applications. Based on a joint work with Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20160106T160000 DTEND:20160106T170000 DTSTAMP:20160105T150000Z UID:25391e2921be1508c7cb84353ebc9bca@cgp.ibs.re.kr SUMMARY:Local observable algebras for 2+1D topological phases of matters LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Liang Kong\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: It is known that quantum field theories can be constructed from the local observable algebras. In this talk, I will discuss a simple realization of this idea for 2+1D topological field theories. More precisely, I will show how to define the local observable algebras in the so-called Levin-Wen models, which is a Hamiltonian version of Turaev-Viro topological field theories. These algebras allow us to classify all topological excitations, which determine global topological invariants via factorization homology. END:VEVENT BEGIN:VEVENT DTSTART:20160109T100000 DTEND:20160109T110000 DTSTAMP:20160108T150000Z UID:53b165a34c3e2461ca6b2928639ed6ae@cgp.ibs.re.kr SUMMARY:Topological B-model and Landau-Ginzburg model LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Qin Li\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Let X be a complex manifold. In physics, the quantum field theory of B-twisted sigma model with target X is fully encoded in the neighborhood of constant maps. In this talk, I will describe a rigorous analysis of the perturbative quantum field theory describing maps in the formal neighborhood of constant maps via renormalization method. This is joint work with Si Li. END:VEVENT BEGIN:VEVENT DTSTART:20160107T160000 DTEND:20160107T170000 DTSTAMP:20160106T150000Z UID:64796695b4e80d0f81d166f61892253b@cgp.ibs.re.kr SUMMARY:Categorification of Donaldson-Thomas invariants LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The Donaldson-Thomas invariant is a virtual count of stable sheaves on a Calabi-Yau 3-fold. A categorified DT invariant refers to a cohomology theory or a motivic invariant whose Euler number is the Donaldson-Thomas invariant. A key ingredient in the categorification is a compatible choice of local holomorphic functions whose critical loci give us an open cover of the moduli space of stable sheaves. I will talk about the notion of a critical virtual manifold which codifies the issue of finding the compatible holomorphic functions, and then will discuss various natural structures on a critical virtual manifold such as semi-perfect obstruction theory, DT type invariant, weighted Euler number, perverse sheaves and mixed Hodge modules, as well as the issue of orientability. Next I will show that a moduli space of simple sheaves on a Calabi-Yau 3-fold is a critical virtual manifold by using the holomorphic Chern-Simons functional and gauge theory. Finally I will discuss several categorified DT invariants and applications. Based on a joint work with Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20160108T160000 DTEND:20160108T170000 DTSTAMP:20160107T150000Z UID:97e589f196e63d72d94a8854ee9b646f@cgp.ibs.re.kr SUMMARY:Categorification of Donaldson-Thomas invariants LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The Donaldson-Thomas invariant is a virtual count of stable sheaves on a Calabi-Yau 3-fold. A categorified DT invariant refers to a cohomology theory or a motivic invariant whose Euler number is the Donaldson-Thomas invariant. A key ingredient in the categorification is a compatible choice of local holomorphic functions whose critical loci give us an open cover of the moduli space of stable sheaves. I will talk about the notion of a critical virtual manifold which codifies the issue of finding the compatible holomorphic functions, and then will discuss various natural structures on a critical virtual manifold such as semi-perfect obstruction theory, DT type invariant, weighted Euler number, perverse sheaves and mixed Hodge modules, as well as the issue of orientability. Next I will show that a moduli space of simple sheaves on a Calabi-Yau 3-fold is a critical virtual manifold by using the holomorphic Chern-Simons functional and gauge theory. Finally I will discuss several categorified DT invariants and applications. Based on a joint work with Jun Li. END:VEVENT BEGIN:VEVENT DTSTART:20160111T143000 DTEND:20160111T153000 DTSTAMP:20160110T150000Z UID:d418cef83449facac3257734242985dc@cgp.ibs.re.kr SUMMARY:Feynman geometry LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Andrey Losev\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The Feynman approach to QFT suffers from ultraviolet divergencies. The origin of these divergencies is the infinite-dimensionality of the DeRham DGA considered as a vector space. We propose to change the DeRham DGA to finite-dimenssional A-infinity algebra (or to A-infinity algebra with operations belonging to the trace class). We will call geometry corresponding to such algebra Feynman geometry. We consider different examples of Feynman geometry and note that the string theory is among them. We further propose to look for a generalization of Dirac-Segal axioms of QFT to Feynman geometry. END:VEVENT BEGIN:VEVENT DTSTART:20160106T100000 DTEND:20160106T110000 DTSTAMP:20160105T150000Z UID:0c57cad088dec3806f6ca7885f9c59f6@cgp.ibs.re.kr SUMMARY:Fusion of defects in Landau-Ginzburg models LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Daniel Murfet\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: There is a rich theory surrounding the fusion of defects in Landau-Ginzburg models. I will review the basic theory of matrix factorisations and their associated categories, and introduce the operation of tensor product of matrix factorisations which is interpreted as fusion of defects. I will then go through numerous examples in the mathematics and physics literature, including permutation type defects (motivated by conformal field theory) and stabilisations of bimodules (coming from knot homology). END:VEVENT BEGIN:VEVENT DTSTART:20160107T100000 DTEND:20160107T110000 DTSTAMP:20160106T150000Z UID:0eedb41d81d241fb4f69319ba3c680e8@cgp.ibs.re.kr SUMMARY:Fusion of defects in Landau-Ginzburg models LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Daniel Murfet\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Potentials, matrix factorisations and their fusion can be organised into the objects, 1-morphisms and composition rule (respectively) for the bicategory of Landau-Ginzburg models. I will present the fundamental properties of this bicategory, and discuss various interesting ways that it has been used in the last several years. This includes the knot homology of Khovanov-Rozansky, generalised orbifolding of Carqueville-Runkel, and Hodge theory following Ballard-Favero-Katzarkov. END:VEVENT BEGIN:VEVENT DTSTART:20160108T100000 DTEND:20160108T110000 DTSTAMP:20160107T150000Z UID:2051ee687767e6c23688e1b85055b565@cgp.ibs.re.kr SUMMARY:Fusion of defects in Landau-Ginzburg models LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Daniel Murfet\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: I will discuss in more depth the technical ingredients necessary to properly treat fusion of defects in Landau-Ginzburg models: Atiyah classes and homological perturbation. This will culminate in a "computable" model of the fusion of defects, which I will demonstrate with software written by myself and Carqueville for this purpose. Time permitting, I will also talk about related work in progress on A-infinity minimal models of DG-endomorphism algebras of matrix factorisations. END:VEVENT BEGIN:VEVENT DTSTART:20160106T143000 DTEND:20160106T153000 DTSTAMP:20160105T150000Z UID:8de026339e7582b3799bc3337358d7b5@cgp.ibs.re.kr SUMMARY:An introduction Primitive Form Theory LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Kyoji Saito\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Classical theory of elliptic integrals END:VEVENT BEGIN:VEVENT DTSTART:20160107T143000 DTEND:20160107T153000 DTSTAMP:20160106T150000Z UID:159bfc51784aed9101b0e20b833b0075@cgp.ibs.re.kr SUMMARY:An introduction Primitive Form Theory LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Kyoji Saito\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Primitive forms for an isolated critical point END:VEVENT BEGIN:VEVENT DTSTART:20160108T143000 DTEND:20160108T153000 DTSTAMP:20160107T150000Z UID:682fee61a47ad0f3ac2f3d6c9675c5d2@cgp.ibs.re.kr SUMMARY:An introduction Primitive Form Theory LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Kyoji Saito\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Applications to conformal field theory and mirror symmetry END:VEVENT BEGIN:VEVENT DTSTART:20160109T143000 DTEND:20160109T153000 DTSTAMP:20160108T150000Z UID:adc7b6cb2c3383ca5290aa14d01abfca@cgp.ibs.re.kr SUMMARY:From Calabi-Yau dg categories to Frobenius manifolds via primitive forms LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Atsushi Takahashi\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: It is one of the most important problems in mirror symmetry to construct functorially Frobenius manifolds from Calabi-Yau dg categories since the Kontsevich's homological mirror symmetry should imply the classical one, the isomorphism of Frobenius manifolds between the one from Gromov-Witten theory and the one from the deformation theory. This talk gives an approach to this problem based on the theory of primitive forms. Under a formality assumption, we shall construct formal primitive forms, which enable us to have formal Frobenius manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20160111T160000 DTEND:20160111T170000 DTSTAMP:20160110T150000Z UID:fdd216b6f5f50bee1b3e8b33be82246a@cgp.ibs.re.kr SUMMARY:Chiral differential operators from curved beta-gamma LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Brian Williams\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: In his 2010 paper, Kevin Costello describes how the partition function of a certain 2-dimensional sigma-model is encoded by the Witten genus of the target complex manifold. While the partition function deals with global observables, we study the structure of the local observables given by quantizing this two-dimensional field theory. In our formalism the local observables form a sheaf of two-dimensional factorization algebras. Our main result is that this construction recovers the sheaf of so-called chiral differential operators introduced by Gorbounov, Malikov, and Schechtman, and discussed by Witten in the context of (0,2)-supersymmetric field theories. This is joint work with Owen Gwilliam, and Vassily Gorbounov. END:VEVENT BEGIN:VEVENT DTSTART:20160107T112000 DTEND:20160107T122000 DTSTAMP:20160106T150000Z UID:d506202acf5f19c88d31d957f90a3aaa@cgp.ibs.re.kr SUMMARY:Cohomological Donaldson-Thomas theory with orientifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Matthew B. Young\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The goal of these lectures is twofold. The first is to introduce Kontsevich and Soibelman's cohomological approach to the Donaldson-Thomas theory of three dimensional Calabi-Yau categories. The second is to present an extension of these ideas that leads to a generalization of Donaldson-Thomas theory which counts stable self-dual objects of a Calabi-Yau category with involution. Such objects are categorical analogues of principal bundles with classical structure group. In particular, this generalization gives a mathematical approach to counting BPS states in orientifold string theory. END:VEVENT BEGIN:VEVENT DTSTART:20160108T112000 DTEND:20160108T122000 DTSTAMP:20160107T150000Z UID:e8ded41c470d1055f252303ff41e7ab4@cgp.ibs.re.kr SUMMARY:Cohomological Donaldson-Thomas theory with orientifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Matthew B. Young\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The goal of these lectures is twofold. The first is to introduce Kontsevich and Soibelman's cohomological approach to the Donaldson-Thomas theory of three dimensional Calabi-Yau categories. The second is to present an extension of these ideas that leads to a generalization of Donaldson-Thomas theory which counts stable self-dual objects of a Calabi-Yau category with involution. Such objects are categorical analogues of principal bundles with classical structure group. In particular, this generalization gives a mathematical approach to counting BPS states in orientifold string theory. END:VEVENT BEGIN:VEVENT DTSTART:20160109T112000 DTEND:20160109T122000 DTSTAMP:20160108T150000Z UID:f397dbd625c3634b76fdc49175e20945@cgp.ibs.re.kr SUMMARY:Cohomological Donaldson-Thomas theory with orientifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Matthew B. Young\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The goal of these lectures is twofold. The first is to introduce Kontsevich and Soibelman's cohomological approach to the Donaldson-Thomas theory of three dimensional Calabi-Yau categories. The second is to present an extension of these ideas that leads to a generalization of Donaldson-Thomas theory which counts stable self-dual objects of a Calabi-Yau category with involution. Such objects are categorical analogues of principal bundles with classical structure group. In particular, this generalization gives a mathematical approach to counting BPS states in orientifold string theory. END:VEVENT BEGIN:VEVENT DTSTART:20160114T112000 DTEND:20160114T122000 DTSTAMP:20160113T150000Z UID:e6edd34b863ddf6e37a5a3ae958109cb@cgp.ibs.re.kr SUMMARY:Effective field theories and elliptic cohomology LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Daniel Berwick-Evans\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: I will describe a geometric model for elliptic cohomology at the Tate curve whose cocycles are a class of 2-dimensional effective field theories. A geometrically-motived modularity condition singles out cocycles whose Chern characters take values in the complexification of topological modular forms (TMF). The Witten genus of a string manifold and the moonshine module furnish examples. END:VEVENT BEGIN:VEVENT DTSTART:20160112T100000 DTEND:20160112T110000 DTSTAMP:20160111T150000Z UID:f33ff95a499fe4d2b914f61ab143364d@cgp.ibs.re.kr SUMMARY:Deformation quantization of Shifted symplectic and Poisson structures LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Damien Calaque\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: I will give an overview of the recent developments in derived symplectic geometry, including:- shifted symplectic and Lagrangian structures, after Pantev-Toën-Vaquié-Vezzosi.- shifted Poisson structures- deformation quantization of these. END:VEVENT BEGIN:VEVENT DTSTART:20160111T100000 DTEND:20160111T110000 DTSTAMP:20160110T150000Z UID:9cc95c666fe36227cbb8e12a8084e9bc@cgp.ibs.re.kr SUMMARY:Perturbative BV-BFV theories on manifolds with boundary LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Alberto S. Cattaneo\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: According to Segal and Atiyah, a quantum field theory on manifolds with boundary should be thought of as, roughly speaking, the assignment of a vector space (space of states) to the boundary and an element thereof (the state or the evolution operator) to the bulk, in a way that is compatible with gluing. In this talk (based on joint work with P. Mnev and N. Reshetikhin) I will describe how this has to be reformulated when working in perturbation theory. In particular, I will discuss the perturbative quantization of gauge theories on manifolds with boundary. It turns out that, under suitable assumptions, the bulk symmetries, treated in the BV formalism, naturally give rise to a cohomological description of the reduced phase space (BFV formalism) in a correlated way that can be quantized. Time permitting, I will present the example of BF theories. END:VEVENT BEGIN:VEVENT DTSTART:20160114T160000 DTEND:20160114T170000 DTSTAMP:20160113T150000Z UID:8115a267a61c4c29fa9230faf2475148@cgp.ibs.re.kr SUMMARY:Perturbative QFT from derived stacks LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Ryan Grady\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: In this talk I will discuss one approach to derived stacks and their utility in QFT constructions. I aim to give many examples, as well as the discuss the resulting theories and their quantizations which often encode geometric/topological invariants. The talk is based on work with Owen Gwilliam. END:VEVENT BEGIN:VEVENT DTSTART:20160114T100000 DTEND:20160114T110000 DTSTAMP:20160113T150000Z UID:085569c139cb11aa79d07aa905e4c657@cgp.ibs.re.kr SUMMARY:Categorical Harmonic Analysis on Reductive groups LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Sam Gunningham\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: In this talk I will survey some recent and ongoing work of myself and collaborators (David Ben-Zvi, David Nadler, Hendrik Orem), and others, concerning certain topological field theories associated to a complex reductive group G. The basic example of such a theory, assigns the cohomology of the character variety (i.e. moduli of representations of the fundamental group) to a topological surface. To a point, it assigns the categorical group algebra of D-modules on G. I will discuss various approaches to studying this theory, including work from my thesis on parabolic induction and restriction functors, work in progress with Ben-Zvi and Nadler on a monoidal quantization of the the group scheme of regular centralizers using translation functors on Whittaker modules, and a categorical highest weight theorem with Ben-Zvi, Nadler and Orem. Our work is partly motivated by the "Arithmetic Harmonic Analysis" developed by Hausel, Rodriguez-Villegas, and Lettalier, to study the cohomology of character and quiver varieties. END:VEVENT BEGIN:VEVENT DTSTART:20160113T100000 DTEND:20160113T110000 DTSTAMP:20160112T150000Z UID:988d45c3100a3bdd4d8f87095cff6996@cgp.ibs.re.kr SUMMARY:Noncommutative Geometry and the BV-formalism in moduli spaces of Riemann surfaces LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Alastair Hamilton\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: In this talk I will discuss how the BV-formalism appears, in a noncommutative incarnation, in the construction of homology and cohomology classes in the moduli space of Riemann surfaces. The ideas involved go back to Kontsevich and his papers on formal noncommutative symplectic geometry and Feynman diagrams. In particular, we will consider one idea put forth by Kontsevich concerning how to express the formal series produced by pairing these homology and cohomology classes as an instance of a BV-type functional integral, and follow up by considering some examples. END:VEVENT BEGIN:VEVENT DTSTART:20160113T112000 DTEND:20160113T122000 DTSTAMP:20160112T150000Z UID:ab4816d759bc6dc181a905a275f4fa32@cgp.ibs.re.kr SUMMARY:Operads, homotopy algebras and strings LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Branislav Jurco\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: We describe certain algebras appearing in string field theory as algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view. END:VEVENT BEGIN:VEVENT DTSTART:20160111T112000 DTEND:20160111T122000 DTSTAMP:20160110T150000Z UID:8b564673628cc00877368f6b74a82299@cgp.ibs.re.kr SUMMARY:Cellular BV-BFV-BF theory LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Pavel Mnev\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: We will introduce the cellular version of BF theory and explain how it fits into symplectic cohomological ("BF-BFV") quantization programme. Partition functions are given by finite-dimensional integrals, satisfy Segal-like gluing property, are invariant with respect to cellular aggregations (which play the role of Wilson's renormalization flow) and satisfy BV quantum master equation modified by a boundary term. Partition functions can be expressed in terms of torsions and the data of rational homotopy type; they also contain a mod 16 phase - a model for the eta invariant appearing in the phase of Chern-Simons partition function. This is a report on joint work with A. S. Cattaneo and N. Reshetikhin. END:VEVENT BEGIN:VEVENT DTSTART:20160112T160000 DTEND:20160112T170000 DTSTAMP:20160111T150000Z UID:f2c660f7efd18f9c1d452e8efcd32f75@cgp.ibs.re.kr SUMMARY:Additivity for Poisson structures and quantization LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Nick Rozenblyum\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: A key construction in quantum field theory is the AKSZ construction. In the setting of derived symplectic geometry, a version of this construction was considered by Pantev-Toen-Vaquie-Vezzosi, who showed that the derived mapping stack from an oriented manifold to a (shifted) symplected stack has a shifted symplectic structure. I will explain local-to-global approach to this construction, which, in particular, shows that the AKSZ/PTVV construction is compatible with deformation quantization in a strong sense and gives a new proof of the formality theorem for the E_n operads, n>2. Moreover, I will explain how every deformation quantization problem reduces to (a version of) BV-quantization. Time permitting, I will describe some geometric applications. END:VEVENT BEGIN:VEVENT DTSTART:20160112T112000 DTEND:20160112T122000 DTSTAMP:20160111T150000Z UID:dbdfd2673c949a672c8994e16bb7e644@cgp.ibs.re.kr SUMMARY:Poisson geometry of groups and shifted Poisson structures LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Pavel Safronov\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: In this talk I will give a modern point of view on some geometric structures underlying classical limits of quantum groups. These include quasi-Poisson groups, quasi-Poisson spaces, infinitesimally braided categories and so on. It turns out that all these notions can be nicely packaged in the framework of shifted Poisson structures of Calaque, Pantev, Toen, Vaquie and Vezzosi which I will briefly review. END:VEVENT BEGIN:VEVENT DTSTART:20160112T143000 DTEND:20160112T153000 DTSTAMP:20160111T150000Z UID:fa3e4045aaae94487f0a8578037e24ca@cgp.ibs.re.kr SUMMARY:Fully extended semi-classical TFTs and linear BV quantization LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Claudia Scheimbauer\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Derived symplectic geometry in the sense of Pantev-Toen-Vaquié-Vezzosi allows for a reinterpretation/analog of the classical AKSZ construction for certain $\sigma$-models. I will explain how this construction can be extended to give a fully extended oriented TFT with values in a higher category whose objects are $n$-shifted symplectic derived stacks and (higher) morphisms are (higher) Lagrangian correspondences. It is given by taking mapping stacks with a fixed target building and describes ``semi-classical TFTs". If time permits, I will give an outlook how, when restricting to the subcategory of $n$-shifted symplectic dg vector spaces and linear Lagrangian correspondences, one can construct a linear BV quantization functor to the higher Morita category using the higher enveloping algebras of Knudsen. The former is joint work in progress with Calaque--Haugseng; the latter is part of a collaboration with Gwilliam--Haugseng--Johnson-Freyd--Li-Bland--Weinstein. END:VEVENT BEGIN:VEVENT DTSTART:20160114T143000 DTEND:20160114T153000 DTSTAMP:20160113T150000Z UID:382c367589e6f4193f7873483392bc14@cgp.ibs.re.kr SUMMARY:Hopf invariants, rational homotopy theory, and physical integrals LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Dev Sinha\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: We discuss a basic question in algebraic topology: given two maps f,g : X —> Y, how can we tell whether or not they are homotopic? One condition is that f and g should pull back cohomology in the same way. But even when X is a sphere, this is far from sufficient. In relatively recent work, Ben Walter and I resolve this question when X is a sphere and Y is simply connected, rationally (that is, up to then multiplying f and g by some non-zero integer). We do so by giving explicit integrals, generalizing Whitehead’s integral formula for the Hopf invariant, which has been cited regularly in the physics literature. Our integrals are special cases of integrals developed by Cattaneo and Mnev in the context of Chern-Simons theory. We speculate on the connection, as well as potential connection with L_\infty models for rational homotopy theory. END:VEVENT BEGIN:VEVENT DTSTART:20160113T143000 DTEND:20160113T153000 DTSTAMP:20160112T150000Z UID:5e691370c1b28ec44d6fa3a8ce3d47cf@cgp.ibs.re.kr SUMMARY:Gravity algebras as obstructions LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Benjamin C. Ward\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: The failure of an associative algebra to be commutative is measured by an instance of the Koszul dual structure; the commutator Lie bracket. In this talk I will discuss a (derived) E_2 analog of this fact. Specifically we construct a (homotopy) gravity algebra as an obstruction to lifting a (homotopy) BV algebra to an algebra over the Deligne-Mumford compactification. END:VEVENT BEGIN:VEVENT DTSTART:20160113T160000 DTEND:20160113T170000 DTSTAMP:20160112T150000Z UID:0bd5047eee1058cac10d14c381d9f338@cgp.ibs.re.kr SUMMARY:Higher Determinants and Double Loop Groups LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Jesse Wolfson\n\nEvent: Mathematics of Quantum Field Theory\n\nAbstract: Determinant lines play a central role in the study of smooth loop groups. In a non-archimedean setting, determinant (n)-gerbes play the analogous role for n-fold loop groups (cf.Arkhipov-Kremnizer and Osipov-Zhu in dimension 2, and joint work with O. Braunling and M. Groechenig in arbitrary dimension). In this talk, I'll describe ongoing joint work with Jens Kaad and Ryszard Nest in which we transport these non-Archimedean constructions to the classical setting to construct determinant gerbes associated to smooth double loop groups, and study the associated higher central extensions. END:VEVENT BEGIN:VEVENT DTSTART:20160204T160000 DTEND:20160204T180000 DTSTAMP:20160203T150000Z UID:22ea1f7718fab317e05b091d671fb6ea@cgp.ibs.re.kr SUMMARY:Vertex algebras and their applications to the denominator identity LOCATION:CGP Main Hall DESCRIPTION:Speaker: Namhee Kwon\n\nEvent: CGP Seminar 2016\n\nAbstract: Vertex algebras were introduced by Richard Borcherds in the 1908s. However, it seems like that the notion of vertex algebras was already known implicitly to physicists much earlier. In fact, the theory of vertex algebras serves as the rigorous mathematical foundation for 2-dimensional quantum field theory. Vertex algebras are also very useful in the representation theory of infinite dimensional Lie algebras.In this talk, we first review free field realization of irreducible representations of affine Lie (super)algebras. Our approach produces vertex operators and relates the representation theory of affine Lie (super)algebras to several product-summation type identities including the denominator identities. At the end of this talk, we will introduce our recent results concerned with this topic. END:VEVENT BEGIN:VEVENT DTSTART:20160128T160000 DTEND:20160128T180000 DTSTAMP:20160127T150000Z UID:4c477b1ea2c87bf79d1ed6dc592aa5e8@cgp.ibs.re.kr SUMMARY:Segre classes and Schur polynomials for algebraic cobordism LOCATION:CGP Main Hall DESCRIPTION:Speaker: Thomas Hudson\n\nEvent: CGP Seminar 2016\n\nAbstract: A classical result in Schubert calculus, known as the Giambelli formula, describes the Schubert classes of the Grassmannian in terms of Schur polynomials evaluated at the Chern classes of the universal bundle. In this talk I will explain how this setting can be generalized from cohomology and the Chow ring to other oriented cohomology theories such as connective K-theory and algebraic cobordism. In the process a key role is played by a generalized version of Segre classes. This is a joint work with Tomoo Matsumura. END:VEVENT BEGIN:VEVENT DTSTART:20160216T160000 DTEND:20160216T180000 DTSTAMP:20160215T150000Z UID:56069148ad989370c69d8a0b34dfbd6e@cgp.ibs.re.kr SUMMARY:Holomorphic disk potential for exotic monotone Lagrangian tori LOCATION:CGP Main Hall DESCRIPTION:Speaker: Grigory Mikhalkin\n\nEvent: Seminar 2016\n\nAbstract: In their 2010 IPMU preprint Galkin and Usnich have suggested a construction of an infinite family of mutations (birational coordinate changes) of the potential x + y + 1/xy into some other Laurent polynomials. They associated such mutations to the so-called Markov triples (integer a,b,c with the property $a^2$+$b^2$+$c^2$=3abs). In their turn, these Markov triples correspond to the weighted projective planes P(a,b,c) that admit smoothing to the ordinary plane CP2=P(1,1,1).In the same preprint Galkin and Usnich have conjectured that the resulting Laurent polynomials correspond to the holomorphic disk potentials of an (infinite) family of exotic monotone Lagrangian tori in CP2. In its weaker version (correspondence on the level of Newton polygons of the potentials) this conjecture was proved in the 2014 preprint of Renato Vianna. This result already implies existence of infinitely many of distinct monotone Lagrangian tori. The talk will present a joint work with Sergey Galkin establishing the original version of the conjecture, i.e. also taking into account correspondence on the level of the coefficients of the potentials. END:VEVENT BEGIN:VEVENT DTSTART:20160218T160000 DTEND:20160218T180000 DTSTAMP:20160217T150000Z UID:f6850126f71b837a144c20c1b6b6c9ee@cgp.ibs.re.kr SUMMARY:Planar and spatial real algebraic curves: (half-) integer indices LOCATION:CGP Main Hall DESCRIPTION:Speaker: Grigory Mikhalkin\n\nEvent: CGP Seminar 2016\n\nAbstract: The question of possible arrangements of ovals in an algebraic curve of a given degree in the real projective plane is a classical question (over 100 years old). It was noted already by Hilbert that the most topologically restrictive case is when the number of ovals is maximal for its degree (the so-called M-curves). Spatial real algebraic curves are links topologically. In particular real rational curves are knots whose topological types are constrained by their degree.In this survey talk we focus on two new quantitative characteristics (indices) of real algebraic curves: one for curves in the plane http://arxiv.org/abs/1505.04338 and one for curves in the 3-space http://arxiv.org/abs/math/0005162. Maximality of these numbers has strong topological implications. The 3-dimensional part of the talk is based on a joint work in progress with Stepan Orevkov. END:VEVENT BEGIN:VEVENT DTSTART:20160225T160000 DTEND:20160225T180000 DTSTAMP:20160224T150000Z UID:bc3e68c443dd797f218aadfb73c8092b@cgp.ibs.re.kr SUMMARY:On energy critical geometric wave equations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sung-Jin Oh\n\nEvent: CGP Seminar 2016\n\nAbstract: The subject of this talk is wave equations that arise from geometric considerations. Prime examples include the wave map equation and the Yang-Mills equation on the Minkowski space. On one hand, these are fundamental field theories arising in physics; on the other hand, they may be thought of as the hyperbolic analogues of the harmonic map and the elliptic Yang-Mills equations, which are interesting geometric PDEs on their own. END:VEVENT BEGIN:VEVENT DTSTART:20160219T160000 DTEND:20160219T180000 DTSTAMP:20160218T150000Z UID:1cc26744cf74acbef1649c934496839f@cgp.ibs.re.kr SUMMARY:A survey of locally conformally Kaehler geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Liviu Ornea\n\nEvent: Seminar 2016\n\nAbstract: Locally conformal Kaehler (LCK) manifolds are complex manifolds whose universal cover bears a Kaehler metric on which the deck group acts by holomorphic homotheties. The typical examples are the Hopf manifolds. In the first part of the talk I shall describe the geometry and topology of these manifolds, while in the end I shall concentrate on recent results. END:VEVENT BEGIN:VEVENT DTSTART:20160211T130000 DTEND:20160211T140000 DTSTAMP:20160210T150000Z UID:f46b22ff86e379ef3dbfadb0749de648@cgp.ibs.re.kr SUMMARY:Invariants of moduli spaces of curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mehdi Tavakol\n\nEvent: Seminar 2016\n\nAbstract: In a series of lectures I will give a review of moduli spaces of curves and their invariants.This involves intersection theory and cohomology of these spaces.The main focus is on the study of tautological classes by giving many concrete examples.I will discuss known results and open questions as well. END:VEVENT BEGIN:VEVENT DTSTART:20160303T160000 DTEND:20160303T180000 DTSTAMP:20160302T150000Z UID:23dcef9c21bbd4cc376a40796318f321@cgp.ibs.re.kr SUMMARY:Classification results for two-dimensional Lagrangian tori LOCATION:CGP Main Hall DESCRIPTION:Speaker: Georgios Dimitroglou Rizell\n\nEvent: CGP Seminar 2016\n\nAbstract: We discuss recent classification results for two-dimensional Lagrangian tori in certain symplectic manifolds, all proven using the splitting construction from symplectic field theory. Notably, these techniques are used to give a complete classification result for Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy. In addition, in joint work with E. Goodman and A. Ivrii, we also show that there is a unique torus up to Lagrangian isotopy inside the symplectic vector space, the projective plane, and the monotone S2 x S2. Finally, the nearby Lagrangian conjecture for the cotangent bundle of the torus is established. END:VEVENT BEGIN:VEVENT DTSTART:20160219T140000 DTEND:20160219T153000 DTSTAMP:20160218T150000Z UID:733b588b550313c7b179f0ccef868a24@cgp.ibs.re.kr SUMMARY:On the Fano visitor problem LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: I will review the Fano visitor problem, its history and recent progress. This talk is based on a joint work with Young-Hoon Kiem, In-Kyun Kim and Hwayoung Lee. END:VEVENT BEGIN:VEVENT DTSTART:20160218T130000 DTEND:20160218T140000 DTSTAMP:20160217T150000Z UID:c9b2e1354a4e4fce32c35acbec115879@cgp.ibs.re.kr SUMMARY:Invariants of moduli spaces of curves II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mehdi Tavakol\n\nEvent: Seminar 2016\n\nAbstract: In a series of lectures I will give a review of moduli spaces of curves and their invariants.This involves intersection theory and cohomology of these spaces.The main focus is on the study of tautological classes by giving many concrete examples.I will discuss known results and open questions as well. END:VEVENT BEGIN:VEVENT DTSTART:20160217T150000 DTEND:20160217T160000 DTSTAMP:20160216T150000Z UID:b63f4cc397b3205b981498e97c8d1001@cgp.ibs.re.kr SUMMARY:Defintion of Maslov class (following Arnold) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seung-ook Yu\n\nEvent: QE Lecture\n\nAbstract: In this talk, I will explain construction of Maslov class which is the characteristic class of the Lagrangian Grassmanian of the symplectic vector space. END:VEVENT BEGIN:VEVENT DTSTART:20160217T140000 DTEND:20160217T150000 DTSTAMP:20160216T150000Z UID:9f6b94527a3e8a823e544b74fe5ccd30@cgp.ibs.re.kr SUMMARY:Convexity of the moment map image of torus action on symplectic manifolds (following Atiyah & Guillemin-Sternberg) LOCATION:CGP Main Hall DESCRIPTION:Speaker: SeongJin Choi\n\nEvent: QE Lecture\n\nAbstract: I'll present the Atiyah-Guillemin-Sternberg's convexity theorem ; If X is a connected compact symplectic manifold with a Hamiltonian torus action, then the image of a moment map is convex. Key part of the proof is to show that the component function of the moment map is a Morse-Bott function with even indices. A Morse-Bott function with even indices has good properties, its level sets are connected(used in the Atiyah's proof) and it has a unique local maximum(used in the Guillemin-Sternberg's proof). END:VEVENT BEGIN:VEVENT DTSTART:20160219T130000 DTEND:20160219T140000 DTSTAMP:20160218T150000Z UID:9c59cd502462d98e5599eb5973e3296a@cgp.ibs.re.kr SUMMARY:Linear recurrence relations in Q-systems via lattice points in polyhedra LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chul-hee Lee (University of Queensland)\n\nEvent: Seminar 2016\n\nAbstract: There exists an interesting family of finite-dimensional representations called the Kirillov-Reshetikhin modules over thequantum affine algebra $U_q(\widehat{\mathfrak{g}})$. The isotypicdecomposition of theses modules or their tensor products as$U_q(\mathfrak{g})$-modules is given by the fermionic formula which can be regarded as a representation theoretic version of completeness of the Bethe ansatz.In spite of its elegance, it quickly becomes impractical as the rank of $\mathfrak{g}$ increases due to its complicated combinatorial nature. Thus it is advantageous to have a more explicit description ofthis decomposition for practical purposes. Such a formula is well-known in classical types, but remains largely conjectural in exceptional types.I will talk about linear recurrence relations satisfied by the sequence $\{Q_m^{(a)}\}_{m=0}^{\infty}$ of the characters of the Kirillov-Reshetikhin modules and how they shed light on the aboveproblem. The key idea is to regard this decomposition as a summation over the lattices points in a suitable polyhedron. END:VEVENT BEGIN:VEVENT DTSTART:20160421T160000 DTEND:20160421T180000 DTSTAMP:20160420T150000Z UID:40616cd47e2e6972513c13120e300866@cgp.ibs.re.kr SUMMARY:No finite index subgroup of a mapping class group embeds into the $C^2$ circle diffeomorphism group LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: CGP Seminar 2016\n\nAbstract: One intriguing direction of research in surface theory is the analogy between mapping class groups and higher rank lattices. However, current knowledge on finite index subgroups of mapping class groups are still scarce. We prove the result in the title, which was originally asked by Farb, and which is analogous to Ghys and Burger─Monod theorem on obstructions of higher rank lattice actions on the circle. (Joint work with Hyungryul Baik and Thomas Koberda) END:VEVENT BEGIN:VEVENT DTSTART:20160309T130000 DTEND:20160309T150000 DTSTAMP:20160308T150000Z UID:056605da4b6a046a680a4f6220dd750c@cgp.ibs.re.kr SUMMARY:From Microlocal Category to Contact Non-squeezability I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sheng-Fu Chiu\n\nEvent: Seminar 2016\n\nAbstract: In the first talk, I will introduce Tamarkin's notion of microlocal category of sheaves based on Kashiwara-Schapira. I will also describe the action of Hamiltonian Symplectomorphism on the microlocal category. END:VEVENT BEGIN:VEVENT DTSTART:20160311T130000 DTEND:20160311T150000 DTSTAMP:20160310T150000Z UID:dfe88106346d42560678f0421bb011a3@cgp.ibs.re.kr SUMMARY:From Microlocal Category to Contact Non-squeezability II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sheng-Fu Chiu\n\nEvent: Seminar 2016\n\nAbstract: In the second talk, I will adopt the microlocal framework to contact topology and define an contact isotopy invariant similar to contact homology when the extra dimension comes from a circle. With this invariant one gives an approach to a contact non-squeezing phenomenon proposed by Elashberg-Kim-Polterovich. END:VEVENT BEGIN:VEVENT DTSTART:20160223T160000 DTEND:20160223T180000 DTSTAMP:20160222T150000Z UID:69d1621da129c768ac132c24219af6b7@cgp.ibs.re.kr SUMMARY:Lorentz symmetry and particle theories from graph LOCATION:CGP Main Hall DESCRIPTION:Speaker: Corneliu Sochichiu\n\nEvent: Seminar 2016\n\nAbstract: We study a fermionic graph models which admit continuum limit. We inquire for which types of graphs the model this limit describes a relativistic Dirac fermion. Then, we consider deformations of such graphs, which still admit a properly defined continuum limit. The continuum limit of deformations is given by gauge fields and gravity coupled to Dirac fermion. The back reaction from fermionic field, presumably, gives the dynamics for these new fields compatible with symmetries. END:VEVENT BEGIN:VEVENT DTSTART:20160308T140000 DTEND:20160308T153000 DTSTAMP:20160307T150000Z UID:6ed3bb9f13d0affe359ff3049f5857fb@cgp.ibs.re.kr SUMMARY:Floer homology for Lagrangian cobordisms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Georgios Dimitroglou Rizell\n\nEvent: Symplectic Tuesday\n\nAbstract: Legendrian contact homology (LCH) is a Legendrian isotopy invariant. We introduce a version of wrapped Floer homology for pairs of Lagrangian cobordisms having Legendrian ends that admit augmentations. This theory is used to establish long exact sequences involving the singular homology of a Lagrangian cobordism and the linearised LCH of its Legendrian ends. As an application we show that an exact Lagrangian cobordism from a Legendrian sphere to itself necessarily is a concordance in high dimensions. This is joint work with B. Chantraine, P. Ghiggini and R. Golovko. END:VEVENT BEGIN:VEVENT DTSTART:20160222T160000 DTEND:20160222T180000 DTSTAMP:20160221T150000Z UID:fa75bc3485f577c116db23e8a81d35e7@cgp.ibs.re.kr SUMMARY:A survey of locally conformally Kaehler geometry (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Liviu Ornea\n\nEvent: Lecture Series\n\nAbstract: I this talk, I shall focus on LCK manifolds admitting coverings with automorphic global Kaehler potentials and I shall give hints for the proofs of their main properties. The results are joint work with Misha Verbitsky. END:VEVENT BEGIN:VEVENT DTSTART:20160224T160000 DTEND:20160224T180000 DTSTAMP:20160223T150000Z UID:895354563fdbd30115a0a8b87975f1a0@cgp.ibs.re.kr SUMMARY:A survey of locally conformally Kaehler geometry (III) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Liviu Ornea\n\nEvent: Lecture Series\n\nAbstract: I this talk, I complete the description of LCK manifolds admitting coverings with automorphic global Kaehler potentials and prove that such compact LCK manifolds always contain Hopf surfaces (joint work with Misha Verbitsky). END:VEVENT BEGIN:VEVENT DTSTART:20160225T130000 DTEND:20160225T140000 DTSTAMP:20160224T150000Z UID:716dc1ed701d921846b43f44c34252c1@cgp.ibs.re.kr SUMMARY:Invariants of moduli spaces of curves III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mehdi Tavakol\n\nEvent: Seminar 2016\n\nAbstract: In a series of lectures I will give a review of moduli spaces of curves and their invariants. This involves intersection theory and cohomology of these spaces. The main focus is on the study of tautological classes by giving many concrete examples. I will discuss known results and open questions as well. END:VEVENT BEGIN:VEVENT DTSTART:20160307T160000 DTEND:20160307T180000 DTSTAMP:20160306T150000Z UID:1f51e6c424b36d878fa9f8753e09545a@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields V (Classical Symmetries and BV-BRST Formalism) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2016\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20160303T200000 DTEND:20160303T220000 DTSTAMP:20160302T150000Z UID:b3d721f8d5392b4e2eba30cf6a4fffd6@cgp.ibs.re.kr SUMMARY:Polynomially convex sets in C^n LOCATION:Math. Bldg. #106 DESCRIPTION:Speaker: Thomas Pawlaschyk (Universität Wuppertal)\n\nEvent: GAIA Seminar on Complex Analytic Geometry\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160304T155000 DTEND:20160304T180000 DTSTAMP:20160303T150000Z UID:1644da2d78ac2461583dd10cbe77610a@cgp.ibs.re.kr SUMMARY:On the Structure of the Singular Sets for Dissipative Kinetic Equations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyung Ju Hwang (POSTECH)\n\nEvent: MATH Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160314T110000 DTEND:20160314T120000 DTSTAMP:20160313T150000Z UID:df26cd575d5eac8f4087a54e49c41eae@cgp.ibs.re.kr SUMMARY:Comparing two mirror symmetries of elliptic curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We study two different kinds of mirror symmetries of elliptic curves. The first one(due to Polishchuk-Zaslow) shows an equivalence between the Fukaya category of the symplectic torus and the derived category of the mirror elliptic curve, and the other(due to Cho-Hong-Lau) is an equivalence between the Fukaya category and the category of matrix factorizations of a cubic polynomial. We review these two equivalences after some preliminaries concerning a little bit of Lagrangian Floer theory and matrix factorizations. Then we recall Orlov’s LG/CY correspondence. Finally, we investigate how two mirror symmetries are related via Orlov’s result. END:VEVENT BEGIN:VEVENT DTSTART:20160315T110000 DTEND:20160315T120000 DTSTAMP:20160314T150000Z UID:03c0ab951fca7516889af348bbdee679@cgp.ibs.re.kr SUMMARY:Comparing two mirror symmetries of elliptic curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We study two different kinds of mirror symmetries of elliptic curves. The first one(due to Polishchuk-Zaslow) shows an equivalence between the Fukaya category of the symplectic torus and the derived category of the mirror elliptic curve, and the other(due to Cho-Hong-Lau) is an equivalence between the Fukaya category and the category of matrix factorizations of a cubic polynomial. We review these two equivalences after some preliminaries concerning a little bit of Lagrangian Floer theory and matrix factorizations. Then we recall Orlov’s LG/CY correspondence. Finally, we investigate how two mirror symmetries are related via Orlov’s result. END:VEVENT BEGIN:VEVENT DTSTART:20160318T110000 DTEND:20160318T120000 DTSTAMP:20160317T150000Z UID:7026a249b821ad081e2ca9da8a60a441@cgp.ibs.re.kr SUMMARY:Comparing two mirror symmetries of elliptic curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We study two different kinds of mirror symmetries of elliptic curves. The first one(due to Polishchuk-Zaslow) shows an equivalence between the Fukaya category of the symplectic torus and the derived category of the mirror elliptic curve, and the other(due to Cho-Hong-Lau) is an equivalence between the Fukaya category and the category of matrix factorizations of a cubic polynomial. We review these two equivalences after some preliminaries concerning a little bit of Lagrangian Floer theory and matrix factorizations. Then we recall Orlov’s LG/CY correspondence. Finally, we investigate how two mirror symmetries are related via Orlov’s result. END:VEVENT BEGIN:VEVENT DTSTART:20160314T160000 DTEND:20160314T180000 DTSTAMP:20160313T150000Z UID:fe3f4ed220dd692b22af7912850b4016@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields VI (Quantum BV Formalism and Symmetries of Quantum Expectation ) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2016\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20160328T160000 DTEND:20160328T180000 DTSTAMP:20160327T150000Z UID:8bc7963c6260432de49f7c827cf7af04@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields VIII (Category of CQFT Algebras and Quantum Correlation Functions) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2016\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20160321T160000 DTEND:20160321T180000 DTSTAMP:20160320T150000Z UID:e3cad42c363165645271f3009c76be14@cgp.ibs.re.kr SUMMARY:Lectures on Homotopy Theory of Quantum Fields VII (Classical to Quantum Spectral Sequence) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2016\n\nAbstract: This series of lectures is about my program to characterize path integrals of quantum field theory in terms of the symmetries of the quantum expectation, which should satisfy a certain coherence with a particular weight filtration generated by the Planck constant ħ. END:VEVENT BEGIN:VEVENT DTSTART:20160323T160000 DTEND:20160323T173000 DTSTAMP:20160322T150000Z UID:c0a93ecfd3dd08fdda68c32228efa185@cgp.ibs.re.kr SUMMARY:Quartic threefolds with many symmetries. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: We study birational geometry of quartic threefolds with large groups of automrophisms. Namely, there is a one-parameter family of singular quartics whose automorphism group contains the symmetric group S6. The family contains some well known rational quartics, including the Burkhardt quartic and the Igusa quartic. It was proved by A.Beauville that a general member of this family is non-rational. I will tell about rationality constructions for remaining quartics in this family (that actually go back to J.Todd). Also, studying these quartics provides information about birational geometry of one more closely related class of Fano varieties, double covers of quadric threefolds. The talk is based on joint works with I.Cheltsov and V.Przyalkowski. END:VEVENT BEGIN:VEVENT DTSTART:20160325T160000 DTEND:20160325T180000 DTSTAMP:20160324T150000Z UID:99f598c7cc2ff484608150defdeaa5db@cgp.ibs.re.kr SUMMARY:Combinatorics of q-integrals over order polytopes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jang Soo Kim\n\nEvent: Seminar 2016\n\nAbstract: Given a poset P, the order polytope O(P) is a polytope obtained naturally from P. In this talk we express a q-integral over an order polytope O(P) as a sum over all linear extensions of the poset P. As an application, we give a combinatorial interpretation of a q-Selberg integral, which generalizes Stanley's combinatorial interpretation of the Selberg integral. END:VEVENT BEGIN:VEVENT DTSTART:20160414T160000 DTEND:20160414T180000 DTSTAMP:20160413T150000Z UID:715eeac2cc09f363eb708c5bcf84d281@cgp.ibs.re.kr SUMMARY:Multigraphs-to-symplectic circle actions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Donghoon Jang\n\nEvent: CGP Seminar 2016\n\nAbstract: Consider a symplectic circle action on a compact symplectic manifold with isolated fixed points. We associate a directed multigraph to the manifold. Y. Karshon proves that if the dimension of the manifold is four, this multigraph completely determines the manifold up to equivariant symplectomorphism. We prove that we can associate a multigraph that does not have any loops. As an application, we complete the proof of symplectic Petrie's conjecture for eight dimensional manifolds. This talk is based on Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets, with Susan Tolman, to appear in Transformation Groups. END:VEVENT BEGIN:VEVENT DTSTART:20160407T160000 DTEND:20160407T180000 DTSTAMP:20160406T150000Z UID:f1a3b981ac4584109e96eb5f5ea52642@cgp.ibs.re.kr SUMMARY:Okounkov bodies associated to pseudoeffective divisors I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Seminar 2016\n\nAbstract: To a big divisor on a variety, one can associate the Okounkov body with respect to an admissible flag. Inspired by Okounkov's work, Lazarsfeld-Mustata and Kaveh-Khovanskii initiated the systematic study of the Okounkov bodies. These convex bodies reflect asymptotic properties of a given big divisor and geometric properties of admissible flags. In the first lecture, I first review some asymptotic invariants of divisors and basic properties of Okounkov bodies of big divisors. In the second lecture, I talk about joint work with Sung Rak Choi, Yoonsuk Hyun, and Joonyeong Won on the Okounkov bodies associated to pseudoeffective divisors. END:VEVENT BEGIN:VEVENT DTSTART:20160408T160000 DTEND:20160408T180000 DTSTAMP:20160407T150000Z UID:7aef32f34eaf81105a50b119fecb616d@cgp.ibs.re.kr SUMMARY:Okounkov bodies associated to pseudoeffective divisors II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Seminar 2016\n\nAbstract: To a big divisor on a variety, one can associate the Okounkov body with respect to an admissible flag. Inspired by Okounkov's work, Lazarsfeld-Mustata and Kaveh-Khovanskii initiated the systematic study of the Okounkov bodies. These convex bodies reflect asymptotic properties of a given big divisor and geometric properties of admissible flags. In the first lecture, I first review some asymptotic invariants of divisors and basic properties of Okounkov bodies of big divisors. In the second lecture, I talk about joint work with Sung Rak Choi, Yoonsuk Hyun, and Joonyeong Won on the Okounkov bodies associated to pseudoeffective divisors. END:VEVENT BEGIN:VEVENT DTSTART:20160412T160000 DTEND:20160412T173000 DTSTAMP:20160411T150000Z UID:d33d22b330c48c9812305ab953ea80dd@cgp.ibs.re.kr SUMMARY:Birational stability of the cotangent bundle of complex projective manifolds and orbifold pairs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Frederic Campana\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: The talk will report on the proof, applications and extension to the orbifold context of the following result: if X is a complex projective manifold with a foliation F such that the slope of every nonzeroquotient Q of F has a positive slope with respect to a ‘movable class’ c, this foliation has algebraic leaves, with rationally connected closures. This strengthens and extends former results of Miyaoka and Bogomolov-Mc Quillan. Of considerable importance in the applications is the fact that the class c is movable, and no longer a complete intersection of polarisations. This result can be applied in particular to the solution of the ‘hyperbolicity conjecture’ of Shafarevich-Viehweg and to the definition of rational connectedness and ‘rational quotient’ in the orbifold context, central in the description of the structure of projective manifolds. This is joint work with M. Paun (KIAS) END:VEVENT BEGIN:VEVENT DTSTART:20160329T140000 DTEND:20160329T153000 DTSTAMP:20160328T150000Z UID:42f4b0ab04c7c313e70900c509ed5eca@cgp.ibs.re.kr SUMMARY:Non-torus Lagrangian fibers on Gelfand-Tsetlin systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Symplectic Tuesday\n\nAbstract: It is well-known that every k-dimensional smooth projective toric variety X ⊂ Pn admits a completely integrable system Φ = (Φ1, · · · , Φk) : X → RkThen the image of Φ is a convex polytope and each ﬁber of Φ is diﬀeomorphic to a compact torus. In particular, Φ−1(r) is Lagrangian if and only if r is an interior point of X .Using the theory of Okounkov bodies and toric degenerations, it was proved that any smooth projective variety Y admits a completely integrable system on a dense open subset of Y which can be extended continuously to the whole space Y . Unlike the toric case, some ﬁbers of the integrable system are non-torus Lagrangian and they might have non-vanishing Lagrangian Floer cohomology.In this talk, we study a certain completely integrable system, called the Genfand-Tsetlin system, on a ﬂag variety and explain how to classify all non-torus Lagrangian ﬁbers in a purely combinatorial way. END:VEVENT BEGIN:VEVENT DTSTART:20160331T200000 DTEND:20160331T213000 DTSTAMP:20160330T150000Z UID:0de7129653103ebeb7e9912f0d09c6e7@cgp.ibs.re.kr SUMMARY:Arithmetic of Weil curves LOCATION:Math. Bldg. #313 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: PMI-IBS 공동정수론 세미나\n\nAbstract: In the series of seminars, we will study a famous paper by Mazur and Swinnerton-Dyer on Weil curves. Our plan of this series is as follows. First, we will review of the theory of modular curves and Weil curves. Then, we will introduce modular symbols, which are crucial tools to construct p-adic L-functions. Last, we will construct p-adic L-functions associated to elliptic curves, which is the goal of of this series of seminars. As this is our first talk, we will start from motivation and introduction to this subject. END:VEVENT BEGIN:VEVENT DTSTART:20160401T155000 DTEND:20160401T180000 DTSTAMP:20160331T150000Z UID:8104797e35deb7d8e54054c9205026f7@cgp.ibs.re.kr SUMMARY:Yukawa Coupling Mirror Conjecture LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Bumsig Kim (KIAS)\n\nEvent: Spring 2016 POSTECH Math Colloquium\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160405T160000 DTEND:20160405T170000 DTSTAMP:20160404T150000Z UID:c94dc6ca544b5b0758eb716e7bcdb2e5@cgp.ibs.re.kr SUMMARY:Foliated manifolds and Supergravity LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Mirela Elena Babalic\n\nEvent: T-Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160406T133000 DTEND:20160406T150000 DTSTAMP:20160405T150000Z UID:bc4dcee9c3e1626f97d9222342bc2994@cgp.ibs.re.kr SUMMARY:Higher algebraic structures and the Segal approach LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Higher algebraic structures and the Segal approach\n\nAbstract: The need to first study algebraic structures satisfying axioms "up to homotopy" first arose in algebraic topology, in the study of infinite loop spaces. Two approaches became well-known: that of May, based on the notion of an operad, and that of Segal, that produces infinite loop spaces directly, with no need for a choice of an operad. In topological applications, e.g. in algebraic K-theory, Segal's approach is the de facto standard. On the other hand, when one works not with topological spacesbut e.g. with chain complexes, Segal's approach does not work and people have to use operads. I want to give a sketch of recent work by E. Balzin, a student of mine, that modifies the Segal approach so that it works in full generality, potentially giving a very powerful new tool for all sortsof homotopical algebra questions. There will be three lectures; here is the rough plan.Lecture 1. We give an oveview of Segal and May approahces to infinite loopspaces, and show how to modify Segal approach so that it at least makessense in an arbitrary monoidal category. As a main technical tool, wereview the notion of a fibration of categories originaly introduced byGrothendieck (the "Grothendieck construction").Lecture 2. We discuss how to make things work "up to homotopy" or "up to aquasiisomorphism". In particular, we review Quillen's notion of a modelcategory and the standard constructions of model structures (cofibrantlygenerated model structures and Reedy model structures).Lecture 3. We combine the results reviewed in the first two lectures. Wedefine the notion of a "derived section" of a Grothendieck fibration, dueto Balzin, and his generalization of the Reedy construction of modelstructures. If time permits, we will also explain how the machinery worksin the situation of the so-called Deligne Conjecture, a good test case forall homotopy algebra machines. END:VEVENT BEGIN:VEVENT DTSTART:20160411T133000 DTEND:20160411T150000 DTSTAMP:20160410T150000Z UID:e3912bce852a183f30daf425eeb3490a@cgp.ibs.re.kr SUMMARY:Higher algebraic structures and the Segal approach LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Higher algebraic structures and the Segal approach\n\nAbstract: The need to first study algebraic structures satisfying axioms "up to homotopy" first arose in algebraic topology, in the study of infinite loop spaces. Two approaches became well-known: that of May, based on the notion of an operad, and that of Segal, that produces infinite loop spaces directly, with no need for a choice of an operad. In topological applications, e.g. in algebraic K-theory, Segal's approach is the de facto standard. On the other hand, when one works not with topological spacesbut e.g. with chain complexes, Segal's approach does not work and people have to use operads. I want to give a sketch of recent work by E. Balzin, a student of mine, that modifies the Segal approach so that it works in full generality, potentially giving a very powerful new tool for all sortsof homotopical algebra questions. There will be three lectures; here is the rough plan.Lecture 1. We give an oveview of Segal and May approahces to infinite loopspaces, and show how to modify Segal approach so that it at least makessense in an arbitrary monoidal category. As a main technical tool, wereview the notion of a fibration of categories originaly introduced byGrothendieck (the "Grothendieck construction").Lecture 2. We discuss how to make things work "up to homotopy" or "up to aquasiisomorphism". In particular, we review Quillen's notion of a modelcategory and the standard constructions of model structures (cofibrantlygenerated model structures and Reedy model structures).Lecture 3. We combine the results reviewed in the first two lectures. Wedefine the notion of a "derived section" of a Grothendieck fibration, dueto Balzin, and his generalization of the Reedy construction of modelstructures. If time permits, we will also explain how the machinery worksin the situation of the so-called Deligne Conjecture, a good test case forall homotopy algebra machines. END:VEVENT BEGIN:VEVENT DTSTART:20160415T133000 DTEND:20160415T150000 DTSTAMP:20160414T150000Z UID:b1c2905e26fe205fc2994a368721e765@cgp.ibs.re.kr SUMMARY:Higher algebraic structures and the Segal approach LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitry Kaledin\n\nEvent: Higher algebraic structures and the Segal approach\n\nAbstract: The need to first study algebraic structures satisfying axioms "up to homotopy" first arose in algebraic topology, in the study of infinite loop spaces. Two approaches became well-known: that of May, based on the notion of an operad, and that of Segal, that produces infinite loop spaces directly, with no need for a choice of an operad. In topological applications, e.g. in algebraic K-theory, Segal's approach is the de facto standard. On the other hand, when one works not with topological spacesbut e.g. with chain complexes, Segal's approach does not work and people have to use operads. I want to give a sketch of recent work by E. Balzin, a student of mine, that modifies the Segal approach so that it works in full generality, potentially giving a very powerful new tool for all sortsof homotopical algebra questions. There will be three lectures; here is the rough plan.Lecture 1. We give an oveview of Segal and May approahces to infinite loopspaces, and show how to modify Segal approach so that it at least makessense in an arbitrary monoidal category. As a main technical tool, wereview the notion of a fibration of categories originaly introduced byGrothendieck (the "Grothendieck construction").Lecture 2. We discuss how to make things work "up to homotopy" or "up to aquasiisomorphism". In particular, we review Quillen's notion of a modelcategory and the standard constructions of model structures (cofibrantlygenerated model structures and Reedy model structures).Lecture 3. We combine the results reviewed in the first two lectures. Wedefine the notion of a "derived section" of a Grothendieck fibration, dueto Balzin, and his generalization of the Reedy construction of modelstructures. If time permits, we will also explain how the machinery worksin the situation of the so-called Deligne Conjecture, a good test case forall homotopy algebra machines. END:VEVENT BEGIN:VEVENT DTSTART:20160411T163000 DTEND:20160411T180000 DTSTAMP:20160410T150000Z UID:6e8a18a60d4b8a71beb4a4147da9f6e7@cgp.ibs.re.kr SUMMARY:Higher enveloping algebras and configuration spaces of manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benjamin Knudsen\n\nEvent: Quantum Monday 2016\n\nAbstract: Drawing inspiration from the theory of chiral algebras due to Beilinson and Drinfeld, I will describe a construction providing Lie algebras with enveloping algebras over the operad of little n-dimensional disks for any n. These algebras enjoy a fortunate combination of good formal properties and computability, the latter afforded by a Poincare-Birkhoff-Witt type result. The main application pairs this theory of higher enveloping algebras with the theory of factorization homology in a study of the rational homology of configuration spaces, leading to a wealth of computations, the recovery and improvement of several classical results, and a new, combinatorial proof of homological stability. END:VEVENT BEGIN:VEVENT DTSTART:20160419T160000 DTEND:20160419T170000 DTSTAMP:20160418T150000Z UID:df1fd7a6d834110e2e3789f673abf962@cgp.ibs.re.kr SUMMARY:Two Facets Birational Geometries of Moduli Space of Sheaves over Surface LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Wanmin Liu\n\nEvent: T-Seminar\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20160427T160000 DTEND:20160427T173000 DTSTAMP:20160426T150000Z UID:41ca45111fe9b318a47acdfd72e1eaaf@cgp.ibs.re.kr SUMMARY:A valuative criterion for uniform K-stability of Fano manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kento Fujita\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: It is an interesting problem whether a given Fano manifold admits Kahler-Einstein metrics or not. It has been known that the condition is equivalent to the condition "K-polystability" which is purely algebraic. In this talk, we mainly treat uniform K-stability of Fano manifolds, which is stronger than K-polystability. More precisely, we give a simple necessary and sufficient condition for uniform K-stability of Fano manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20160512T160000 DTEND:20160512T180000 DTSTAMP:20160511T150000Z UID:667df52a445077df3614a35815b5d69d@cgp.ibs.re.kr SUMMARY:Koszul duality patterns in Floer theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yanki Lekili\n\nEvent: CGP Seminar 2016\n\nAbstract: We study symplectic invariants of the open symplectic manifolds $X_Γ$ obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree $Γ$. For any tree $Γ$, we calculate (DG-)algebra models of the Fukaya category $F(X_Γ)$ of closed exact Lagrangians in $X_Γ$ and the wrapped Fukaya category $W(X_Γ)$. When $Γ$ is a Dynkin tree of type $An$ or $Dn$ (and conjecturally also for E6 , E7, E8 ), we prove that these models for the Fukaya category $F(X_Γ)$ and $W(X_Γ)$ are related by (derived) Koszul duality. As an application, we give explicit computations of symplectic cohomology of $X_Γ$ for $Γ = An, Dn$ , based on the Legendrian surgery formula. This is joint work with Tolga Etgu. END:VEVENT BEGIN:VEVENT DTSTART:20160519T160000 DTEND:20160519T180000 DTSTAMP:20160518T150000Z UID:4094f7074be7dc87c75665932f56ee0b@cgp.ibs.re.kr SUMMARY:Talking about my G-generation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yanki Lekili\n\nEvent: CGP Seminar 2016\n\nAbstract: Let G be a compact Lie group and k be a field of characteristic $p >= 0$ such that $H*(G)$ does not have p-torsion. We show that a free Lagrangian orbit of a Hamiltonian G-action on a compact, monotone, symplectic manifold $X$ split-generates an idempotent summand of the monotone Fukaya category over $k$ if and only if it represents a non-zero object of that summand. Our result is based on: an explicit understanding of the wrapped Fukaya category of $T*G$ through Koszul twisted complexes involving the zero-section and a cotangent fibre; and a functor canonically associated to the Hamiltonian G-action on $X$. Several examples can be studied in a uniform manner including toric Fano varieties and certain Grassmannians. Time permitting, I will also discuss how our result leads to examples of symplectic (possibly Kähler) manifolds with a non-formal $A_\infty$ structure on their quantum cohomology. This is joint work with Jonny Evans. END:VEVENT BEGIN:VEVENT DTSTART:20160428T170000 DTEND:20160428T180000 DTSTAMP:20160427T150000Z UID:b64210f921115da9c047bf0a81cd6869@cgp.ibs.re.kr SUMMARY:BV quantization and geometric applications LOCATION:CGP Main Hall DESCRIPTION:Speaker: Si Li\n\nEvent: Lecture Series\n\nAbstract: In this mini course, we discuss the homological method of BV quantization in quantum field theory, with emphasis on geometric applications. We introduce the basics of infinite dimensional techniques of renormalization method in QFT, and discuss the geometry of BV quantization in low dimensional examples. As applications, we explain its relation with index theorems in 1d, integrable hierarchies in 2d, and also B-model aspect of mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20160427T133000 DTEND:20160427T153000 DTSTAMP:20160426T150000Z UID:d656c65d6cf000aa2ff2ab379560efa5@cgp.ibs.re.kr SUMMARY:BV quantization and geometric applications LOCATION:CGP Main Hall DESCRIPTION:Speaker: Si Li\n\nEvent: Lecture Series\n\nAbstract: In this mini course, we discuss the homological method of BV quantization in quantum field theory, with emphasis on geometric applications. We introduce the basics of infinite dimensional techniques of renormalization method in QFT, and discuss the geometry of BV quantization in low dimensional examples. As applications, we explain its relation with index theorems in 1d, integrable hierarchies in 2d, and also B-model aspect of mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20160506T140000 DTEND:20160506T153000 DTSTAMP:20160505T150000Z UID:0e36ba364283bdb1be1f1fc61a343412@cgp.ibs.re.kr SUMMARY:Arithmetic of Weil curves LOCATION:Math. Bldg. #313 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: PMI-IBS joint Number Theory Seminar\n\nAbstract: In the series of seminars, we will study a famous paper by Mazur and Swinnerton-Dyer on Weil curves. Our plan of this series is as follows. First, we will review of the theory of modular curves and Weil curves. Then, we will introduce modular symbols, which are crucial tools to construct p-adic L-functions. Last, we will construct p-adic L-functions associated to elliptic curves, which is the goal of of this series of seminars. As this is our first talk, we will start from motivation and introduction to this subject. END:VEVENT BEGIN:VEVENT DTSTART:20160510T140000 DTEND:20160510T153000 DTSTAMP:20160509T150000Z UID:fb0ed2c9548c51d3efad426baad2e338@cgp.ibs.re.kr SUMMARY:Heavy subsets and non-contractible trajectories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Morimichi Kawasaki\n\nEvent: Symplectic Tuesday\n\nAbstract: Biran, Polterovich and Salamon defined a relative symplectic capacity which indicates existence of non-contractible trajectories(orbits) of certain Hamiltonian isotopies(flows).In this talk, we give an upper bound of the Biran-Polterovich-Salamon capacity relative to heavy subsets in the sense of Entov and Polterovich. Heavy subsets are defined in terms of the Oh-Schwarz spectral invariants which are defined in terms of the Hamiltonian Floer theory on contractible trajectories.It means that we can find non-contractible trajectories by the Floer theory on contractible trajectories. END:VEVENT BEGIN:VEVENT DTSTART:20160512T110000 DTEND:20160512T120000 DTSTAMP:20160511T150000Z UID:5a6d9b09029cad8aecdef064e92f2a40@cgp.ibs.re.kr SUMMARY:On orbifold Jacobian algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Atsushi Takahashi\n\nEvent: Intensive Lecture Series by Atsushi Takahashi\n\nAbstract: To a polynomial with an isolated singularity at the origin, one can associate the Jacobian algebra. It is a finite dimensional algebra with a structure of a Frobenius algebra. We propose axioms for "orbifold Jacobian algebras" which generalize the Jacobian algebras to pairs of such a polynomial with a group action. We shall prove the existence and the uniqueness for invertible polynomials in three variables with group actions and show a compatibility with the geometry of vanishing cycles. This is a joint work with Alexey Basalaev and Elisabeth Werner. END:VEVENT BEGIN:VEVENT DTSTART:20160511T160000 DTEND:20160511T180000 DTSTAMP:20160510T150000Z UID:ca10392f067630e74b581d5727889385@cgp.ibs.re.kr SUMMARY:On entropies of autoequivalences on smooth projective varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Atsushi Takahashi\n\nEvent: Intensive Lecture Series by Atsushi Takahashi\n\nAbstract: Entropy for endofunctors on triangulated categories is defined by Dmitrov-Haiden-Katzarkov-Kontsevich. Based on the joint work with Kohei Kikuta, one of my students, I show that the categorical entropy of an automorphism of a complex smooth projective variety is equal to the topological entropy, which is done by DHKK under a certain technical condition. It is natural to expect a generalization of the fundamental theorem by Gromov-Yomdin; the entropy of an autoeuqivalence on a complex smooth projective variety should be given by the logarithm of the spectral radius of the induced map on the numerical Grothendieck group. I also show that this conjecture holds for elliptic curves (Kikuta's result) and if the canonical or anti-canonical sheaf is ample. END:VEVENT BEGIN:VEVENT DTSTART:20160413T160000 DTEND:20160413T180000 DTSTAMP:20160412T150000Z UID:3654ace1562fed18f6d31b5fc3c79c3a@cgp.ibs.re.kr SUMMARY:Quantum master equation and deformation theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander A. Voronov\n\nEvent: Quantum Monday 2016\n\nAbstract: Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation (QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \Delta S + 1/2 {S,S} = 0. The CME is deﬁned in a differential graded (dg) Lie algebra g, whereas the QME is deﬁned in a space V [[h]] of formal power series with values in a dg BV algebra V. One can anticipate a generalization of classical deformation theory arising from the QME or quantum deformation theory. This theory has been emerging with people like K. Costello, Jae-Suk Park, J. Terilla, and T. Tradler making ﬁrst steps in abstract quantum deformation theory. Main ideas of quantum deformation theory and further steps will be discussed in the talk. END:VEVENT BEGIN:VEVENT DTSTART:20160518T170000 DTEND:20160518T180000 DTSTAMP:20160517T150000Z UID:d6f8417886554de3ed67e83edb24da25@cgp.ibs.re.kr SUMMARY:The MV formalism for IBL-infty and BV-infty algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Martin Markl\n\nEvent: Seminar 2016\n\nAbstract: (joint work with Alexander A. Voronov)We introduce a new formalism for the Quantum Master Equation and for the category of IBL-infty$-algebras that simplifies some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which contains such important categories as those of IBL-infty- and L-infty-algebras, and allows for a simple solution of the quantum master equation. We also show that IBL-infty morphisms are closed under composition, a nontrivial property which seems to be taken for granted in the literature. END:VEVENT BEGIN:VEVENT DTSTART:20160516T160000 DTEND:20160516T180000 DTSTAMP:20160515T150000Z UID:a5ea9efb6a7edd13fa9326c6766b77b0@cgp.ibs.re.kr SUMMARY:Quantum master equation and deformation theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander A. Voronov\n\nEvent: Quantum Monday 2016\n\nAbstract: Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation (QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \Delta S + 1/2 {S,S} = 0. The CME is deﬁned in a differential graded (dg) Lie algebra g, whereas the QME is deﬁned in a space V [[h]] of formal power series with values in a dg BV algebra V. One can anticipate a generalization of classical deformation theory arising from the QME or quantum deformation theory. This theory has been emerging with people like K. Costello, Jae-Suk Park, J. Terilla, and T. Tradler making ﬁrst steps in abstract quantum deformation theory. Main ideas of quantum deformation theory and further steps will be discussed in the talk. END:VEVENT BEGIN:VEVENT DTSTART:20160524T160000 DTEND:20160524T180000 DTSTAMP:20160523T150000Z UID:ad0709bdc372600429226bcf7dc5ee89@cgp.ibs.re.kr SUMMARY:t-structures and their behaviours under Fourier-Mukai transforms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jason Lo\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In this talk, we will review the notion of t-structures, and discuss the various ways of thinking about them. For example, a t-structure can be interpreted as a cohomology theory. On the other hand, it can also be considered as a 'first approximation' of a notion of stability. We will see the many t-structures that can arise in the derived category of coherent sheaves on elliptic fibrations, and get a glimpse of how they behave under Fourier-Mukai transforms. END:VEVENT BEGIN:VEVENT DTSTART:20160526T160000 DTEND:20160526T180000 DTSTAMP:20160525T150000Z UID:53e6bd44326354ac3aad194cf5e478a4@cgp.ibs.re.kr SUMMARY:Notions of stability and their behaviours under Fourier-Mukai transforms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jason Lo\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In this talk, we will consider t-structures together with slope functions. This will bring us to the various notions of stability, including the classical slope stability for sheaves, and Bridgeland stability conditions. We will discuss a simple way to define a notion of stability, and discuss results on how these notions of stability behave under Fourier-Mukai transforms on elliptic fibrations. END:VEVENT BEGIN:VEVENT DTSTART:20160523T160000 DTEND:20160523T180000 DTSTAMP:20160522T150000Z UID:6059e772ba89993a33fc3111f2746bb1@cgp.ibs.re.kr SUMMARY:Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sergei Merkulov\n\nEvent: Quantum Monday 2016\n\nAbstract: We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves (which, according to Penner, is controlled by the ribbon graph complex) and the homotopy theory of operads (controlled by ordinary graph complexes with no ribbon structure, introduced first by Kontsevich). The talk is based on a joint work with Thomas Willwacher. END:VEVENT BEGIN:VEVENT DTSTART:20160613T160000 DTEND:20160613T180000 DTSTAMP:20160612T150000Z UID:d341428f543e8f7b359a43ed971b3b54@cgp.ibs.re.kr SUMMARY:On classical affine W-superalgebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: UhiRinn Suh\n\nEvent: Quantum Monday 2016\n\nAbstract: A classical affine W-algebra associated to a finite simple Lie algebra and its nilpotent element is a Poisson vertex algebra which is closely related to integrable systems. In 1980's, Drinfel'd-Sokolov discovered relations between a W-algebra associated to a principal nilpotent element and integrable systems. Recently, by De Sole-Kac-Valeri, algebraic structures of W-algebras associated to any nilpotent elements and integrable systems associated to those algebras are completely understood. For a W-superalgebra (or W-algebra associated to a Lie superalgebra), there is a natural definition introduced by De Sole-Kac. However, it is not known if W-superalgebras are related to super-integrable systems. In this talk, I will explain W-superalgebras can be understood by an analogous argument of Drinfel'd-Sokolov. If time allows, I will propose a way to associate a W-superalgebra to super-integrable systems, in the simplest case. END:VEVENT BEGIN:VEVENT DTSTART:20160531T130000 DTEND:20160531T150000 DTSTAMP:20160530T150000Z UID:42e0b0850ca4083325ec2f032c2431ff@cgp.ibs.re.kr SUMMARY:On the uniqueness of the complex projective spaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ping Li\n\nEvent: Seminar 2016\n\nAbstract: A classical result of Hirzebruch-Kodaira and Yau says that a Kahler manifold homeomorphic to $CP^n$ must be biholomorphic to $CP^n$. In this talk I will show that the hypothesis "homeomorphism" can be technically refined. This observation, together with a result of Dessai and Wilking, enables us to characterize all CPn in terms of homotopy type under mild symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20160802T160000 DTEND:20160802T170000 DTSTAMP:20160801T150000Z UID:ed018ce722b11077922580742caedf89@cgp.ibs.re.kr SUMMARY:Chain level transversality for string topology coproduct LOCATION:CGP Main Hall DESCRIPTION:Speaker: Manuel Rivera\n\nEvent: String Topology Mini-workshop\n\nAbstract: I will describe a geometric chain level formulation for a “secondary" coproduct on a suitable chain model for the free loop space of a manifold. This operation- which combines a 1-parameter family of self-intersections on a family of loops- was originally described by Goresky and Hingston at the level of the (relative) homology by using a finite dimensional approximation of Morse for the free loop space. The operation is also analogue to a coproduct described by Abbondandolo and Schwarz on (a version of) the symplectic Floer homology of the cotangent bundle.To have a better grasp of the properties of this coproduct and to relate it to constructions in symplectic topology it is convenient to describe explicitly the transversality perturbations made at the chain level to obtain an operation parametrized by a nice geometric object. I will explain why this process is more subtle for this operation than for other string topology operations (such as the Chas-Sullivan loop product) and will outline how Dingyu Yang and I have achieved this in work in progress using the formalism of De Rham chains. There is also a rich algebraic theory behind this secondary coproduct and its compatibilities with other operations. Time permitting, I will describe some of the algebraic theory as well. END:VEVENT BEGIN:VEVENT DTSTART:20160804T160000 DTEND:20160804T170000 DTSTAMP:20160803T150000Z UID:f251eb7b8033e34c353312892eea91cc@cgp.ibs.re.kr SUMMARY:String diagrams and directed graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kate Poirier\n\nEvent: String Topology Mini-workshop\n\nAbstract: In ongoing joint work with Drummond-Cole and Rounds, we show that the space of string diagrams acts on the chains of the free loop space of a manifold. Previously, Tradler and Zeinalian showed that a chain complex of directed graphs acts on the Hochschild complex of a V-infinity algebra. It is thought that these actions should be a topological and algebraic version of the same story. In this talk, we report on current joint work with Tradler on the first step describing the relationship between these two actions. In particular, we describe a map relating the two spaces of operations. END:VEVENT BEGIN:VEVENT DTSTART:20160803T160000 DTEND:20160803T170000 DTSTAMP:20160802T150000Z UID:f85e377574672abcdacb3b5ff5178d8c@cgp.ibs.re.kr SUMMARY:Chain level transversality for string topology coproduct LOCATION:CGP Main Hall DESCRIPTION:Speaker: Manuel Rivera\n\nEvent: String Topology Mini-workshop\n\nAbstract: I will describe a geometric chain level formulation for a “secondary" coproduct on a suitable chain model for the free loop space of a manifold. This operation- which combines a 1-parameter family of self-intersections on a family of loops- was originally described by Goresky and Hingston at the level of the (relative) homology by using a finite dimensional approximation of Morse for the free loop space. The operation is also analogue to a coproduct described by Abbondandolo and Schwarz on (a version of) the symplectic Floer homology of the cotangent bundle.To have a better grasp of the properties of this coproduct and to relate it to constructions in symplectic topology it is convenient to describe explicitly the transversality perturbations made at the chain level to obtain an operation parametrized by a nice geometric object. I will explain why this process is more subtle for this operation than for other string topology operations (such as the Chas-Sullivan loop product) and will outline how Dingyu Yang and I have achieved this in work in progress using the formalism of De Rham chains. There is also a rich algebraic theory behind this secondary coproduct and its compatibilities with other operations. Time permitting, I will describe some of the algebraic theory as well. END:VEVENT BEGIN:VEVENT DTSTART:20160802T110000 DTEND:20160802T120000 DTSTAMP:20160801T150000Z UID:34e6941f681c2ba348f106e4684de6a5@cgp.ibs.re.kr SUMMARY:String topology operations and the diagonal map LOCATION:CGP Main Hall DESCRIPTION:Speaker: Nissim Ranade\n\nEvent: String Topology Mini-workshop\n\nAbstract: We will examine how the string topology loop product relates algebraically to the diagonal map on spaces. We will use algebraic models for manifolds developed be Cameron Crowe and appropriate algebraic models for the figure-8 space to understand these operations better. END:VEVENT BEGIN:VEVENT DTSTART:20160803T110000 DTEND:20160803T120000 DTSTAMP:20160802T150000Z UID:3bec14f5634fe6d787a49d3238659406@cgp.ibs.re.kr SUMMARY:Sullivan diagrams and homological stability LOCATION:CGP Main Hall DESCRIPTION:Speaker: Daniela Egas Santander\n\nEvent: String Topology Mini-workshop\n\nAbstract: In string topology one studies the algebraic structures of the chains of the free loop space of a manifold by defining operations on them. Recent results show that these operations are parametrized by certain graph complexes that compute the homology of compatifications of the Moduli space of Riemann surfaces. Finding non-trivial homology classes of these compactifications is related to finding non-trivial string operations. However, the homology of these complexes is largely unknown. In this talk I will describe one of these complexes: the chain complex of Sullivan diagrams. I will describe two stabilization maps for Sullivan diagrams one with respect to genus and one with respect to punctures and describe how some components of this complex have homological stability with respect to these maps. I will also give some computational results for small genus and number of punctures. END:VEVENT BEGIN:VEVENT DTSTART:20160804T110000 DTEND:20160804T120000 DTSTAMP:20160803T150000Z UID:64e1c070330d978c84ddd9ae16a94c05@cgp.ibs.re.kr SUMMARY:Sullivan diagrams and homological stability LOCATION:CGP Main Hall DESCRIPTION:Speaker: Daniela Egas Santander\n\nEvent: String Topology Mini-workshop\n\nAbstract: In string topology one studies the algebraic structures of the chains of the free loop space of a manifold by defining operations on them. Recent results show that these operations are parametrized by certain graph complexes that compute the homology of compatifications of the Moduli space of Riemann surfaces. Finding non-trivial homology classes of these compactifications is related to finding non-trivial string operations. However, the homology of these complexes is largely unknown. In this talk I will describe one of these complexes: the chain complex of Sullivan diagrams. I will describe two stabilization maps for Sullivan diagrams one with respect to genus and one with respect to punctures and describe how some components of this complex have homological stability with respect to these maps. I will also give some computational results for small genus and number of punctures. END:VEVENT BEGIN:VEVENT DTSTART:20160530T160000 DTEND:20160530T180000 DTSTAMP:20160529T150000Z UID:c87b65b37f39a2415df971347618fee4@cgp.ibs.re.kr SUMMARY:Non-commutative quantum field theory and Chen’s iterated path integrals LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday 2016\n\nAbstract: Iterated path integrals, generalising the familiar line integrals, are functions in the path space of smooth manifold which notion has introduced and used to extend de Rham cohomology theory to a homotopy theory on the fundamental group level by by K.-T. Chen and has found many interesting applications, beyond algebraic topology, in algebraic geometry and number theory. Theory of homotopy category of homotopy QFT algebras is this speaker’s attempts to understand quantum field theory mathematically. In this lecture I will show that iterated integral(s) is quantum expectation of a (0+0)-dimensional non-commutative QFT obtained by certain quantisation of the algebra of differential forms on a manifold such that Chen’s homotopy functionals are equivalent to semi-classical quantum correlation functions. The theory may be used to quantise the rational homotopy theory itself. END:VEVENT BEGIN:VEVENT DTSTART:20160607T140000 DTEND:20160607T150000 DTSTAMP:20160606T150000Z UID:e68d186e019c95315d542a8477f95d2f@cgp.ibs.re.kr SUMMARY:SINGULARITY AND LOCAL SYSTEMS LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Singularities appear in many areas of mathematics. Especially we focus on the singularities of a function on a space of complex eld (or a subspace of a complex space). There are many invariants of singularities depending on the category of the complex space such as topological, analytic, and algebraic category. We will review several invariants of singularities at the rst lecture.Local system will be explained at the second lecture as an important tool for the study of these invariants. I will introduce my recent work with Nero Budur and Botong Wang at the last talk. END:VEVENT BEGIN:VEVENT DTSTART:20160608T140000 DTEND:20160608T150000 DTSTAMP:20160607T150000Z UID:2d692f2165a044006742c4e1bc5076d9@cgp.ibs.re.kr SUMMARY:SINGULARITY AND LOCAL SYSTEMS LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Singularities appear in many areas of mathematics. Especially we focus on the singularities of a function on a space of complex eld (or a subspace of a complex space). There are many invariants of singularities depending on the category of the complex space such as topological, analytic, and algebraic category. We will review several invariants of singularities at the rst lecture.Local system will be explained at the second lecture as an important tool for the study of these invariants. I will introduce my recent work with Nero Budur and Botong Wang at the last talk. END:VEVENT BEGIN:VEVENT DTSTART:20160609T140000 DTEND:20160609T150000 DTSTAMP:20160608T150000Z UID:8c7246ae42844b7e82b5e568415df90a@cgp.ibs.re.kr SUMMARY:SINGULARITY AND LOCAL SYSTEMS LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Singularities appear in many areas of mathematics. Especially we focus on the singularities of a function on a space of complex eld (or a subspace of a complex space). There are many invariants of singularities depending on the category of the complex space such as topological, analytic, and algebraic category. We will review several invariants of singularities at the rst lecture.Local system will be explained at the second lecture as an important tool for the study of these invariants. I will introduce my recent work with Nero Budur and Botong Wang at the last talk. END:VEVENT BEGIN:VEVENT DTSTART:20160706T160000 DTEND:20160706T180000 DTSTAMP:20160705T150000Z UID:61b97f6ae9f07605b669549744100ee8@cgp.ibs.re.kr SUMMARY:Lectures on cylinders in rational surfaces, I LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In affine geometry, a cylinder is an affine variety isomorphic to \mathbb{A}^1\times Z, where Z is an affine variety.A quasi-projective variety is called affine-ruled or \mathbb{A}^1-ruled if it contains a cylinder. Since cylinders are strongly related to unipotent group actions, they often appear in the study of biregular and birational automorphisms of affine varieties. In this series of lectures, I will explain how to construct cylinders in various rational surfaces and how to show that certain rational surfaces contain no cylinders. I will also introduce some open problems for beginners. END:VEVENT BEGIN:VEVENT DTSTART:20160713T160000 DTEND:20160713T180000 DTSTAMP:20160712T150000Z UID:6a14973398f2ea1cffd6388746266b5b@cgp.ibs.re.kr SUMMARY:Lectures on cylinders in rational surfaces, II LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In affine geometry, a cylinder is an affine variety isomorphic to \mathbb{A}^1\times Z, where Z is an affine variety.A quasi-projective variety is called affine-ruled or \mathbb{A}^1-ruled if it contains a cylinder. Since cylinders are strongly related to unipotent group actions, they often appear in the study of biregular and birational automorphisms of affine varieties. In this series of lectures, I will explain how to construct cylinders in various rational surfaces and how to show that certain rational surfaces contain no cylinders. I will also introduce some open problems for beginners. END:VEVENT BEGIN:VEVENT DTSTART:20160720T160000 DTEND:20160720T180000 DTSTAMP:20160719T150000Z UID:67826f7ba5facc5ed2994a2464164f22@cgp.ibs.re.kr SUMMARY:Lectures on cylinders in rational surfaces,III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In affine geometry, a cylinder is an affine variety isomorphic to \mathbb{A}^1\times Z, where Z is an affine variety.A quasi-projective variety is called affine-ruled or \mathbb{A}^1-ruled if it contains a cylinder. Since cylinders are strongly related to unipotent group actions, they often appear in the study of biregular and birational automorphisms of affine varieties. In this series of lectures, I will explain how to construct cylinders in various rational surfaces and how to show that certain rational surfaces contain no cylinders. I will also introduce some open problems for beginners. END:VEVENT BEGIN:VEVENT DTSTART:20160630T160000 DTEND:20160630T180000 DTSTAMP:20160629T150000Z UID:87515abf4f10a063a7174988f8b7a77b@cgp.ibs.re.kr SUMMARY:Divisors on some surfaces with $p_g=q=0.$ LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: CGP Seminar 2016\n\nAbstract: Investigation on divisors on a surface is essential to understand its geometry and birational properties. In this talk, I will discuss about Picard lattices, effective cones, nef cones, Cox rings and exceptional collections on some surfaces with $p_g=q=0.$ END:VEVENT BEGIN:VEVENT DTSTART:20160701T150000 DTEND:20160701T160000 DTSTAMP:20160630T150000Z UID:9d15f3f00d3deb93f9584d853ad2252a@cgp.ibs.re.kr SUMMARY:Line arrangements in the plane LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dmitrijs Sakovics\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: Take a (projective) plane and draw some lines in it. Look at their intersections. If the lines are chosen arbitrarily, any intersection point will have exactly two lines going through it. Thus, one can ask how we can minimize the number of points where only two lines intersect. I will talk about one of the ways to find such minimizing arrangements and some very classical group theory associated with that problem. END:VEVENT BEGIN:VEVENT DTSTART:20160726T160000 DTEND:20160726T180000 DTSTAMP:20160725T150000Z UID:68eec7eacef6e4bb3e3eae2f9abba80d@cgp.ibs.re.kr SUMMARY:Cohomology Jump Loci in Algebraic Geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Botong Wang\n\nEvent: Seminar 2016\n\nAbstract: Cohomology jump loci are topological invariants generalizing the usual singular cohomology groups. In the first part of the talk, I will give a survey on the theory of cohomology jump locus, especially the structure theorems developed by Simpson, Schnell, Budur and myself. As an application, I will give an example of non-Kahler Calabi-Yau symplectic-complex manifold. This example is joint work with Lizhen Qin. In the second part of the talk, I will present an ongoing project with Nero Budur exploring the notion of “absoluteness”. In the late 70's, Deligne introduced the notion of absolute Hodge cycles. They are cohomology classes of a complex projective variety in some sense compatible with Galois actions of $Gal(\mathbb{C}/mathbb{Q})$. Inspired by the work of Deligne, Simpson defined the notion of absolute constructible sets. They are subvarieties of the moduli space of local systems on a projective variety. With his notion of absolute constructible sets, Simpson proved the structure theorem of cohomology jump loci for projective varieties. This is one of the main achievements in the subject of cohomology jump loci, and has many applications in algebraic geometry. I will give a further generalization of Simpson’s absolute constructible sets in two directions: (i) projective varieties are replaced by quasi-projective varieties. (ii) moduli spaces of local systems are replaced by the derived categories of constructible complexes. With this new notion of absoluteness, we can prove some strong generalizations of the structure theorems of Simpson and Schnell. END:VEVENT BEGIN:VEVENT DTSTART:20160727T160000 DTEND:20160727T173000 DTSTAMP:20160726T150000Z UID:1f6e9efba511e67d1f5a375b43a1977b@cgp.ibs.re.kr SUMMARY:Syzygies, Hermitian Symmetric Spaces, and Positive Energy Representations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Markus Hunziker\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In his 1890 Mathematische Annalen paper, David Hilbert proved two theorems that gave birth to modern commutative and homological algebra. The two theorems are known as the basis theorem and the syzygy theorem. In this general audience lecture, I will first explain why Hilbert proved these theorems and then present a new approach to solve several old problems in classical invariant theory. This new approach involves a syzygy of an entirely different kind: a wonderful alignment of algebra, geometry, combinatorics, and representation theory. END:VEVENT BEGIN:VEVENT DTSTART:20160711T160000 DTEND:20160711T180000 DTSTAMP:20160710T150000Z UID:06d0f37cc0b57f178cce7f64bf4c67f6@cgp.ibs.re.kr SUMMARY:Topological types of Algebraic stacks LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chang-Yeon Chough\n\nEvent: Quantum Monday 2016\n\nAbstract: In developing homotopy theory in algebraic geometry, Michael Artin and BarryMazur studied the étale homotopy types of schemes. Later Eric Friedlander generalized them to the étale topological types of simplicial schemes. The aim of this talk is to extend further these theories to algebraic stacks by using the derived functor approach for schemes by Ilan Barnea and Tomer Schlank. I'll then use this general framework for the theory topological types to given an alternative proof of Arnav Tripathy's theorem on the commutativity of étale homotopy types and symmetric powers. END:VEVENT BEGIN:VEVENT DTSTART:20160714T160000 DTEND:20160714T180000 DTSTAMP:20160713T150000Z UID:cc3b2d3ef76b7030f5e40e05a062abb0@cgp.ibs.re.kr SUMMARY:Homology of Hurwitz spaces and the Cohen-Lenstra heuristics for function fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Craig Westerland\n\nEvent: CGP Seminar 2016\n\nAbstract: We will discuss a homological stability theorem for Hurwitz spaces (moduli spaces of branched covers). This result may be used to get bounds on the number of points of these moduli over finite fields, using the Grothendieck-Lefschetz fixed point theorem. This, in turn, allows us to address the question of the distribution of class groups of function fields; the results that we obtain are consistent with Cohen-Lenstra’s heuristics on the distribution of class groups of number fields. If time permits, we will discuss other problems in arithmetic statistics, and how tools from topology may be used to address their function field analogues. END:VEVENT BEGIN:VEVENT DTSTART:20160728T160000 DTEND:20160728T180000 DTSTAMP:20160727T150000Z UID:1b2071302d956d983c99c3823381cdda@cgp.ibs.re.kr SUMMARY:Homotopy L-infinity spaces and Kuranishi manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Junwu Tu\n\nEvent: CGP Seminar 2016\n\nAbstract: Homotopy L-infinity spaces were introduced by Kevin Costello in order to formulate quantum field theory in physics.On the other hand, global Kuranishi theory was first pioneered by Fukaya-Oh-Ono-Ohta about twenty years ago! Recently, the categorical aspects of Kuranishi theory were studied by Joyce. I will explain an interesting and useful relationship between these two seemingly different subjects. END:VEVENT BEGIN:VEVENT DTSTART:20160801T140000 DTEND:20160801T160000 DTSTAMP:20160731T150000Z UID:a1877afd65d0a80d67f924040eb246ad@cgp.ibs.re.kr SUMMARY:1. An invitation to contact homology 2. Semi-global Kuranishi structures and contact homology LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Erkao Bao\n\nEvent: Seminar 2016\n\nAbstract: 1. Contact homology is an invariant of a contact structure. In this talk, we will start with the definition of a contact structure, then build up our way by looking at the Morse homology, and finally we will have a gentle definition of contact homology, which can be viewed as an infinite dimensional Morse homology. 2. Contact homology was proposed and studied by Eliashberg,Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until last year. In this talk, we will first see that the naive definition does not work because the spaces of "trajectories" that we count to define the differential of contact homology are not transversally cut out. Then we will construct a finite dimensional space K around the spaces of "trajectories" in a systematical way, and inside K we perturb the "trajectories" so that now they are transversally cut out. The space K together with the perturbation is called a semi-global Kuranishi structure, which is a variation of the Kuranishi structure by FOOO. END:VEVENT BEGIN:VEVENT DTSTART:20160801T160000 DTEND:20160801T170000 DTSTAMP:20160731T150000Z UID:7fb846f85b9b7458b48b1fd3c3be4937@cgp.ibs.re.kr SUMMARY:Chain-level string topology operations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kate Poirier\n\nEvent: String Topology Mini-workshop\n\nAbstract: String topology studies algebraic invariants of manifolds arising from intersecting loops in the manifolds. Traditionally, the algebraic structure is phrased in terms of an action of the homology of the moduli space of Riemann surfaces on the homology of the free loop space of the manifold. It is expected that this action should be induced by an action of the chains on a compactification of moduli space on the chains of the free loop space. In this talk, we report on recent joint work with Drummond-Cole and Rounds constructing a space of operations on the chains of the free loop space which describes part of this action. END:VEVENT BEGIN:VEVENT DTSTART:20160718T103000 DTEND:20160718T120000 DTSTAMP:20160717T150000Z UID:74610fbfd0e12dcdf74426fa1af986c6@cgp.ibs.re.kr SUMMARY:Discrete harmonic analysis (I) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joonil Kim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160719T140000 DTEND:20160719T153000 DTSTAMP:20160718T150000Z UID:9ed9b2936b640df43432714aad2649c9@cgp.ibs.re.kr SUMMARY:Discrete harmonic analysis (II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joonil Kim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160720T103000 DTEND:20160720T120000 DTSTAMP:20160719T150000Z UID:c7b71c86f13d29edc3e9810cbd01dd22@cgp.ibs.re.kr SUMMARY:Discrete harmonic analysis (III) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joonil Kim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160718T160000 DTEND:20160718T173000 DTSTAMP:20160717T150000Z UID:8da454e16b092781e9e0b0a2ad22d5bb@cgp.ibs.re.kr SUMMARY:Discontinuous solutions to nonlinear PDEs (I) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Myoungjean Bae\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160719T160000 DTEND:20160719T173000 DTSTAMP:20160718T150000Z UID:3e578e20ed29be9e340bc4a4e9b8a934@cgp.ibs.re.kr SUMMARY:Discontinuous solutions to nonlinear PDEs (II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Myoungjean Bae\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160721T103000 DTEND:20160721T120000 DTSTAMP:20160720T150000Z UID:4a056afd0ad4c5d407d8cb7d95c46bc1@cgp.ibs.re.kr SUMMARY:Discontinuous solutions to nonlinear PDEs (III) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Myoungjean Bae\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160718T140000 DTEND:20160718T153000 DTSTAMP:20160717T150000Z UID:68f6cb7f06859b0dba06f4e3b44022f1@cgp.ibs.re.kr SUMMARY:Random walks and spectral gaps on graphs (I) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seon Hee Lim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160719T103000 DTEND:20160719T120000 DTSTAMP:20160718T150000Z UID:dcb0dd03643e762bca29e36f0ad89893@cgp.ibs.re.kr SUMMARY:Random walks and spectral gaps on graphs (II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seon Hee Lim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160721T140000 DTEND:20160721T153000 DTSTAMP:20160720T150000Z UID:dc96f344e3b1fbc1a06f4c72dd490959@cgp.ibs.re.kr SUMMARY:Random walks and spectral gaps on graphs (III) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seon Hee Lim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160803T140000 DTEND:20160803T153000 DTSTAMP:20160802T150000Z UID:dc19d8995659826611b8183764d913ff@cgp.ibs.re.kr SUMMARY:Thin exceptional sets in Manin’s conjecture for Fano 3-folds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sho Tanimoto\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: Manin’s conjecture predicts an asymptotic formula for Fano varieties, and it has an explicit asymptotic formula in terms of geometric invariants of the underlying variety. However, the original conjecture which predicts formulae after removing proper closed subsets is wrong due to the existence of the covering families of subvarieties violating compatibility of Manin’s conjecture, its refinement, suggested by Peyre, removes thin sets instead of closed sets. In this talk, I would like to present some positive evidences of this refinement using birational geometry, e.g., the minimal model program. This is joint work with Brian Lehmann. END:VEVENT BEGIN:VEVENT DTSTART:20160721T160000 DTEND:20160721T173000 DTSTAMP:20160720T150000Z UID:6a34806f9c48b510ffcccfbd57c415ed@cgp.ibs.re.kr SUMMARY:Some remarks on arithmetic and geometry (I) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Minhyong Kim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160722T103000 DTEND:20160722T120000 DTSTAMP:20160721T150000Z UID:b1cd4fce137b2f5a7b00532dceb4e1c6@cgp.ibs.re.kr SUMMARY:Some remarks on arithmetic and geometry (II) LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Minhyong Kim\n\nEvent: 2016 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20160816T160000 DTEND:20160816T173000 DTSTAMP:20160815T150000Z UID:9518f409c0a712a559013de822014f0f@cgp.ibs.re.kr SUMMARY:Sutures and Higher Rank Bundles I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Aliakbar Daemi\n\nEvent: Seminar 2016\n\nAbstract: Donaldson's polynomials are strong invariants of smooth closed 4-manifolds which are defined using certain moduli spaces associated to complex vector bundles of rank 2. Later on, these invariants were generalized to higher rank bundles, firstly in physics and then in math. However, the role of these 4-manifold invariants in low dimensional topology are largely mysterious. The physicists expect that these invariants do no contain any new information about 4-manifolds.In my talks, I'll explain how to confirm the predictions from physics about some families of 4-manifolds including elliptic surfaces. Nevertheless, these computations can be used to gain new information about manifolds of lower dimensions. In particular, I'll discuss how one can define an invariant of sutured 3-manifolds and obtain structural results about the quantum cohomology of moduli spaces of stable bundles on a Riemann surface. The sutured invariant is a potential tool to study rank three unitary representations of knot groups. This talk is based on an ongoing project, joint with Yi Xie. END:VEVENT BEGIN:VEVENT DTSTART:20160818T160000 DTEND:20160818T173000 DTSTAMP:20160817T150000Z UID:eb4575dbf7fd786945cc0f5df3e46a95@cgp.ibs.re.kr SUMMARY:Sutures and Higher Rank Bundles II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Aliakbar Daemi\n\nEvent: CGP Seminar 2016\n\nAbstract: Donaldson's polynomials are strong invariants of smooth closed 4-manifolds which are defined using certain moduli spaces associated to complex vector bundles of rank 2. Later on, these invariants were generalized to higher rank bundles, firstly in physics and then in math. However, the role of these 4-manifold invariants in low dimensional topology are largely mysterious. The physicists expect that these invariants do no contain any new information about 4-manifolds.In my talks, I'll explain how to confirm the predictions from physics about some families of 4-manifolds including elliptic surfaces. Nevertheless, these computations can be used to gain new information about manifolds of lower dimensions. In particular, I'll discuss how one can define an invariant of sutured 3-manifolds and obtain structural results about the quantum cohomology of moduli spaces of stable bundles on a Riemann surface. The sutured invariant is a potential tool to study rank three unitary representations of knot groups. This talk is based on an ongoing project, joint with Yi Xie. END:VEVENT BEGIN:VEVENT DTSTART:20160817T160000 DTEND:20160817T180000 DTSTAMP:20160816T150000Z UID:de7e94ea084e55f8b3a1a257c7948f77@cgp.ibs.re.kr SUMMARY:Lectures on cylinders in rational surfaces IV LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In affine geometry, a cylinder is an affine variety isomorphic to \mathbb{A}^1\times Z, where Z is an affine variety.A quasi-projective variety is called affine-ruled or \mathbb{A}^1-ruled if it contains a cylinder. Since cylinders are strongly related to unipotent group actions, they often appear in the study of biregular and birational automorphisms of affine varieties. In this series of lectures, I will explain how to construct cylinders in various rational surfaces and how to show that certain rational surfaces contain no cylinders. I will also introduce some open problems for beginners. END:VEVENT BEGIN:VEVENT DTSTART:20160824T170000 DTEND:20160824T180000 DTSTAMP:20160823T150000Z UID:4148f6e76ac6120e5141d47529ea152f@cgp.ibs.re.kr SUMMARY:Lectures on cylinders in rational surfaces V LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar 2016\n\nAbstract: In affine geometry, a cylinder is an affine variety isomorphic to \mathbb{A}^1\times Z, where Z is an affine variety.A quasi-projective variety is called affine-ruled or \mathbb{A}^1-ruled if it contains a cylinder. Since cylinders are strongly related to unipotent group actions, they often appear in the study of biregular and birational automorphisms of affine varieties. In this series of lectures, I will explain how to construct cylinders in various rational surfaces and how to show that certain rational surfaces contain no cylinders. I will also introduce some open problems for beginners. END:VEVENT BEGIN:VEVENT DTSTART:20160808T160000 DTEND:20160808T180000 DTSTAMP:20160807T150000Z UID:f4abd703dc403e41d0c41d39f7331c24@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence functor and compactification of holomorphic quilt moduli space LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence functor and compactification of holomorphic quilt moduli space\n\nAbstract: In this lecture I will explain compactification of the moduli space of pseudoholomorphic quilts and its usage in the construction of correpondence functors in the Fukaya category.In particular I will focus on the Y diagram and construction of the correspondence 2-functor. END:VEVENT BEGIN:VEVENT DTSTART:20160810T103000 DTEND:20160810T120000 DTSTAMP:20160809T150000Z UID:7d41423dba52e0579d2894a190394bfa@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence functor and compactification of holomorphic quilt moduli space LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence functor and compactification of holomorphic quilt moduli space\n\nAbstract: In this lecture I will explain compactification of the moduli space of pseudoholomorphic quilts and its usage in the construction of correpondence functors in the Fukaya category.In particular I will focus on the Y diagram and construction of the correspondence 2-functor. END:VEVENT BEGIN:VEVENT DTSTART:20160811T160000 DTEND:20160811T180000 DTSTAMP:20160810T150000Z UID:9daed85cc73a3cc8f235774bd6cd3ef3@cgp.ibs.re.kr SUMMARY:Lagrangian correspondence functor and compactification of holomorphic quilt moduli space LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Lagrangian correspondence functor and compactification of holomorphic quilt moduli space\n\nAbstract: In this lecture I will explain compactification of the moduli space of pseudoholomorphic quilts and its usage in the construction of correpondence functors in the Fukaya category.In particular I will focus on the Y diagram and construction of the correspondence 2-functor. END:VEVENT BEGIN:VEVENT DTSTART:20160809T160000 DTEND:20160809T180000 DTSTAMP:20160808T150000Z UID:b883ce10e3f164f06bdc3dbf7b209681@cgp.ibs.re.kr SUMMARY:Complex cobordisms, formal groups, and quantization LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Complex cobordisms, formal groups, and quantization\n\nAbstract: In his 1994 paper "Enumeration of rational curves via tori actions" Maxim Kontsevich, remarks that using characteristic classes of tangent bundles to moduli spaces, one can defiine Gromov-Witten invariants with values in cobordisms. In these lectures, we'll give a relatively slow introduction into complex cobordisms, Gromov-Witten theory, and the quantization formula from the thesis of Tom Coates expressing cobordism-valued GW-invariants in terms of cohomologocal ones. Mysteriously, in this formula, formal group laws on a line encode information about variations of complex structures on Riemann surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20160810T140000 DTEND:20160810T153000 DTSTAMP:20160809T150000Z UID:7130781d69afdea848353013f2ede557@cgp.ibs.re.kr SUMMARY:Complex cobordisms, formal groups, and quantization LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Complex cobordisms, formal groups, and quantization\n\nAbstract: In his 1994 paper "Enumeration of rational curves via tori actions" Maxim Kontsevich, remarks that using characteristic classes of tangent bundles to moduli spaces, one can defiine Gromov-Witten invariants with values in cobordisms. In these lectures, we'll give a relatively slow introduction into complex cobordisms, Gromov-Witten theory, and the quantization formula from the thesis of Tom Coates expressing cobordism-valued GW-invariants in terms of cohomologocal ones. Mysteriously, in this formula, formal group laws on a line encode information about variations of complex structures on Riemann surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20160812T160000 DTEND:20160812T180000 DTSTAMP:20160811T150000Z UID:9819b59bad6f53c6a4efdce2f731b459@cgp.ibs.re.kr SUMMARY:Complex cobordisms, formal groups, and quantization LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Givental\n\nEvent: Complex cobordisms, formal groups, and quantization\n\nAbstract: In his 1994 paper "Enumeration of rational curves via tori actions" Maxim Kontsevich, remarks that using characteristic classes of tangent bundles to moduli spaces, one can defiine Gromov-Witten invariants with values in cobordisms. In these lectures, we'll give a relatively slow introduction into complex cobordisms, Gromov-Witten theory, and the quantization formula from the thesis of Tom Coates expressing cobordism-valued GW-invariants in terms of cohomologocal ones. Mysteriously, in this formula, formal group laws on a line encode information about variations of complex structures on Riemann surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20160816T140000 DTEND:20160816T150000 DTSTAMP:20160815T150000Z UID:021f8784ebb2e76caa1a3191f15a0f96@cgp.ibs.re.kr SUMMARY:Geometric transitions and SYZ mirror symmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Atsushi Kanazawa\n\nEvent: Seminar 2016\n\nAbstract: I will speak about two conjectures about mirror symmetry. One is Morrison's conjecture, which says geometric transitions of Calabi-Yau manifolds are reversed under mirror symmetry. The other is the Strominger-Yau-Zaslow conjecture, which says mirror Calabi-Yau manifolds admit dual torus Lagrangian fibrations. I will demonstrate by examples these two conjectures are compatible in a sense. This is joint work with Siu-Cheong Lau. END:VEVENT BEGIN:VEVENT DTSTART:20160819T140000 DTEND:20160819T144500 DTSTAMP:20160818T150000Z UID:4004f11d14f481ed3b73b2a349412bfe@cgp.ibs.re.kr SUMMARY:Examples and Counterexamples of the quadrisecant approximation conjecture LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Gyo Taek Jin\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: We show smooth knots and polygonal knots, trivial and nontrivial, on which the quadrisecant approximation conjecture holds. We also show the counterexamples created by Bai-Wang-Wang, and discuss a possible modificaton of the conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20160819T150000 DTEND:20160819T154500 DTSTAMP:20160818T150000Z UID:247caf358fc39778cc899d778310159a@cgp.ibs.re.kr SUMMARY:Introduction to Legendrian knot theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: After a brief introduction to the concept of contact topology, we focus on Legendrin knots in R^3 with the standard contact structure. Classical invariants for Legendrin knots and their relation will be discussed. If time permits Chekanov's differential graded algebra will be introduced. END:VEVENT BEGIN:VEVENT DTSTART:20160819T161500 DTEND:20160819T170000 DTSTAMP:20160818T150000Z UID:6cb194a997273f73d37ae29ffeabc9c3@cgp.ibs.re.kr SUMMARY:3-manifolds and 3 dimensional superconformal field theories LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dongmin Gang\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: In this talk, I will review so-called 3d-3d relation which relates some topological invariants of a 3-manifold to some physical quantities of a 3d superconformal field theory (SCFT) corresponding to the 3-manifold. After reviewing various aspects of the relation, I will give several examples of non-trivial mathematical predictions on 3-manifold invariants obtained from physical principal on 3d SCFTs. END:VEVENT BEGIN:VEVENT DTSTART:20160819T171500 DTEND:20160819T180000 DTSTAMP:20160818T150000Z UID:be4879689bd3fd2d5d84747e8c78f13d@cgp.ibs.re.kr SUMMARY:An infinite-rank summand of knots with trivial Alexander polynomial LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Minhoon Kim\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: We show that there exists an infinite-rank summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial. To this end we use the Upsilon invariant recently introduced by Ozsvath, Stipsicz and Szabo using knot Floer homology. We partially compute the upsilon of (n,1)-cable of the Whitehead double of the trefoil knot. For the computation, we determine a sufficient condition for two satellite knots to have identical upsilon for any pattern with nonzero winding number. This work is joint with Kyungbae Park. END:VEVENT BEGIN:VEVENT DTSTART:20160820T093000 DTEND:20160820T101500 DTSTAMP:20160819T150000Z UID:0df5efca784ba82844ea9c2c0d6940db@cgp.ibs.re.kr SUMMARY:The restoring argument and some intrinsically knotted graphs. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyoungjun Kim\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: A graph is called intrinsically knotted if every embedding of the graph contains a non-trivially knotted cycle. Robertson and Seymour proved that there are only finitely many minor minimal intrinsically knotted graphs, but finding the complete set of them is still an open problem. Johnson, Kidwell and Michael showed that intrinsically knotted graphs have at least 21 edges. Lee, Kim, Lee, and Oh found the complete set of minor minimal intrinsically knotted graphs with 21 edges. It is also shown by Barsotti and Mattman, independently. Since Y∇ move preserve intrinsic knotting, every intrinsically knotted graph has at least one cousin that is triangle-free intrinsically knotted. This means that finding the set of triangle-free intrinsically knotted graphs is the first step for classifying the complete set of minor minimal intrinsically knotted graphs. The restoring argument is the constructing operation which helps us to determine the given graph is IK or not. By using operation, I will show that there are five triangle-free intrinsically knotted graphs with 22 edges and a single degree 5 vertex. This work is collaborated with Thomas Mattman and Seungsang Oh. END:VEVENT BEGIN:VEVENT DTSTART:20160820T114500 DTEND:20160820T123000 DTSTAMP:20160819T150000Z UID:d9beaaca9cfce620cb32a52bb526a93d@cgp.ibs.re.kr SUMMARY:Volume conjecture of trivalent graph LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jinseok Cho\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: We introduce the colored Jones polynomials of knotted trivalent graphs and suggest generalized volume conjecture. The volume in this conjecture is of the hyperbolic manifold with parabolic meridians and we introduce a method to obtain the hyperbolic volume combinatorially.This work is joint with Roland van der Veen of Leiden University. END:VEVENT BEGIN:VEVENT DTSTART:20160820T104500 DTEND:20160820T113000 DTSTAMP:20160819T150000Z UID:af9cdc7ed20e249721090a3816965820@cgp.ibs.re.kr SUMMARY:Half way between Jones and Alexander LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Roland van der Veen\n\nEvent: Mini Workshop on Knot theory\n\nAbstract: We define a new knot invariant that is in some sense half way between the Jones polynomial and the Alexander polynomial.It is easy to compute like the Alexander polynomial yet retains some stronger 'quantum' properties of the Jones polynomial.Our framework for this discussion is the quantum double D of the two-dimensional non-commutative Lie algebra. First I will show how the Alexander polynomial arises from D and indicate how it naturally interpolates towards quantum sl_2 and hence the Jones polynomial.Time permitting we will also speculate on a four-dimensional interpretation.Joint work with Dror Bar-Natan END:VEVENT BEGIN:VEVENT DTSTART:20160906T160000 DTEND:20160906T180000 DTSTAMP:20160905T150000Z UID:85c99915d0efe2033da7530d6e38e915@cgp.ibs.re.kr SUMMARY:Singularities in symplectic geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: David Nadler\n\nEvent: Seminar 2016\n\nAbstract: The basic objects of symplectic geometry are smooth manifolds, but many natural questions and constructions lead to singular spaces. This talk will be an introduction to singular Lagrangian subspaces, their role in symplectic geometry, and tools to study them. END:VEVENT BEGIN:VEVENT DTSTART:20160908T160000 DTEND:20160908T180000 DTSTAMP:20160907T150000Z UID:0459af04f6f439010517ab2160382a87@cgp.ibs.re.kr SUMMARY:Landau-Ginzburg models LOCATION:CGP Main Hall DESCRIPTION:Speaker: David Nadler\n\nEvent: CGP Seminar 2016\n\nAbstract: Given a symplectic fibration with singularities, Landau-Ginzburg models encode the "vanishing geometry" along the critical locus. This talk will be an introduction to the geometry of Landau-Ginzburg models from the perspective of sheaf theory (vanishing cycles, perverse schobers,...). END:VEVENT BEGIN:VEVENT DTSTART:20160822T100000 DTEND:20160822T105000 DTSTAMP:20160821T150000Z UID:117c61619070830e2e685be513890dbe@cgp.ibs.re.kr SUMMARY:Some remarks on the geometry of Galois representations LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Minhyong Kim\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: This will be a mostly expository talk on the occurrence in arithmetic geometry of structures familiar to topology and quantum field theory. END:VEVENT BEGIN:VEVENT DTSTART:20160822T111000 DTEND:20160822T120000 DTSTAMP:20160821T150000Z UID:9b1ec917890fc262fdbdd14234bab460@cgp.ibs.re.kr SUMMARY:Is there common ground, of interest to both number theorists and physicists? LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Philip Candelas\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: The answer to the stated question must be yes, since, to give but two examples, both physicists and number theorists have an interest in modular functions, and number theoretic considerations play a role in the study of (quantum) field theory amplitudes. Similar methods, such as those of cohomology, are also useful in both disciplines. It is a very interesting question, and to which there is as yet no definitive answer, as to whether there is a deeper relationship that goes beyond the possibility that there may be only a few methods open to us and the two disciplines both exploit some of these because these are the only techniques available. I will try review areas where there may be common interest and will discuss, in particular, analogies and possible application between path integration and the conjecture of Birch and Swinnerton-Dyer. END:VEVENT BEGIN:VEVENT DTSTART:20160822T143000 DTEND:20160822T152000 DTSTAMP:20160821T150000Z UID:e9a7ba32737a7709cdfaf816945862b7@cgp.ibs.re.kr SUMMARY:Batalin-Vilkovisky algebra for algebraic varieties LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: Differential Gerstenhaber Batalin-Vilkovisky (DGBV) algebra is an important ingredient to describe hidden structures on the cohomology of algebraic varieties. In this talk, we present a purely algebraic method (based on a (0+0)-dimensional quantum field theory and algebraic Dwork complexes) of constructing DGBV algebras for smooth projective complete intersection varieties and describe its application to computation of period matrices. If time permits, we compare our construction with a well-known construction of DGBV algebras in the case of smooth Calabi-Yau manifolds (due to Barannikov-Kontsevich based on Lie algebras of polyvector fields) and explain how to remedy our method to construct DGBV algebras for singular Calabi-Yau hypersurfaces. The talk is based on joint works with Yesule Kim and Dokyoung Kim. END:VEVENT BEGIN:VEVENT DTSTART:20160822T160000 DTEND:20160822T165000 DTSTAMP:20160821T150000Z UID:a1529ad9726fa32555adf0e5843f787a@cgp.ibs.re.kr SUMMARY:Counting BPS states in N=4 string vacua LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Shamit Kachru\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: I describe various automorphic forms which arise in answering the question, 'How many BPS states are there in an N=4 string compactification with given electric and magnetic charges?' These counting functions enjoy relations to enumerative and arithmetic algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20160822T171000 DTEND:20160822T180000 DTSTAMP:20160821T150000Z UID:c7bbbb760f26941e6a65e1abf69ec7aa@cgp.ibs.re.kr SUMMARY:Arithmetic Mirror Symmetry of K3 Surfaces and Hypergeometric Functions LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Adriana Salerno\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: Mirror symmetry predicts surprising geometric correspondences between distinct families of algebraic varieties. In some cases, these correspondences have arithmetic consequences. Among the arithmetic correspondences predicted by mirror symmetry are correspondences between point counts over finite fields. In particular, we explore closed formulas for the point counts for our alternate mirror families of K3 surfaces, their relation to their Picard-Fuchs equations and hypergeometric functions. This is joint work with: Charles Doran (University of Alberta, Canada), Tyler Kelly (University of Cambridge, UK), Steven Sperber (University of Minnesota, USA), John Voight (Dartmouth College, USA), and Ursula Whitcher (University of Wisconsin, Eau Claire, USA). END:VEVENT BEGIN:VEVENT DTSTART:20160823T100000 DTEND:20160823T105000 DTSTAMP:20160822T150000Z UID:3598c00c9f8aa1c6794f392d9a26b059@cgp.ibs.re.kr SUMMARY:Arithmetic of Calabi-Yau manifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Xenia de la Ossa\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: 1) A brief introduction to CY varieties and their moduli2) Counting of points over finite fields and the relation to periods3) The form of the zeta function for one parameter families, the L-function; the relations of the zeta functions for pairs of mirror manifolds; 4) singularities (time permitting) modular properties END:VEVENT BEGIN:VEVENT DTSTART:20160823T111000 DTEND:20160823T120000 DTSTAMP:20160822T150000Z UID:686c801b33be4dd6fa453a96b2a4eaed@cgp.ibs.re.kr SUMMARY:Categorification of hyperbolic geometry LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Tudor Dimofte\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: It has been known for a long time that hyperbolic geometry of three-manifolds is intimately connected with number theory. For example, each closed hyperbolic three-manifold defines a number field; and its hyperbolic volume is associated to a class in the Bloch group of that number field. In recent years, physicists have found that one can associate not just a number field or a volume but an entire three-dimensional supersymmetric quantum field theory T[M] to a 3-manifold M -- such that invariants like the volume are recovered as simple observables in T[M]. One prediction of this so-called 3d-3d correspondence is that three-dimensional hyperbolic geometry has a natural categorification. I will explain what this means at a mathematical level; and discuss some inroads toward practical computations. END:VEVENT BEGIN:VEVENT DTSTART:20160823T143000 DTEND:20160823T152000 DTSTAMP:20160822T150000Z UID:dd5d7da1e17570f5f50db330a24c071a@cgp.ibs.re.kr SUMMARY:Iterated p-adic integrals and rational points on curves LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Jennifer Balakrishnan\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: I will discuss some new relationships between iterated p-adic line integrals (Coleman integrals), motivated by the problem of explicitly finding rational points on curves. In particular, I will describe the link between p-adic heights and double integrals, as well as a p-adic analogue of the work of Goncharov and Levin on Zagier's conjecture, resulting in a new identity between triple Coleman integrals. This is joint work with Netan Dogra. END:VEVENT BEGIN:VEVENT DTSTART:20160823T160000 DTEND:20160823T165000 DTSTAMP:20160822T150000Z UID:8cd7196b87dee9507235ecfe2d5f25e2@cgp.ibs.re.kr SUMMARY:Categorical geometric Langlands through the lens of QFT LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Philsang Yoo\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: The geometric Langlands program arose in the 1980's as an analogue of the Langlands program for algebraic curves, but only in the last few years were Arinkin and Gaitsgory (2012) able to formulate a plausible categorical version of the conjecture. A few years earlier, Kapustin and Witten (2006) placed a form of the categorical conjecture in a physical context, but their work didn't capture the algebro-geometric nature of the conjecture nor did it address the subtleties Arinkin and Gaitsgory had to overcome. After setting up a rigorous mathematical model for Kapustin and Witten's theory, we realize the categorical geometric Langlands conjecture as an instance of S-duality after choosing a point in the moduli space of vacua. Along the way, we also find some curious new structures in geometric Langlands. This talk is based on an ongoing project with Chris Elliott. END:VEVENT BEGIN:VEVENT DTSTART:20160824T100000 DTEND:20160824T110000 DTSTAMP:20160823T150000Z UID:8043bbf950a591cfd3ba1de7ecc1542e@cgp.ibs.re.kr SUMMARY:Periods and Feynman amplitudes LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Francis Brown\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: The discovery of new particles in particle accelerators relies in a fundamental way on the calculation of Feynman amplitudes. After discussing their various integral representations, I will explain how they fit into a general philosophy of periods and are related to number theoretic quantities related to the Riemann zeta function. I will finish by showing how the nature of amplitudes is revealed by counting points of certain hypersurfaces over finite fields, which leads to the surprising appearance of modular forms. END:VEVENT BEGIN:VEVENT DTSTART:20160824T111000 DTEND:20160824T121000 DTSTAMP:20160823T150000Z UID:c8873ddaf7a1c4245c34502a5c314952@cgp.ibs.re.kr SUMMARY:Periods and Feynman amplitudes LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Francis Brown\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: The discovery of new particles in particle accelerators relies in a fundamental way on the calculation of Feynman amplitudes. After discussing their various integral representations, I will explain how they fit into a general philosophy of periods and are related to number theoretic quantities related to the Riemann zeta function. I will finish by showing how the nature of amplitudes is revealed by counting points of certain hypersurfaces over finite fields, which leads to the surprising appearance of modular forms. END:VEVENT BEGIN:VEVENT DTSTART:20160825T100000 DTEND:20160825T105000 DTSTAMP:20160824T150000Z UID:2303c2f8691621f6e7fdc2a7c33215cb@cgp.ibs.re.kr SUMMARY:Arithmetic topology on deformations of knot group representations LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Masanori Morishita\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: Following after the deformation theory of Galois representations, we will discuss deformations for knot group representations and associated invariants. END:VEVENT BEGIN:VEVENT DTSTART:20160823T171000 DTEND:20160823T180000 DTSTAMP:20160822T150000Z UID:151f5e1046cd9eff4a817de40b837526@cgp.ibs.re.kr SUMMARY:Ambitwistor Strings and Amplitudes: the Mathematical Structure of Scattering Amplitudes in massless QFTs LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Yvonne Geyer\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: Scattering amplitudes in massless field theories exhibit a surprising simplicity that is entirely unexpected from the Feynman diagram approach, with an underlying structure that is strongly reminiscent of worldsheet theory correlators, yet intrinsically algebraic. I will explain how these features can be described by so-called ambitwistor strings - two-dimensional chiral CFTs in an auxiliary target space, the phase space of complex null geodesics. This provides an excellent example of the wide-reaching impact worldsheet formulation have on the study of scattering amplitudes. On the higher-genus worldsheets required to describe loop effects, however, the mathematical framework becomes computationally challenging. Yet something remarkable happens for ambitwistor strings: due to the algebraic nature, the higher genus expressions can be transformed into simple formulae on the Riemann sphere. I will end with a brief discussion of two loops, and a proposal for the all-loop integrand. END:VEVENT BEGIN:VEVENT DTSTART:20160825T111000 DTEND:20160825T120000 DTSTAMP:20160824T150000Z UID:5685f96c52ac32edf68e827911f84d33@cgp.ibs.re.kr SUMMARY:Mock modular forms and BPS spectra of 3-manifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Sergei Gukov\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: In this talk I explain how integrality and modularity emerge in two completely groups of problems, where one would not expect to find them. The first group of problems has to do with curve counting (Gromov-Witten invariants) of Calabi-Yau 3-folds, and the other is about invariants of 3-manifolds (Witten-Reshetikhin-Turaev invariants). The definition of these invariants shows no sign of integrality or modularity. However, resurgence (Borel resummation) yields a q-series which, when applied to degenerate saddle points, turns out to be modular and has integer coefficients! This is based on very recent work with Marcos Marino, Pavel Putrov, and Cumrun Vafa. END:VEVENT BEGIN:VEVENT DTSTART:20160825T143000 DTEND:20160825T152000 DTSTAMP:20160824T150000Z UID:81661df7b404539eaa1b2213fabe08f7@cgp.ibs.re.kr SUMMARY:Landau-Ginzburg mirror symmetry for toric stacks LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Hiroshi Iritani\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: I will discuss Landau-Ginzburg description for the big and equivariant quantum cohomology of toric Deligne-Mumford stacks (orbifolds). I will also discuss a version of Gamma conjecture for toric discrepant transformations. END:VEVENT BEGIN:VEVENT DTSTART:20160825T160000 DTEND:20160825T165000 DTSTAMP:20160824T150000Z UID:ce1d12d6d8c3c92d8e81db17ca5f109d@cgp.ibs.re.kr SUMMARY:Yang-Mills Theory and the ABC Conjecture LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Yang-Hui He\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: We establish a correspondence between the ABC Conjecture and N=4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies' method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d'enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The Conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of N=4 SYM. END:VEVENT BEGIN:VEVENT DTSTART:20160825T171000 DTEND:20160825T180000 DTSTAMP:20160824T150000Z UID:d2b45b1c9bbf4cca0da7652359b43f08@cgp.ibs.re.kr SUMMARY:Topological String theory and Jacobi forms LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Albrecht Klemm\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: We show that the partition function Z of the topological string on elliptically fibred Calabi-Yau manifolds has an all genus expansion in terms of Jacobi-forms, where the elliptic arguments is identified with the string coupling. This can be proven using on Witten's reformulation of the holomorphicanomaly equations as wave function equation and modular properties of elliptic fibrations that can be inferred from homological mirror symmetry. If the pole structure in the elliptic arguments is know the determinationof Z becomes a finite problem, that in many cases is completely fixed by vanishing conditions of BPS invariants. The latter observation determines many theories e.g. the partition function for the E-string completely. END:VEVENT BEGIN:VEVENT DTSTART:20160826T100000 DTEND:20160826T105000 DTSTAMP:20160825T150000Z UID:51c2d4deed21be01344ad41f19a3b470@cgp.ibs.re.kr SUMMARY:Arithmetic of Calabi-Yau manifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Xenia de la Ossa\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: 1) A brief introduction to CY varieties and their moduli2) Counting of points over finite fields and the relation to periods3) The form of the zeta function for one parameter families, the L-function; the relations of the zeta functions for pairs of mirror manifolds; 4) singularities (time permitting) modular properties END:VEVENT BEGIN:VEVENT DTSTART:20160826T111000 DTEND:20160826T120000 DTSTAMP:20160825T150000Z UID:aa0dd0de190f91d31902c270c931dcd0@cgp.ibs.re.kr SUMMARY:Is there common ground, of interest to both number theorists and physicists? LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Philip Candelas\n\nEvent: Number Theory and Quantum Field Theory\n\nAbstract: The answer to the stated question must be yes, since, to give but two examples, both physicists and number theorists have an interest in modular functions, and number theoretic considerations play a role in the study of (quantum) field theory amplitudes. Similar methods, such as those of cohomology, are also useful in both disciplines. It is a very interesting question, and to which there is as yet no definitive answer, as to whether there is a deeper relationship that goes beyond the possibility that there may be only a few methods open to us and the two disciplines both exploit some of these because these are the only techniques available. I will try review areas where there may be common interest and will discuss, in particular, analogies and possible application between path integration and the conjecture of Birch and Swinnerton-Dyer. END:VEVENT BEGIN:VEVENT DTSTART:20160922T160000 DTEND:20160922T180000 DTSTAMP:20160921T150000Z UID:0a9459d1110c1316da348896869ea61e@cgp.ibs.re.kr SUMMARY:CR GEOMETRY ON THE BOUNDARIES OF FLAG DOMAINS LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sung Yeon Kim\n\nEvent: CGP Seminar 2016\n\nAbstract: Flag domain is an open orbit of a real form G0 in a flag manifold G=Q. In the first part of the talk, we introduce a relation between flag domains and the variation of Hodge structures.In the second part of the talk, we study geometric structures of SU(p; q) orbits and their boundarycomponents in a flag manifold with G = SL(n;C). Then we introduce a differential geometric methodfor the rigidity of proper holomorphic maps between them. We use CR structure on the boundarycomponents as geometric structures preserved by proper holomorphic maps extending smoothly toan open piece of a boundary component. We follow Cartan's moving frame method which was firstadopted by S. Webster in the study of rigidity of locally defined CR maps between spheres. END:VEVENT BEGIN:VEVENT DTSTART:20160912T100000 DTEND:20160912T110000 DTSTAMP:20160911T150000Z UID:c2689fbdc1fd55f9292068c833942309@cgp.ibs.re.kr SUMMARY:Survey of the McKay correspondence, Background, examples and open problems. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Miles Reid\n\nEvent: Seminar 2016\n\nAbstract: The lecture will cover some of the material in the title. END:VEVENT BEGIN:VEVENT DTSTART:20160912T160000 DTEND:20160912T170000 DTSTAMP:20160911T150000Z UID:62ca8e8ebb9b3fd77e888f97390c152e@cgp.ibs.re.kr SUMMARY:The Tate-Oort group scheme of order p. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Miles Reid\n\nEvent: Seminar 2016\n\nAbstract: I discuss an approach to the famous group scheme of order p introduced a long time ago by Oort and Tate. END:VEVENT BEGIN:VEVENT DTSTART:20160920T100000 DTEND:20160920T113000 DTSTAMP:20160919T150000Z UID:c31da1f077b2da8fadda5389670d9228@cgp.ibs.re.kr SUMMARY:In the philosophy of the McKay correspondence II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Seminar 2016\n\nAbstract: These talks are aimed at graduate students and young post-docs. I discuss the following:(1) Classical McKay correspondence : ADE classification,(2) G-Hilbert Schemes and their variations, and(3) Moduli spaces and quotient singularities. END:VEVENT BEGIN:VEVENT DTSTART:20160919T100000 DTEND:20160919T113000 DTSTAMP:20160918T150000Z UID:e5f5b4dcca1d524f85e34128e85e1b4c@cgp.ibs.re.kr SUMMARY:In the philosophy of the McKay correspondence I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Seminar 2016\n\nAbstract: These talks are aimed at graduate students and young post-docs. I discuss the following:(1) Classical McKay correspondence : ADE classification,(2) G-Hilbert Schemes and their variations, and(3) Moduli spaces and quotient singularities. END:VEVENT BEGIN:VEVENT DTSTART:20160921T100000 DTEND:20160921T113000 DTSTAMP:20160920T150000Z UID:93d6c9afadfe4576e32f899ac5dd84ac@cgp.ibs.re.kr SUMMARY:In the philosophy of the McKay correspondence III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Seminar 2016\n\nAbstract: These talks are aimed at graduate students and young post-docs. I discuss the following:(1) Classical McKay correspondence : ADE classification,(2) G-Hilbert Schemes and their variations, and(3) Moduli spaces and quotient singularities. END:VEVENT BEGIN:VEVENT DTSTART:20160919T160000 DTEND:20160919T180000 DTSTAMP:20160918T150000Z UID:07aa02a65068be4427391d8aa9764049@cgp.ibs.re.kr SUMMARY:Introduction to derived McKay correspondence LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar 2016\n\nAbstract: The aim of these talks is to complement talks given(or will be given) by Miles Reid and Seung-Jo Jung. We will discuss derived McKay correspondence and its applications. END:VEVENT BEGIN:VEVENT DTSTART:20160920T160000 DTEND:20160920T180000 DTSTAMP:20160919T150000Z UID:0984aaf4d4a5afac859aa2d92def0b30@cgp.ibs.re.kr SUMMARY:Introduction to derived McKay correspondence LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar 2016\n\nAbstract: The aim of these talks is to complement talks given(or will be given) by Miles Reid and Seung-Jo Jung. We will discuss derived McKay correspondence and its applications. END:VEVENT BEGIN:VEVENT DTSTART:20160927T160000 DTEND:20160927T180000 DTSTAMP:20160926T150000Z UID:3b2001a7f8409ed8311ff85b08805aa4@cgp.ibs.re.kr SUMMARY:Divisors on Dolgachev surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yonghwa Cho\n\nEvent: Seminar 2016\n\nAbstract: In this talk, we use deformation theoretic approach to study the Dolgachev surfaces. In particular, we discuss the divisors on such surfaces. Also for simple cases, we present exceptional collections of maximal length which gives a semiorthogonal decomposition of the derived categories. END:VEVENT BEGIN:VEVENT DTSTART:20161004T160000 DTEND:20161004T170000 DTSTAMP:20161003T150000Z UID:e11a121224dd7ac8d2c5b42bbbd06d17@cgp.ibs.re.kr SUMMARY:Double covers: Involutions on surfaces of general type with p_g=0 LOCATION:CGP Main Hall DESCRIPTION:Speaker: YongJoo Shin\n\nEvent: Seminar 2016\n\nAbstract: In this talk we consider involutions on surfaces of general type with p_g=0. We especially explain involutions on a surface S of general type with p_g=0, and K^2=7. We deal with possible branch divisors of the surface S by involutions. In particular we discuss two possible branch divisors of a quotient of S by an involution when the quotient is birational to an Enriques surface. Also we briefly introduce known examples supporting the two branch divisors. END:VEVENT BEGIN:VEVENT DTSTART:20161005T160000 DTEND:20161005T170000 DTSTAMP:20161004T150000Z UID:b7f33cdc5874fab1ce6685d7dcf16443@cgp.ibs.re.kr SUMMARY:Bidouble covers: Characterizations of Burniat surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: YongJoo Shin\n\nEvent: Seminar 2016\n\nAbstract: In this talk we discuss characterizations of Burniat surfaces constructed by bidouble covers. Mendes Lopes and Pardini dealt with a characterization of a Burniat surface with K^2=6. They showed that a minimal surface S of general type with p_g=0, K^2=6 and the degree 4 of the bicanonical map of S is a Burniat surface with K^2=6. Zhang considered the surface S with K^2=5. He proved that the surface S with K^2=5 is a Burniat surface with K^2=5 when the image of the bicanonical map of S is smooth. We consider that a minimal surface S of general type with p_g=0, K^2=4 and the degree 4 of the bicanonical morphism of S is a Burniat surface with K^2=4 and of non nodal type when the image of the bicanonical morphism of S is smooth. END:VEVENT BEGIN:VEVENT DTSTART:20161011T160000 DTEND:20161011T180000 DTSTAMP:20161010T150000Z UID:ea558e6119236a235dffbedf62bee514@cgp.ibs.re.kr SUMMARY:Alpha invariants of birationally birigid Fano threefolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: In-kyun Kim\n\nEvent: Seminar 2016\n\nAbstract: We calculate the alpha invariants of birationlly birigid orbifold Fano threefolds embedded in weighted projective spaces as codimension two. As an important application we show that most of them are weakly exceptional and admit K¨ahler-Einstein metric. This is a joint work with Takuzo Okada and Joonyeong Won. END:VEVENT BEGIN:VEVENT DTSTART:20161019T160000 DTEND:20161019T180000 DTSTAMP:20161018T150000Z UID:84ba1df0be11cf0501e10c11e336fe19@cgp.ibs.re.kr SUMMARY:Generalized Killing spinors (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Andrei Moroianu\n\nEvent: Seminar 2016\n\nAbstract: A generalized Killing spinor is a spinor field $\psi$ satisfying the equation $\nabla_X\psi=A(X)\cdot\psi$ for some symmetric endomorphism field $A\in End(TM)$. The restriction of a parallel spinor on some spin manifold to a hypersurface $M$ defines a generalized Killing spinor on $M$ whose associated tensor $A$ is related to the second fundamental form of $M$. Our first goal is to show that, conversely, in the real analytic category, every spin manifold $M$ carrying a generalized Killing spinor $\psi$ can be isometrically embedded as a hypersurface in a spin manifold carrying a parallel spinor whose restriction to $M$ is $\psi$. In low dimensions, generalized Killing spinors correspond to special geometries and provide a unifying framework for hypo structures in dimension 5, half-flat structures in dimension 6 and co-calibrated $G_2$-structures in dimension 8. Their description, even on the simplest manifolds, like the round sphere $S^3$, is not yet available. We will obtain some classification results on 4-dimensional Einstein manifolds, low-dimensional spheres, and explain the relationship between generalized Killing spinors on S^3 and Lagrangian graphs on the nearly Kähler manifold $S^3\times S^3$. END:VEVENT BEGIN:VEVENT DTSTART:20161020T160000 DTEND:20161020T180000 DTSTAMP:20161019T150000Z UID:0420091a5071150712b5ed5a610e9acd@cgp.ibs.re.kr SUMMARY:Generalized Killing spinors (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Andrei Moroianu\n\nEvent: Seminar 2016\n\nAbstract: A generalized Killing spinor is a spinor field $\psi$ satisfying the equation $\nabla_X\psi=A(X)\cdot\psi$ for some symmetric endomorphism field $A\in End(TM)$. The restriction of a parallel spinor on some spin manifold to a hypersurface $M$ defines a generalized Killing spinor on $M$ whose associated tensor $A$ is related to the second fundamental form of $M$. Our first goal is to show that, conversely, in the real analytic category, every spin manifold $M$ carrying a generalized Killing spinor $\psi$ can be isometrically embedded as a hypersurface in a spin manifold carrying a parallel spinor whose restriction to $M$ is $\psi$. In low dimensions, generalized Killing spinors correspond to special geometries and provide a unifying framework for hypo structures in dimension 5, half-flat structures in dimension 6 and co-calibrated $G_2$-structures in dimension 8. Their description, even on the simplest manifolds, like the round sphere $S^3$, is not yet available. We will obtain some classification results on 4-dimensional Einstein manifolds, low-dimensional spheres, and explain the relationship between generalized Killing spinors on S^3 and Lagrangian graphs on the nearly Kähler manifold $S^3\times S^3$. END:VEVENT BEGIN:VEVENT DTSTART:20161021T160000 DTEND:20161021T180000 DTSTAMP:20161020T150000Z UID:2e58647676c22c1da61627d7156f57d1@cgp.ibs.re.kr SUMMARY:The holonomy problem for locally conformally Kähler metrics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Andrei Moroianu\n\nEvent: Seminar 2016\n\nAbstract: A locally conformally Kähler (lcK) manifold is a complex manifold $(M,J)$ together with a $J$-compatible Riemannian metric $g$ which has the property that around every point of $M$ there exists a locally defined Kähler metric belonging to the conformal class of $g$. In this talk I will explain the classification of compact lcK manifolds with special holonomy, obtained in collaboration with Farid Madani and Mihaela Pilca. In particular, I will describe all compact manifolds admitting two non-homothetic Kähler metrics in the same conformal class. END:VEVENT BEGIN:VEVENT DTSTART:20161027T100000 DTEND:20161027T113000 DTSTAMP:20161026T150000Z UID:91a275e43072d5cbef5471bb5ece34a0@cgp.ibs.re.kr SUMMARY:Introduction to horospherical varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Shin-Young Kim\n\nEvent: Seminar 2016\n\nAbstract: We introduce horospherical vareites, and consider filtration of its tangent space when the varieties are smooth projective nonhomogeneous of picard number one, which give us a differential system. END:VEVENT BEGIN:VEVENT DTSTART:20161028T100000 DTEND:20161028T113000 DTSTAMP:20161027T150000Z UID:a05fa1f39950d6908da07b78aac63a5a@cgp.ibs.re.kr SUMMARY:Geometric structures modeled on horospherical varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Shin-Young Kim\n\nEvent: Seminar 2016\n\nAbstract: People studied geometric structures to solve equivalence problems. Specially, geometric structures modeled on rational homogeneous manifolds were studied to characterize rational homogeneous manifolds and to prove their deformation rigidity.Using Cartan geometry based on differential system, we prove that a geometric structure modeled on a smooth projective horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one. END:VEVENT BEGIN:VEVENT DTSTART:20161025T170000 DTEND:20161025T180000 DTSTAMP:20161024T150000Z UID:a669a6095bcad0ed36fed1297007acc7@cgp.ibs.re.kr SUMMARY:Classification of purely non-symplectic automorphisms of K3-covers of Enriques surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kwangwoo Lee\n\nEvent: Seminar 2016\n\nAbstract: Let X be a K3 surface with a fixed point free involution $\tau$. For an automorphism on the Enriques surface $X/\tau$, we study the orders of lifted automorphisms on X. Moreover we classify the triples (X,g,H), where g is a purely non-symplectic lifted automorphism and H is a g-invariant and $\tau$-invariant ample divisor of degree 2. Thus we classify K3-covers with a purely non-symplectic automorphism represented as a double cover of a smooth quadric or a singular cone in $\BP^3$.This is a joint work with H. Kenji. END:VEVENT BEGIN:VEVENT DTSTART:20161026T170000 DTEND:20161026T180000 DTSTAMP:20161025T150000Z UID:ef2819f07c36a4f13bdee3093e8b36b1@cgp.ibs.re.kr SUMMARY:Salem numbers of automorphisms of K3 surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kwangwoo Lee\n\nEvent: Seminar 2016\n\nAbstract: We determine all possible Salem numbers of degree 2 whose logarithms arise as the entropies of automorphisms of K3 surfaces of Picard number 2. This is a joint work with H. Kenji. END:VEVENT BEGIN:VEVENT DTSTART:20170112T160000 DTEND:20170112T180000 DTSTAMP:20170111T150000Z UID:091e93344c56639fd74c56908f751fab@cgp.ibs.re.kr SUMMARY:Stable and unstable del Pezzo surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: CGP Seminar\n\nAbstract: Yau-Tian-Donaldson conjecture, recently proved by Chen, Donaldson and Sun, says that a Fano manifold is Kahler-Einstein if and only if it is K-stable.Its stronger form, still open, says that a polarized manifold (M,L) is K-stable if and only if M admits a constant scalar curvature with Kahler class in L.In this talk, I will describe K-stability of ample line bundles on smooth del Pezzo surfaces (two-dimensional Fano manifolds).I will show how to apply recent result of Dervan to prove K-stability and how to use flop-version of Ross and Thomas's obstruction to prove instability.The talk is based on my joint work with Jesus Martinez-Garcia (Max-Plank Institute, Bonn, Germany). END:VEVENT BEGIN:VEVENT DTSTART:20161213T100000 DTEND:20161213T120000 DTSTAMP:20161212T150000Z UID:f4cc4d1a6ebaa39560410e4848751504@cgp.ibs.re.kr SUMMARY:Cellular stratiﬁed spaces I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dai Tamaki\n\nEvent: Seminar 2016\n\nAbstract: This is the ﬁrst of a series of three talks. In this part I, we ﬁrst review notions of stratiﬁed spaces, cells, and cellular stratiﬁed spaces with an emphasis on the diﬀerence from usual cell complexes. We also take a look at various examples of cellular stratiﬁed spaces. END:VEVENT BEGIN:VEVENT DTSTART:20161214T160000 DTEND:20161214T180000 DTSTAMP:20161213T150000Z UID:9df9ef38e19a71ce47632b2764ddd4df@cgp.ibs.re.kr SUMMARY:Cellular stratiﬁed spaces II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dai Tamaki\n\nEvent: Seminar 2016\n\nAbstract: In part II, the notion of totally normal cellular stratiﬁed spaces and their face categories are introduced. For a totally normal stratiﬁed space X, its face category C(X) is an acyclic category and thus its classifying space BC(X) is a regular cell complex. One of the most useful properties of totally normal cellular stratiﬁed spaces is the existence of an embedding BC(X) → X as a strong deformation retract. In this talk, the constructions of this embedding and deformation retraction are sketched. As an application, we review a construction of a combinatorial model for conﬁguration spaces of graphs. END:VEVENT BEGIN:VEVENT DTSTART:20161215T160000 DTEND:20161215T180000 DTSTAMP:20161214T150000Z UID:4c692624aa3f5221eb64552c01b099cd@cgp.ibs.re.kr SUMMARY:Cellular stratiﬁed spaces III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dai Tamaki\n\nEvent: CGP Seminar 2016\n\nAbstract: In part III, we introduced a further generalization, cylindrically normal cel-lular stratiﬁed spaces, and discuss its possible applications. We also discuss the duality in the classifying spaces of acyclic categories and its relation to the cell decomposition of the Salvetti complex for complexiﬁed hyperplane arrange-ments. END:VEVENT BEGIN:VEVENT DTSTART:20161024T160000 DTEND:20161024T180000 DTSTAMP:20161023T150000Z UID:e98423ed0a74ca1e9e83b0ae68511838@cgp.ibs.re.kr SUMMARY:Colored fans of spherical varieties (Spherical varieties Seminar) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyeong-Dong Park\n\nEvent: Seminar 2016\n\nAbstract: The aim of this seminar is to give an introductory overview on spherical varieties. Varieties with an action of an algebraic group G arise naturally in geometry. The remarkable class of G-varieties is provided by spherical varieties which are normal G-varieties containing an open orbit under the action of a Borel subgroup of G. Toric varieties, flag varieties, horospherical varieties, symmetric varieties and wonderful varieties are interesting examples of spherical varieties. Amazingly, they are classified in a combinatorial description, a colored fan, by the Luna-Vust theory. A lot of geometric properties such as completeness, affinity and local factoriality can be read off its colored fan as in the theory of toric varieties. But the criterion on smoothness for spherical varieties is more complicated so that we have to take into account the root systems illustrated by marked Dynkin diagrams or Luna diagrams. END:VEVENT BEGIN:VEVENT DTSTART:20161107T160000 DTEND:20161107T173000 DTSTAMP:20161106T150000Z UID:52cf156666b24d60dacad1f79352b1d6@cgp.ibs.re.kr SUMMARY:On K-homology of affine Grassmannians and quantum K-theory of complete flag manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Changzheng Li\n\nEvent: Seminar 2016\n\nAbstract: In this talk, I will present a conjecture that relates the K-homology of affine Grassmannians with the quantum K-theory of complete flag manifolds. It gives the K-theoretical analogy of the celebrated Peterson's isomorphism on the quantum cohomology level. This is based on my on-going joint work with Thomas Lam, Leonardo Mihalcea and Mark Shimozono. END:VEVENT BEGIN:VEVENT DTSTART:20161031T100000 DTEND:20161031T105000 DTSTAMP:20161030T150000Z UID:f298e706728fc6adca7bc034284ecf85@cgp.ibs.re.kr SUMMARY:Localized mirror functors LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: We explain a localized mirror functor, which uses Maurer-Cartan formalism to construct an A-infinity functor from Fukaya category to the category of matrix factorizations. We will illustrate this functor in the case of toric Fano manifolds and show that Lagrangian torus fibers map to split-generators of the matrix factorization category. This is a joint work with Siu-Cheong Lau and Hansol Hong. END:VEVENT BEGIN:VEVENT DTSTART:20161031T110000 DTEND:20161031T115000 DTSTAMP:20161030T150000Z UID:f2bd77617c8d33ae06139685587af7d9@cgp.ibs.re.kr SUMMARY:Non-displaceable Gelfand-Cetlin fibers on monotone complete flag manifolds. LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: In this talk, we first classify all Lagrangian fibers on Gelfand-Cetlin systems of partial flag manifolds. We locate a continuum of non-displaceable Gelfand-Cetlin fibers on the monotone full flag manifold $\mathcal{F}(n)$ for $n \geq 3$, which appears over the line segments connecting the position of the monotone fiber and the centers of certain Lagrangian faces. We then discuss how to show non-displaceability by using Lagrangian Floer theory deformed by Schubert cycles. This is based on the ongoing joint work with Yunhyung Cho and Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20161031T140000 DTEND:20161031T145000 DTSTAMP:20161030T150000Z UID:13eaecf1afd031b398f6b9699571740d@cgp.ibs.re.kr SUMMARY:The conifold transition of a torus knot and open invariants LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Bohan Fang\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: The conifold transition of the conormal bundle of a torus knot in the cotangent bundle of a 3-sphere is a non-compact Lagrangian submanifold in the resolved conifold. I will review the open Gromov-Witten invariants w.r.t. this Lagrangian defined via localization by Diaconescu-Shende-Vafa, and will introduce another definition by relative Gromov-Witten invariants. Then I will describe an effective algorithm to compute these invariants using the Eynard-Orantin recursion. This talk is based on the joint work with Zhengyu Zong. END:VEVENT BEGIN:VEVENT DTSTART:20161031T150000 DTEND:20161031T155000 DTSTAMP:20161030T150000Z UID:58f1fdeb91099f625324e0ace8b8632d@cgp.ibs.re.kr SUMMARY:From Witten-Morse theory to SYZ mirror symmetry LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Ziming Nikolas Ma\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Wedge product on deRham complex of a Riemannian manifold M can be pulled back to H∗(M) via explicit homotopy, constructed using Green’s operator, to give higher product structures. Fukaya conjectures the Witten deformation of these higher product structures have semi-classical limits as operators deﬁned by counting gradient ﬂow trees with respect to Morse functions, which generalizes the remarkable Witten deformation of deRham diﬀerential. We will describe brieﬂy the proof of Fukaya’s conjecture, and an application to Mirror symmetry which realizes the scattering diagram as semi-classical limit of solution to the Maurer-Cartan equation. END:VEVENT BEGIN:VEVENT DTSTART:20161031T162000 DTEND:20161031T171000 DTSTAMP:20161030T150000Z UID:6d1d4fb19d66c7129527c3ff1ed3d69e@cgp.ibs.re.kr SUMMARY:Constructing GW invariants without gluing LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Gang Tian\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: The GW invariants were constructed in 90s by using virtual cycle techniques which use a non-trivial analytic tool, often referred as the gluing technique. In this talk, I will discuss a new method of constructing GW invariants. This method does not use gluing, so it is topological. This talk is based on joint works with S.F. Wang. END:VEVENT BEGIN:VEVENT DTSTART:20161101T093000 DTEND:20161101T102000 DTSTAMP:20161031T150000Z UID:c6b36051584dadded7fe52296a3e10d1@cgp.ibs.re.kr SUMMARY:Lecture Series I "Introduction to the Yau-Donaldson-Tian conjecture" LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Gang Tian\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: The first two will be more introductory, such as, K-stability and what the conjecture is, while the third one is more advanced. END:VEVENT BEGIN:VEVENT DTSTART:20161101T150000 DTEND:20161101T155000 DTSTAMP:20161031T150000Z UID:dc151442b07121a5ddf5fdefef841720@cgp.ibs.re.kr SUMMARY:Floer-Novikov cohomology revisited LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Kaoru Ono\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Floer-Novikov cohomology is Floer cohomology for ymplectomorhisms simplistically isotopic to the identity. Its variant was used in the proof of the flux conjecture (GAFA 2005). I start by recalling some of my old results (Topology 1995 with H.-V. Le and JSG 2005) and present a slight improvement of a result in the paper (JSG 2005). END:VEVENT BEGIN:VEVENT DTSTART:20161101T162000 DTEND:20161101T171000 DTSTAMP:20161031T150000Z UID:1fffb5fc729d66f89fa8e2b7045f4de0@cgp.ibs.re.kr SUMMARY:Complete partition and application to autoequivalence LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Hiroshi Ohta\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20161101T140000 DTEND:20161101T145000 DTSTAMP:20161031T150000Z UID:1c248822097dd54c7ceb90ba33c384e8@cgp.ibs.re.kr SUMMARY:Open-closed topological B-model on Calabi-Yau geometry LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Si Li\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: We introduce a formalism of open-closed B-model on Calabi-Yau geometry via coupling Kodaira-Spencer theory with holomorphic Chern-Simons theory. This can be viewed as a open-closed string field theory for B-twisted topological string on Calabi-Yau target. END:VEVENT BEGIN:VEVENT DTSTART:20161101T103000 DTEND:20161101T112000 DTSTAMP:20161031T150000Z UID:ce5b0a8e52945cd5ad2f4d93d3431b59@cgp.ibs.re.kr SUMMARY:Quasimap Wall-crossings LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Bumsig Kim\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: We introduce a wall-crossing formula for the virtual classes of epsilon-stable quasimaps to GIT quotients and show it for complete intersections in products of projective spaces, with no positivity restrictions on their first Chern class. As a consequence, the wall-crossing formula relating the genus g descendant Gromov-Witten potential and the genus g epsilon-quasimap descendant potential is established. For the quintic threefold, the results may be interpreted as giving a rigorous and geometric interpretation of the holomorphic limit of the BCOV B-model partition function of the mirror family. This is a joint work with I. Ciocan-Fontanine. END:VEVENT BEGIN:VEVENT DTSTART:20161101T113000 DTEND:20161101T122000 DTSTAMP:20161031T150000Z UID:478b2765e73faae39147e71f7f7c8659@cgp.ibs.re.kr SUMMARY:Curve counting on abelian threefolds LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Qizheng Yin\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: I will discuss the (reduced) Gromov-Witten theory of abelian threefolds. A formula governing invariants in all genera and all curve classes is proposed. I will explain various techniques and partial results that lead to the proposed formula. Joint work with Jim Bryan, Georg Oberdieck, and Rahul Pandharipande. END:VEVENT BEGIN:VEVENT DTSTART:20161102T093000 DTEND:20161102T102000 DTSTAMP:20161101T150000Z UID:f22a653e045db725947354500303fdd3@cgp.ibs.re.kr SUMMARY:Lecture Series II "Introduction to the Yau-Donaldson-Tian conjecture" LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Gang Tian\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: The first two will be more introductory, such as, K-stability and what the conjecture is, while the third one is more advanced. END:VEVENT BEGIN:VEVENT DTSTART:20161102T103000 DTEND:20161102T112000 DTSTAMP:20161101T150000Z UID:e07daeda9faee03393de39d8070612e7@cgp.ibs.re.kr SUMMARY:Correspondence between Gromov-Witten invariants for weighted blow-ups LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Bohui Chen\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Given a symplectic manifold $X$ and its symplectic submanifold $S$, let $\bar{X}$ be the blow-up of $X$ along $S$. It is known that there is a correspondence between relative Gromov-Witten invariants of $\bar X$ relative to the exceptional divisor and absolute Gromov-Witten invariants of $X$ (relative to $S$) by the work of Maulick-Pandharipande, Hu-Li-Ruan. In this talk, I will explain that such correspondence can be generalized to the orbifold case and for any weighted blow-ups. This is the joint work with Chengyong Du and Jianxun Hu. END:VEVENT BEGIN:VEVENT DTSTART:20161103T100000 DTEND:20161103T105000 DTSTAMP:20161102T150000Z UID:e07a8e57f2a592ab63ec51e3918371d5@cgp.ibs.re.kr SUMMARY:On Conjecture O LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Changzheng Li\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: In this talk, we will discuss the Conjecture O of Galkin, Golyshev and Iritani, which‘underlies’ Gamma conjectures I and II of them. Conjecture O is concerned with the eigenvalues of the operator on the small quantum cohomology of a Fano manifold X given by the quantum multiplication of the first Chern class of X. We will prove the conjecture for homogeneous varieties G/P and odd symplectic Grassmannians. This is my joint works with Daewoong Cheong. Leonardo Mihalcea, and Ryan Shifler. END:VEVENT BEGIN:VEVENT DTSTART:20161103T110000 DTEND:20161103T115000 DTSTAMP:20161102T150000Z UID:c699e95b32b70e17d71c998d743885d8@cgp.ibs.re.kr SUMMARY:Compact moduli of K3 surfaces LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: We discuss two compactifications of moduli spaces of lattice polarized K3 surfaces in explicit examples.One is based on realizations as anticanonical divisors in toric varieties, and the other is based on Gromov-Hausdorff limits of Calabi-Yau metrics. Both of them are motivated by mirror symmetry. This is a joint work with Atsuhira Nagano, Kenji Hashimoto, and Yuichi Nohara. END:VEVENT BEGIN:VEVENT DTSTART:20161103T150000 DTEND:20161103T155000 DTSTAMP:20161102T150000Z UID:25c4fe723f8b695241104682f3751e22@cgp.ibs.re.kr SUMMARY:Coisotropic A-branes and their SYZ transformations LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Nai Chung Conan Leung\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Coisotropic A-branes are natural boundary conditions for strings in A-model. Lagrangian submanifolds are examples of them. Kapustin and Orlov observed that coisotropic A-branes are needed for the homological mirror symmetry to hold in general. In the semi-flat case, SYZ transformation takes Lagrangian sections on X to holomorphic line bundles L over its mirror Y, in which these line bundles are flat along fibers. Chan, Zhang and I showed that if instead of fiberwise flat, L are fiberwise Yang-Mills, then their mirror are precisely coisotropic A-branes. This construction used fiberwise Nahm transformation. This work is supported by a RGC research grant from the Hong Kong Government. END:VEVENT BEGIN:VEVENT DTSTART:20161103T162000 DTEND:20161103T171000 DTSTAMP:20161102T150000Z UID:e98c74cf255eba08b0238c29d49f1d6c@cgp.ibs.re.kr SUMMARY:Lecture Series III "Introduction to the Yau-Donaldson-Tian conjecture" LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Gang Tian\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: The first two will be more introductory, such as, K-stability and what the conjecture is, while the third one is more advanced. END:VEVENT BEGIN:VEVENT DTSTART:20161104T100000 DTEND:20161104T105000 DTSTAMP:20161103T150000Z UID:b1953fbcd33d48da4332411cd26a47d4@cgp.ibs.re.kr SUMMARY:Isotopy of monotone Lagrangian surfaces invariant under special $S^1$ actions LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Mei-Lin Yau\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Let $W$ be a 1-connected parallelizable symplectic 4-manifold together with a special Hamiltonian $S^1$ action and a complex framing of the tangent bundle $T$$W$ compatible with the $S^1$ action. To each $S^1$-invariant monotone Lagrangian surface $L$ we associate a numerical invariant that roughly describes the winding/twisting of $L$ relative to the complex framing. We will discuss properties of this type of invariant under Hamiltonian isotopy and its relation with surgery of Lagrangian surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20161103T140000 DTEND:20161103T145000 DTSTAMP:20161102T150000Z UID:cf184e90261b5e48c6f83c4e67d1d32d@cgp.ibs.re.kr SUMMARY:Inequivalent Lefschetz bration structures on knot surgery 4-manifolds LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Jongil Park\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Since it was known that any closed symplectic 4-manifold admits a Lefschetz pencil and a Lefschetz fibration structure can be obtained from a Lefschetz pencil by blowing-up the base loci, a study on Lefschetz fibrations have become an important theme to understand symplectic 4-manifolds topologically.By the way, R. Fintushel and R. Stern introduced a new surgery technique, called $a$ $knot$ $surgery$, to show that a large class of simply connected smooth 4-manifolds admit infinitely many distinct smooth structures. The knot surgery technique is following: Suppose that $X$ is a simply connected smooth 4-manifold containing an embedded torus $T$ of square $0$. Then, for any knot $K$ $\subset$ $S^3$, one can construct a new 4-manifold, called $a$ $knot$ $surgery$ $4$ - $manifold$,$\mathbf{X}_K$ = $X$ $\mathbf{\sharp}_{T = \mathbf{T}_m}$ ($\mathbf{S}^1$ X $\mathbf{M}_K$) (1) by taking a fiber sum along a torus $T$ in $X$ and $\mathbf{T}_m$ = $S^1$ x $m$ in $S^1$ x $\mathbf{M}_K$, where $\mathbf{M}_K$ is the 3-manifold obtained by doing 0-framed surgery along $K$ and $m$ is the meridian of $K$. For example, if $X$ is a simply connected elliptic surface $E(n)$, $T$ is the elliptic fiber, and $K$ is a fibered knot, then the knot surgery 4-manifold $\mathbf{E(n)}_K$ admits not only a symplectic structure but also a genus $2g(K) + n – 1$Lefschetz fibration structure. In this article we investigate Lefschetz fibration structures on knot surgery 4-manifold $\mathbf{E(n)}_K$ and we answer the following question proposed by I. Smith: Does the diffeomorphism type of a smooth 4-manifold determine the equivalence class of a Lefschetz fibration by curves of some given genus?This is a joint work with Ki-Heon Yun. END:VEVENT BEGIN:VEVENT DTSTART:20161104T110000 DTEND:20161104T115000 DTSTAMP:20161103T150000Z UID:f8eb2cdcab60f6bacd57124f557c6a82@cgp.ibs.re.kr SUMMARY:Almost-toric Lagrangian fibrations and their bifurcations LOCATION:Seogwipo KAL Hotel, Jeju DESCRIPTION:Speaker: Christophe Wacheux\n\nEvent: BICMR & IBS-CGP Joint Sympletic Geometry Workshop\n\nAbstract: Almost-toric Lagrangian fibrations are a generalization of the famous toricintegrable Hamiltonian systems. In almost-toric fibrations one allows in additionto elliptic singularities of toric systems another type of non-degenerate singularity,the so-called focus-focus singularities. These singularities can be “traded” one toanother, thus giving insights in the moduli space of these Lagrangian fibrations.However, such modification implies degenerate singularities at the bifurcation of thesystem.Strominger-Yau-Zaslow (SYZ) approach of Homological Mirror Symmetry conjecturesthe existence between M and its mirror $\check{M}$ of special Lagrangian fibrationsby tori over a same base space, whose associated affine structure are related by aLegendre transform. In dimension 2$n$ = 4, the fiber can pinch at prescribed loci:they are almost-toric fibrations. Trading is then used in constructions associated toSYZ.In dimension 2$n$ = 6 singularities occur that drastically affect the regularity ofthe fibration, some of them causing it to be only piece-wise smooth. In particular,the singularities are degenerate. Yet, their study is still necessary as they occurin important non-trivial examples such as the quintic threefold, where homologicalmirror symmetry is proven.In this talk, I will first present almost-toric Lagrangian fibrations results concerningtheir classification in dimension 2$n$ = 4 and higher. I will then discussbifurcations of these fibrations and how one can understand them as degeneratesingularities in higher dimension and vice-versa, through examples coming from theSYZ conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20161115T160000 DTEND:20161115T180000 DTSTAMP:20161114T150000Z UID:65b3eba430f8387c25cf77ac34971aab@cgp.ibs.re.kr SUMMARY:Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat data LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sung-Jin Oh\n\nEvent: Seminar 2016\n\nAbstract: In this talk, I will present a recent work (joint with J. Luk) on the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended asymptotically flat data. END:VEVENT BEGIN:VEVENT DTSTART:20161114T160000 DTEND:20161114T173000 DTSTAMP:20161113T150000Z UID:b9124c105d522f1b1d065cbf3cb4b06a@cgp.ibs.re.kr SUMMARY:Arithmetic Chern-Simons theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We will introduce ideas in the paper Arithmetic Chern-Simons theory II by me and collaborators. In the first talk, we start with motivation of ACST. Then, we will present some definitions and their expected roles in the theory.In the second talk, we compute arithmetic Chern-Simons invariants in some special cases.In the final talk, we will prove our main theorem in the paper as an application of computations. END:VEVENT BEGIN:VEVENT DTSTART:20161116T160000 DTEND:20161116T173000 DTSTAMP:20161115T150000Z UID:73356f0f8a15fbc5b700b173b08252d6@cgp.ibs.re.kr SUMMARY:Arithmetic Chern-Simons theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We will introduce ideas in the paper Arithmetic Chern-Simons theory II by me and collaborators. In the first talk, we start with motivation of ACST. Then, we will present some definitions and their expected roles in the theory.In the second talk, we compute arithmetic Chern-Simons invariants in some special cases.In the final talk, we will prove our main theorem in the paper as an application of computations. END:VEVENT BEGIN:VEVENT DTSTART:20161118T160000 DTEND:20161118T173000 DTSTAMP:20161117T150000Z UID:3735965b0b6235aa0cb838d60b8f33ba@cgp.ibs.re.kr SUMMARY:Arithmetic Chern-Simons theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We will introduce ideas in the paper Arithmetic Chern-Simons theory II by me and collaborators. In the first talk, we start with motivation of ACST. Then, we will present some definitions and their expected roles in the theory.In the second talk, we compute arithmetic Chern-Simons invariants in some special cases.In the final talk, we will prove our main theorem in the paper as an application of computations. END:VEVENT BEGIN:VEVENT DTSTART:20161205T160000 DTEND:20161205T180000 DTSTAMP:20161204T150000Z UID:0d2b6cd6eeb57583d5c09f583228fe6c@cgp.ibs.re.kr SUMMARY:Singularities and invariants of discrete dynamical systems LOCATION:CGP Main Hall DESCRIPTION:Speaker: Adrian Stefan Carstea\n\nEvent: Seminar 2016\n\nAbstract: We discuss the complete integrability of discrete mappings of order two (three point nonlinear reccurences) by resolution of singularities. Accordingly the mappings are lifted to automorphisms of certain rational surfaces. Eigenspaces of the linear induced bundle mappings acting on the associated Picard lattices provides linear systems of curves which allow computations of invariants. The effects on the singular fibers and the case of non-minimal rational elliptic surfaces are also dicussed. END:VEVENT BEGIN:VEVENT DTSTART:20161207T160000 DTEND:20161207T180000 DTSTAMP:20161206T150000Z UID:7e2cabb537cdd0da4b69b9a7985122d9@cgp.ibs.re.kr SUMMARY:Fiber-dependent deautonomizations and discrete Painleve Equations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Adrian Stefan Carstea\n\nEvent: Seminar 2016\n\nAbstract: Integrable mappings on the projective plane can be lifted by blow-ups to automorphisms of rational elliptic surfaces preserving an elliptic fibration. We want to deautonomize these mappings by allowing blow-up points to move (and in this case the mappings are lifted to isomorphisms of a family of generalized Halohen surfaces). Because we have many singular fibers, the invariant divizor class can be decomposed in many ways, and accordingly, many root subsystems of E8 inside the Picard lattice can appear. Expressing the mappings in terms of the elementary reflections of these root subsystems, provides new discrete Painlev e equations (as related to translations in the corresponding affine Weyl group). END:VEVENT BEGIN:VEVENT DTSTART:20161208T140000 DTEND:20161208T153000 DTSTAMP:20161207T150000Z UID:a19db0d2d687e0ef4f3c1e53be1a0708@cgp.ibs.re.kr SUMMARY:Bilinear Integrability and Supersymmetry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Adrian Stefan Carstea\n\nEvent: Seminar 2016\n\nAbstract: We discuss the extension of bilinear formalism to supersymmetric nonlinear hyperbolic equations. It is important not only for the study of the non-perturbative multiple collisions of an arbitrary number of super-solitons but also to establish the complete integrability of the underlying equations. Various examples and extension to integrable discretizations (lattice) of nonlinear super-equations are considered. END:VEVENT BEGIN:VEVENT DTSTART:20161219T140000 DTEND:20161219T153000 DTSTAMP:20161218T150000Z UID:68eebb85ecc1fd56dbca67eb23560994@cgp.ibs.re.kr SUMMARY:The construction of the moduli space of Spin(7) instantons (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: Seminar 2016\n\nAbstract: I will construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed eight-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. I will find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus. END:VEVENT BEGIN:VEVENT DTSTART:20161220T140000 DTEND:20161220T153000 DTSTAMP:20161219T150000Z UID:1b73875c3f2ce0def10a9f365bb3292b@cgp.ibs.re.kr SUMMARY:The construction of the moduli space of Spin(7) instantons (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Carlos Shahbazi Alonso\n\nEvent: Seminar 2016\n\nAbstract: I will construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed eight-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. I will find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus. END:VEVENT BEGIN:VEVENT DTSTART:20161220T160000 DTEND:20161220T180000 DTSTAMP:20161219T150000Z UID:e6471957cc1c6a3fe77831909a2c29c7@cgp.ibs.re.kr SUMMARY:Lectures on supersymmetric solutions of N=1,d=5 supergravities (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tomas Ortin Miguel\n\nEvent: Seminar 2016\n\nAbstract: In these lectures I will review some of the main results on the search and construction of supersymmetric solutions of N=1,d=5 (often called N=2,d=5) supergravity theories, both gauged (Abelian and non-Abelian) and ungauged, with general matter content. END:VEVENT BEGIN:VEVENT DTSTART:20161122T160000 DTEND:20161122T180000 DTSTAMP:20161121T150000Z UID:5994e4e3680b8fe3b4a3dd737dea710f@cgp.ibs.re.kr SUMMARY:Chord diagram expansions in quantum field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Karen Yeats\n\nEvent: Seminar 2016\n\nAbstract: We can think of perturbative expansions in quantum field theory as kinds of generating functions and Dyson-Schwinger equations (the quantum equations of motion) as functional equations. We can combinatorially solve many Dyson-Schwinger equations in terms of chord diagram expansions. I will explain how this works and some physical consequences. END:VEVENT BEGIN:VEVENT DTSTART:20161215T130000 DTEND:20161215T150000 DTSTAMP:20161214T150000Z UID:e79c62fc8c7457a5aa012f684ebcbbcf@cgp.ibs.re.kr SUMMARY:Finite transformation groups in differential and symplectic geometry and Jordan's theorem LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ignasi Mundet\n\nEvent: Seminar 2016\n\nAbstract: A number C is called a Jordan constant for a group G if any finite subgroup H of G has an abelian subgroup whose index in H is at most C. We say that G is Jordan if it admits some Jordan constant. A classic theorem of Camille Jordan states that GL(n,R) is Jordan for every n (Jordan, of course, used a different terminology). Some twenty five years ago ?ienne Ghys asked whether diffeomorphism groups of compact manifolds are Jordan. This is known to be true in many cases (including spheres, tori, and manifolds with nonzero Euler characteristic), but it is false in other cases. The easiest counterexample is the product T^2 x S^2. After discussing these facts, I will explain why, in contrast, the symplectomorphism group of T^2 x S^2 endowed with any symplectic form is Jordan, and one can compute almost exactly the optimal Jordan constant for it. So, at least for T^2 x S^2, the finite transformation group theories in the smooth and the symplectic categories differ qualitatively. Time permitting, I will talk about other symplectic 4-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20161216T100000 DTEND:20161216T120000 DTSTAMP:20161215T150000Z UID:46cd0a3915975ff57347816b7bbfc408@cgp.ibs.re.kr SUMMARY:Jordan property for Hamiltonian diffeomorphism groups of compact symplectic manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ignasi Mundet\n\nEvent: Seminar 2016\n\nAbstract: I will talk about the following theorem: Hamiltonian diffeomorphism groups of compact symplectic manifolds are Jordan. I will explain the structure of the proof, which combines the classification of finite simple groups, the topological rigidity of Hamiltonian loops, and a not-so-standard localisation theorem for actions of finite p-groups. A consequence of the theorem is the existence of infinitely many compact symplectic manifolds on which the finite transformation group theories in the smooth and the Hamiltonian categories differ qualitatively. I will also talk about weaker results for the symplectomorphism group of compact symplectic manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20161221T160000 DTEND:20161221T180000 DTSTAMP:20161220T150000Z UID:8758abc9e4271858545412c4c2d6f3e9@cgp.ibs.re.kr SUMMARY:Lectures on supersymmetric solutions of N=1,d=5 supergravities (III) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tomas Ortin Miguel\n\nEvent: Seminar 2016\n\nAbstract: In these lectures I will review some of the main results on the search and construction of supersymmetric solutions of N=1,d=5 (often called N=2,d=5) supergravity theories, both gauged (Abelian and non-Abelian) and ungauged, with general matter content. END:VEVENT BEGIN:VEVENT DTSTART:20161219T160000 DTEND:20161219T180000 DTSTAMP:20161218T150000Z UID:132b85daaf1a5a5386ed06c3753697d2@cgp.ibs.re.kr SUMMARY:Lectures on supersymmetric solutions of N=1,d=5 supergravities (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tomas Ortin Miguel\n\nEvent: Seminar 2016\n\nAbstract: In these lectures I will review some of the main results on the search and construction of supersymmetric solutions of N=1,d=5 (often called N=2,d=5) supergravity theories, both gauged (Abelian and non-Abelian) and ungauged, with general matter content. END:VEVENT BEGIN:VEVENT DTSTART:20161116T170000 DTEND:20161116T183000 DTSTAMP:20161115T150000Z UID:30cc0f74923fe5d2cee35ed4891e72f6@cgp.ibs.re.kr SUMMARY:The geometry and topology of hyperbolic 3-manifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: BoGwang Jeon\n\nEvent: Math. Dept. Seminar\n\nAbstract: In this talk, I will give a general introduction to the geometry and topology of hyperbolic 3-manifolds. Starting with Thurston-Perelman's geometrization theorem, I will go over some major theorems such as Mostow's rigidity theorem and Thurston's hyperbolic Dehn filling theorem. Then I will focus on my contributions to this field, including finiteness of the number of hyperbolic 3-manifolds of bounded volume and trace field degree, and the generalized cosmetic surgery conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20161115T170000 DTEND:20161115T183000 DTSTAMP:20161114T150000Z UID:c09043eb9d0e9825935eee0fa841d92c@cgp.ibs.re.kr SUMMARY:Uncertainty Quantification for large-scale complex systems: algorithms and its application LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Minseok Choi\n\nEvent: Math. Dept. Seminar\n\nAbstract: Uncertainty Quantification (UQ) has recently received an increasing amount of attention and is a fundamental challenge in numerical simulations of many physical complex problems such as climate modeling. Models of physical systems typically involve uncertainty in the input data such as those associated with coefficients, initial or boundary conditions, geometry, etc. Estimating the propagation of this uncertainty into computational model ouput predictions is crucial to provide more insight to the true physics and produce predictions with high fidelity.In this talk, we will discuss some of the recent devleoped UQ algorithms based on the generalized polynomial chaos, one of the most widely used approaches. Emphasis will be placed on tackling the "curse of dimensionality", and two dfferent approaches will be introduced that reduce the effective dimensionality in the parametric space. We will discuss ANOVA methods combined with polynomial chaos to deal with high dimensional problems. We will present a unified framework of time-dependent Karhunen-Loeve expansions that extracts a low-dimensional structure on-the-fly to the stochastic solutions offering siginificant computational saving over some existing methods. We demonstrate the efficiency of our methods through various numerical examples. END:VEVENT BEGIN:VEVENT DTSTART:20161124T150000 DTEND:20161124T155000 DTSTAMP:20161123T150000Z UID:656bb69ded8a313d05845d802a55c96f@cgp.ibs.re.kr SUMMARY:Mirror symmetry between Calabi-Yau categories LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: We review Calabi-Yau category structures on Fukaya categories and matrix factorization categories. Then we investigate relations between them via localized mirror functors(due to Cho-Hong-Lau), boundary-bulk maps and Kodaira-Spencer maps(due to Fukaya-Oh-Ohta-Ono). This is a work-in-progress jointly with Cheol-hyun Cho and Hyung-seok Shin. END:VEVENT BEGIN:VEVENT DTSTART:20161124T160000 DTEND:20161124T165000 DTSTAMP:20161123T150000Z UID:fdef6b9712205ceede8149f29b4224a3@cgp.ibs.re.kr SUMMARY:Combinatorics of hyperplane arrangements LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Youngho Yoon\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: Hyperplane arrangements connect many areas of mathematics. An important question is the following: how many algebraic/geometric/topological properties and invariants are determined combinatorially? I will introduce some of known results and open problems. END:VEVENT BEGIN:VEVENT DTSTART:20161125T111000 DTEND:20161125T120000 DTSTAMP:20161124T150000Z UID:dcac6b674bd20fa23a52bb662649641a@cgp.ibs.re.kr SUMMARY:Frobenius manifolds and topological conformal field theories LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Byeongho Lee\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: Frobenius manifolds are central figures in classical mirror symmetry. For example, (big) quantum cohomology in the A model or universal unfolding in the Landau-Ginzburg B model are examples of Frobenius manifolds. Since Dubrovin introduced this notion, the main tool to investigate them has been mostly geometric and analytic. However, it was introduced as a theory of a type of conformal field theory, as can be seen from one of his earlier papers on this subject. Then a natural question is, what the relationships are with representations of the Virasoro-type algebra that is associated with this specific conformal field theory, as is usual in the literature on conformal field theories. We expect a new tool to analyze problems in Frobenius manifolds, such as orbifolding. This is a work in progress, and we will report on the current status in this approach. END:VEVENT BEGIN:VEVENT DTSTART:20161127T111000 DTEND:20161127T120000 DTSTAMP:20161126T150000Z UID:9c330b4131aa2fba6215aff65cb6e07b@cgp.ibs.re.kr SUMMARY:On Lie group structure of automorphism groups LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Yoshikazu Nagata\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: We give a sufficient condition for complex manifolds that the automorphism groups become Lie groups. As an application we see that the automorphism group of any strictly pseudoconvex domain has a Lie group structure. END:VEVENT BEGIN:VEVENT DTSTART:20161125T150000 DTEND:20161125T155000 DTSTAMP:20161124T150000Z UID:54a9e6dd6f480200258d2268c01ce6b2@cgp.ibs.re.kr SUMMARY:Introduction to potential pairs LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: I will explain the notion of potential pairs. This is a generalization of the usual klt, lc singularities studied in the minimal model program.Since the notion of potential pairs also captures the positivity of the divisors, we expect that the new results for potential pairs will be useful in understanding the varieties with negative Kodaira dimension.Some ongoing project will be also discussed. END:VEVENT BEGIN:VEVENT DTSTART:20161125T160000 DTEND:20161125T165000 DTSTAMP:20161124T150000Z UID:df8c82a2c0d2f20a97dda6afa096eea0@cgp.ibs.re.kr SUMMARY:Various aspects of the volume conjecture LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Jinseok Cho\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: In this talk, I will explain my personal viewpoint of the volume conjecture. Especially, the physical, combinatorial and geometrical aspects of the volume conjecture will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20161126T111000 DTEND:20161126T120000 DTSTAMP:20161125T150000Z UID:8d50ffab658a27ac2177e575ed5829dc@cgp.ibs.re.kr SUMMARY:Symplectic fillings and rational blowdowns LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Jongil Park\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: In this talk, I'd like to explain that any minimal symplectic filling of the link of a quotient surface singularity equipped with the canonical contact structure can be obtained by a sequence of rational blowdowns and blowing-ups from the minimal resolution the corresponding quotient surface singularity. END:VEVENT BEGIN:VEVENT DTSTART:20161124T171000 DTEND:20161124T180000 DTSTAMP:20161123T150000Z UID:d35c28c84b50db23d98bea62d12f668f@cgp.ibs.re.kr SUMMARY:Differential models for B-type open-closed topological Landau-Ginzburg theories LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Mehdi Tavakol\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: I will describe a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X,W), where X is a non-compact Calabi-Yau manifold and W is a holomorphic complex-valued function defined on X whose critical set is compact. For the particular case of Stein manifolds there is more explicit description of the differential model. This is based on recent joint works with Mirela Babalic, Dmitry Doryn and Calin Iuliu Lazaroiu. END:VEVENT BEGIN:VEVENT DTSTART:20161125T171000 DTEND:20161125T180000 DTSTAMP:20161124T150000Z UID:e83cc29a400fd4ff7959385136bba13f@cgp.ibs.re.kr SUMMARY:Morse-Bott spectral sequences and the links of weighted homogeneous polynomials LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Myeonggi Kwon\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: In this talk, we introduce a version of Morse-Bott spectral sequences for (equivariant) symplectic homology. We apply this to a special kind of symplectic manifolds, named Milnor fibers, whose contact type boundary is the links of isolated hypersurface singularities. In particular, for weighted homogeneous polynomials, the links admit a periodic Reeb flow. This periodicity is useful for computing an invariant of contact structures extracted from equivariant symplectic homology, called the mean Euler characteristic. We give some applications, for example, to exotic contact structures. END:VEVENT BEGIN:VEVENT DTSTART:20161126T100000 DTEND:20161126T105000 DTSTAMP:20161125T150000Z UID:dcf27a1e7cc5317d49f215a7b769cf86@cgp.ibs.re.kr SUMMARY:The $c_2$ invariant of completed Feynman graphs in $\phi^4$ LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Dmitry Doryn\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: The $c_2$ invariant is the coefficient of $q^2$ in the $q$-expansion of the number of $\mathbb{F}_q$-rational points of the (graph) hypersurface associated to a Feynman graph. It is considered to be an arithmetic analogue of the Feynman period. I will discuss the properties of the $c_2$ invariant and the ways it can be computed. I will present the formula that can be used for calculation of this invariant for graphs without a vertex of degree less than 4. In particular, this allows to compute the $c_2$ for small 4-regular graphs in $\phi^4$ theory. END:VEVENT BEGIN:VEVENT DTSTART:20161125T100000 DTEND:20161125T105000 DTSTAMP:20161124T150000Z UID:3b734e860ae4c647e3136b71993eab96@cgp.ibs.re.kr SUMMARY:On normal crossing singularities LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Florin Ambro\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: I will discuss Kodaira type vanishing theorems for varieties with certain mild singularities, which generalize normal crossing singularities. END:VEVENT BEGIN:VEVENT DTSTART:20161127T100000 DTEND:20161127T105000 DTSTAMP:20161126T150000Z UID:e0140dd05e1ed6b667f1f8c995adb4b7@cgp.ibs.re.kr SUMMARY:Global well-posedness and stability of the relativistic Boltzmann equation without angular cut-off LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: We prove the unique existence and exponential decay of global in time classical solutions to the special relativistic Boltzmann equation without any angular cut-off assumptions with initial perturbations in some weighted Sobolev spaces. We consider perturbations of the relativistic Maxwellian equilibrium states. We work in the case of spatially periodic box. We consider the general conditions on the collision kernel from Dudynski and Ekiel-Jezewska (Commun Math Phys 115(4):607–629, 1985). Additionally, we prove sharp constructive upper and coercive lower bounds for the linearized relativistic Boltzmann collision operator in terms of a geometric fractional Sobolev norm; this shows a spectral gap exists and this behavior is similar to that of non-relativistic case as shown by Gressman and Strain(Journal of AMS 24(3), 771–847, 2011). This is the first global existence and stability result for relativistic Boltzmann equation without angular cutoff and this resolves the open question of perturbative global existence for the relativistic kinetic theory without the Grad's angular cut-off assumption. END:VEVENT BEGIN:VEVENT DTSTART:20161117T160000 DTEND:20161117T180000 DTSTAMP:20161116T150000Z UID:8180184387707506e7e16940346ee873@cgp.ibs.re.kr SUMMARY:Curves with ordinary singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Florin Ambro\n\nEvent: CGP Seminar 2016\n\nAbstract: I will discuss the classification of projective curves with ordinary singularities (simplest kind), in a way parallel to the classification of projective curves with no singularities. END:VEVENT BEGIN:VEVENT DTSTART:20161125T140000 DTEND:20161125T145000 DTSTAMP:20161124T150000Z UID:da2d07313cf252fcc22744d230d13123@cgp.ibs.re.kr SUMMARY:Factorisation Algebras and Vertex Algebras LOCATION:Novotel Ambassador Busan, Busan DESCRIPTION:Speaker: Damien Lejay\n\nEvent: 2016 Pohang Mathematics Workshop\n\nAbstract: Both factorisation algebras and vertex algebras are tools to encode themathematics of field theories. The former is much newer than the latter. We shall review the ideas leading to the definition of the two objects and have a look at the known links between them. END:VEVENT BEGIN:VEVENT DTSTART:20161122T140000 DTEND:20161122T150000 DTSTAMP:20161121T150000Z UID:1a44786597274693eda3e18b13066b39@cgp.ibs.re.kr SUMMARY:$C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: $C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology\n\nAbstract: In this lecture series, I will explain how one can employ the analytic machinery of Floer homologyin study of continous Hamiltonian dynamics, expecially towards the application to the simpleness question of the area-preserving homeomorphism group of the 2-disc and the 2-sphere. The orgarnization of the lecture series is as follows:Lecture 1: Continuous Hamiltonian flows and area-preserving homeomorphismsLecture 2: Lagrangian spectral invariants and graph selectorLecture 3: Calabi invaraints and Floer graph selectorLedture 4: Topological extension of Calabi invariants END:VEVENT BEGIN:VEVENT DTSTART:20161129T140000 DTEND:20161129T150000 DTSTAMP:20161128T150000Z UID:1b2fb2700d766772a763eed5f2f6809f@cgp.ibs.re.kr SUMMARY:$C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: $C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology\n\nAbstract: In this lecture series, I will explain how one can employ the analytic machinery of Floer homologyin study of continous Hamiltonian dynamics, expecially towards the application to the simpleness question of the area-preserving homeomorphism group of the 2-disc and the 2-sphere. The orgarnization of the lecture series is as follows:Lecture 1: Continuous Hamiltonian flows and area-preserving homeomorphismsLecture 2: Lagrangian spectral invariants and graph selectorLecture 3: Calabi invaraints and Floer graph selectorLedture 4: Topological extension of Calabi invariants END:VEVENT BEGIN:VEVENT DTSTART:20161206T140000 DTEND:20161206T150000 DTSTAMP:20161205T150000Z UID:865c66b69698f957040a7cf4dfd2ae18@cgp.ibs.re.kr SUMMARY:$C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: $C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology\n\nAbstract: In this lecture series, I will explain how one can employ the analytic machinery of Floer homologyin study of continous Hamiltonian dynamics, expecially towards the application to the simpleness question of the area-preserving homeomorphism group of the 2-disc and the 2-sphere. The orgarnization of the lecture series is as follows:Lecture 1: Continuous Hamiltonian flows and area-preserving homeomorphismsLecture 2: Lagrangian spectral invariants and graph selectorLecture 3: Calabi invaraints and Floer graph selectorLedture 4: Topological extension of Calabi invariants END:VEVENT BEGIN:VEVENT DTSTART:20161213T140000 DTEND:20161213T150000 DTSTAMP:20161212T150000Z UID:c61710fb9b220cbfd675bd97f6f3b397@cgp.ibs.re.kr SUMMARY:$C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: $C^0$ Hamiltonian geometry, area-preserving homeomorphism group and Floer homology\n\nAbstract: In this lecture series, I will explain how one can employ the analytic machinery of Floer homologyin study of continous Hamiltonian dynamics, expecially towards the application to the simpleness question of the area-preserving homeomorphism group of the 2-disc and the 2-sphere. The orgarnization of the lecture series is as follows:Lecture 1: Continuous Hamiltonian flows and area-preserving homeomorphismsLecture 2: Lagrangian spectral invariants and graph selectorLecture 3: Calabi invaraints and Floer graph selectorLedture 4: Topological extension of Calabi invariants END:VEVENT BEGIN:VEVENT DTSTART:20161216T140000 DTEND:20161216T144500 DTSTAMP:20161215T150000Z UID:7fb556ffa1a0dc94ab8c2ce10a2ee806@cgp.ibs.re.kr SUMMARY:Minimal stick number of tangles LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngsik Huh\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: A tangle is a set of disjoint arcs properly embedded in the standard 3-ball, and a stick tangle is a tangle such that every arc consists of finitely many line segments, called sticks. In this talk we give an elementary fact on the minimal number of sticks necessary for nontrivial tangles. This is a joint work with Jeonghoon Lee at CBU and Kouki Taniyama at Waseda Univ. END:VEVENT BEGIN:VEVENT DTSTART:20161216T150000 DTEND:20161216T154500 DTSTAMP:20161215T150000Z UID:5c081f49fd14f7427f2c491b24b0d737@cgp.ibs.re.kr SUMMARY:Arc index and stick number of spatial graphs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sungjong No\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. We extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index $\alpha (G)$ of any spatial graph $G$ such as $$\alpha (G) \leq c(G) + e + b,$$ where $c(G)$ is the minimal crossing number of $G$, $e$ is the number of edges, and $b$ is the number of bouquet cut-components. This upper bound is lowest possible. Furthermore, we find an upper bound of stick number $s(G)$ by using the upper bound of the arc index as follow: $$s(G) \leq \frac{3}{2}c(G)+2e+\frac{3b}{2}-\frac{v}{2}$$ where $v$ is the number of vertices of G. END:VEVENT BEGIN:VEVENT DTSTART:20161216T161500 DTEND:20161216T170000 DTSTAMP:20161215T150000Z UID:ff7c07c2f8f54f6330e2f3d8361863f2@cgp.ibs.re.kr SUMMARY:A combinatorial model for graph braid groups LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Dai Tamaki\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: Given a graph G, regarded as a 1-dimensional cell complex, the fundamental group of the unordered configuration space $Conf_n(G)/\Sigma_n$ of $n$ distinct points in $G$ is called the graph braid group of $n$ strands in $G$. After the pioneering work by Rob Ghrist [Ghr01], the structure of graph braid groups has been investigated by many people.A standard technique is to use Abrams' combinatorial model for $Conf_n(G)$ described in his thesis [Abr00] and then use discrete Morse theory to reduce the number of cells.Here we propose an alternative model based on the notion of cellular stratified spaces and its face categories, developed in [Tam]. Sample computations will be given based on the works [FMT15; Uno16] of former students of mine. END:VEVENT BEGIN:VEVENT DTSTART:20161216T171500 DTEND:20161216T180000 DTSTAMP:20161215T150000Z UID:337a17bfea6c06af9b638417af35577c@cgp.ibs.re.kr SUMMARY:Presentations and homologies of graph braid groups LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyo Won Park\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: A graph braid group is the fundamental group of the configuration space on a connected graph as 1-dimensional finite CW-complex. In this talk, I will survey results about presentations and homologies of graph braid groups since 1998, in which graph braid groups were introduced by Ghrist as motivated by robotics. END:VEVENT BEGIN:VEVENT DTSTART:20161217T093000 DTEND:20161217T101500 DTSTAMP:20161216T150000Z UID:a54b30107bc79ff46cc6bc26a7825376@cgp.ibs.re.kr SUMMARY:Enumeration of rigid lattice links LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seungsang Oh\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: The author recently introduced the state matrix recursion algorithm to enumerate various two-dimensional lattice models. In this talk, stepping up a dimension, we extend this algorithm to the enumeration of rigid lattice links which are links in the three-dimensional cubic lattice. We also consider the enumeration of fully-packed rigid lattice links. Lastly, their asymptotic behaviors are also discussed. END:VEVENT BEGIN:VEVENT DTSTART:20161217T104500 DTEND:20161217T113000 DTSTAMP:20161216T150000Z UID:899c47b16d39fe3d93fb3e005f0f97d4@cgp.ibs.re.kr SUMMARY:Simplicity in Legendrian graphs and Legendrian theta-graphs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Danielle O'Donnol\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: We will work in three-space with the standard contact structure. An embedded graph is Legendrian if it is everywhere tangent to the contact structure. I will give an overview of a few different invariants. Then I will talk about our recent work on Legendrian simplicity for topologically planar Legendrian graphs and our classification of planar Legendrian theta-graphs. This is joint with Peter Lambert-Cole (Indiana). END:VEVENT BEGIN:VEVENT DTSTART:20161217T114500 DTEND:20161217T123000 DTSTAMP:20161216T150000Z UID:1417bc363ee8c261fa72055504056172@cgp.ibs.re.kr SUMMARY:DGA invariants for Legendrian spatial graphs LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byung Hee An\n\nEvent: The 2nd Mini Workshop on Knot theory\n\nAbstract: The Chekanov-Eliashberg DGA is an invariant of Legendrian knots consisting of a differential graded algebra(DGA) whose differential is determined by counting rigid, punctured holomorphic disks in the plane with exactly one positive puncture and with boundary on the Lagrangian projection of a knot L. We extend this invariant to Legendrian spatial graphs. This is a joint work with Youngjin Bae. END:VEVENT BEGIN:VEVENT DTSTART:20161214T140000 DTEND:20161214T153000 DTSTAMP:20161213T150000Z UID:a18a016586a59d48416f5af205bad887@cgp.ibs.re.kr SUMMARY:Global aspects of quantum gauge theories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Siye Wu\n\nEvent: Seminar 2016\n\nAbstract: We revisit a few aspects of gauge theories in four dimensions related to the topology of principal gauge bundles. We found that the usual concept of discrete electric and magnetic fluxes of 't Hooft requires a modification when the gauge group is an arbitrary compact semisimple Lie group and when the spatial slice is an arbitrary compact 3-manifold. We investigate quantum gauge theory, S-duality, and dimensional reduction in light of this adjustment. END:VEVENT BEGIN:VEVENT DTSTART:20161205T140000 DTEND:20161205T153000 DTSTAMP:20161204T150000Z UID:d21f3ee0ae524b59f28aa6c4fc660cae@cgp.ibs.re.kr SUMMARY:Subadditivity of Kodaira dimension in positive characteristics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yifei Chen\n\nEvent: Seminar 2016\n\nAbstract: In this talk, we shall survey on recent progress of the subadditivity of Kodaira dimension in positive characteristics. We will start from some examples to illustrate the difference between characteristic 0 and positive characteristic. Then we will introduce the relation of subadditivity and the birational geometry in positive characteristic. The results of Birkar, Hacon-Xu, Ejiri and Yifei Chen-Lei Zhang will be mentioned. END:VEVENT BEGIN:VEVENT DTSTART:20161207T140000 DTEND:20161207T153000 DTSTAMP:20161206T150000Z UID:ba787ef25a263152c575972ab6ea1493@cgp.ibs.re.kr SUMMARY:Canonical bundle formula in positive characteristics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yifei Chen\n\nEvent: Seminar 2016\n\nAbstract: In this talk, we shall study canonical bundle formula in positive characteristics. Compared with Kodaira's canonical bundle formula in char 0, and Bombieri-Mumford canonical bundle formula in char p, we want to derive a similar formula for Kodaira-Kawamata's canonical bundle formula for elliptic fibration. As well, semi-positivity for a fibration will be discussed. This is a joint work with Yi Gu. END:VEVENT BEGIN:VEVENT DTSTART:20161222T160000 DTEND:20161222T180000 DTSTAMP:20161221T150000Z UID:07cea7001d4a2691c69f90752c3bef48@cgp.ibs.re.kr SUMMARY:A systolic inequality on contact 3-manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jungsoo Kang\n\nEvent: CGP Seminar 2016\n\nAbstract: We call a contact form Zoll if all of whose Reeb orbits are closed and have the same period. I will show that if a contact form on a 3-manifold is close to a Zoll one then a systolic inequality holds: the minimal period of closed Reeb orbits is bounded above by the contact volume. This yields that every Zoll contact form is a local maximizer for the systolic ratio in dimension 3. This is joint work with G. Benedetti. END:VEVENT BEGIN:VEVENT DTSTART:20161202T160000 DTEND:20161202T180000 DTSTAMP:20161201T150000Z UID:1c8c530fac0556df8c18badc03331eb5@cgp.ibs.re.kr SUMMARY:Spectra and Floer Theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Seminar 2016\n\nAbstract: In this series of talks, we'll talk about conjectural ways to enrich Floer theory over spectra (in the sense of stable homotopy theory). I'll put a special emphasis on Lagrangian cobordisms and their relationship to Floer theory in later talks. END:VEVENT BEGIN:VEVENT DTSTART:20161206T160000 DTEND:20161206T180000 DTSTAMP:20161205T150000Z UID:428b2f6dcbb92d33bfd8af9072f33b93@cgp.ibs.re.kr SUMMARY:Lagrangian cobordisms and Floer Theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Seminar 2016\n\nAbstract: In this series of talks, we'll talk about conjectural ways to enrich Floer theory over spectra (in the sense of stable homotopy theory). I'll put a special emphasis on Lagrangian cobordisms and their relationship to Floer theory in later talks. END:VEVENT BEGIN:VEVENT DTSTART:20161208T160000 DTEND:20161208T180000 DTSTAMP:20161207T150000Z UID:41c5c05efd3fd72ebc41e0f8f3778309@cgp.ibs.re.kr SUMMARY:Lagrangian cobordisms and Floer theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: CGP Seminar 2016\n\nAbstract: In this series of talks, we'll talk about conjectural ways to enrich Floer theory over spectra (in the sense of stable homotopy theory). I'll put a special emphasis on Lagrangian cobordisms and their relationship to Floer theory in later talks. END:VEVENT BEGIN:VEVENT DTSTART:20161221T160000 DTEND:20161221T180000 DTSTAMP:20161220T150000Z UID:bfb835d13740e0130380bd5b79bf8d52@cgp.ibs.re.kr SUMMARY:Fano-Mukai fourfolds of genus 10 as compactifications of C^4 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Seminar 2016\n\nAbstract: We discuss Fano-Mukai fourfolds of genus 10 in details. In particular, we show that any such variety is a natural compactification of the affine space C^4. We also construct a special quasihomogeneous variety of this type. END:VEVENT BEGIN:VEVENT DTSTART:20161223T160000 DTEND:20161223T180000 DTSTAMP:20161222T150000Z UID:3869515ee5b01297924e58846ece5189@cgp.ibs.re.kr SUMMARY:Birational automorphisms of threefolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Seminar 2016\n\nAbstract: I will discuss various boundedness properties for finite groups of birational automrophisms of threefolds. In particular, I will explain the classification of threefolds whose birational automorphism groups are not Jordan. Also, I will prove that p-subgroups of the Cremona group of rank 3 are abelian starting from p=17. The talk is based on joint works with Yu.Prokhorov. END:VEVENT BEGIN:VEVENT DTSTART:20161228T160000 DTEND:20161228T173000 DTSTAMP:20161227T150000Z UID:dab7b55fb545af52d967461dc3fa5076@cgp.ibs.re.kr SUMMARY:Ergodic theory of flows on homogeneous spaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sanghoon Kwon\n\nEvent: Seminar 2016\n\nAbstract: Over the past three decades, the ergodic theory for flows on homogeneous spaces has produced many beautiful applications in number theory, geometry and mathematical physics. We start with reviewing some basic concepts such as ergodicity, rates of mixing, and some flows on homogeneous spaces. We will discuss some of the rigidity phenomena and equidistribution for Lie group actions on homogeneous spaces and will present how to use those to solve problems in number theory. Further, we explore some of the dynamical results for Lie groups such as Ratner’s equidistribution theorem and the theorem about measure rigidity of diagonalizable actions. END:VEVENT BEGIN:VEVENT DTSTART:20161229T160000 DTEND:20161229T173000 DTSTAMP:20161228T150000Z UID:68715068fc0c36e55de9516b20124c69@cgp.ibs.re.kr SUMMARY:Trees and discrete subgroups of Lie groups over local fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sanghoon Kwon\n\nEvent: CGP Seminar 2016\n\nAbstract: We study the action on trees of rank one groups over locally compact nonarchimedean fields. We will also describe the result of Lubotzky on the structure of lattices in such groups, as well as some constructions of such lattices. The idea of proof for the exponential decay of correlaions of geodesic flows in the quotient of trees by geometrically finite groups will be provided. END:VEVENT BEGIN:VEVENT DTSTART:20161212T160000 DTEND:20161212T180000 DTSTAMP:20161211T150000Z UID:46450e060d3d7a4de4eef6b726cf7a36@cgp.ibs.re.kr SUMMARY:Towards Verdier duality LOCATION:CGP Main Hall DESCRIPTION:Speaker: Damien Lejay\n\nEvent: Quantum Monday 2016\n\nAbstract: The first part of the lecture shall be dedicated to understanding the statement of Verdier duality in the infinity-categorical context. In the second part, we shall see how exponentiable infinity-toposes are linked to this duality. END:VEVENT BEGIN:VEVENT DTSTART:20161220T103000 DTEND:20161220T113000 DTSTAMP:20161219T150000Z UID:019d3e5b4e14bfe4ecd04fbc4c44693f@cgp.ibs.re.kr SUMMARY:A characterization of complex hyperbolic Kleinian groups with trace fields contained in R I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonhyung Kim\n\nEvent: Seminar 2016\n\nAbstract: Let G < SU(2, 1) be a non-elementary complex hyperbolic Kleinian group. The trace field of G is the field generated by the traces of all the elements of G over the base field Q. In 1988, B. Maskit characterized non-elementary hyperbolic Kleinian groups of SL(2,C) whose trace fields are contained in R. After that, this theorem has been generalized in SU(n, 1) and Sp(n, 1) cases. In 2012, X. Fu, L. Li and X. Wang generalized this theorem in SU(2, 1) case and I generalized further in SU(3, 1) case (joint work with Sungwoon Kim) and Sp(2; 1) case.In this talk, I will explain previous results and present current results on most generel case, that is SU(n, 1) case for all n. This is a joint work with Sungwoon Kim. END:VEVENT BEGIN:VEVENT DTSTART:20161221T100000 DTEND:20161221T110000 DTSTAMP:20161220T150000Z UID:eb4dcc5a880c906d7b2a51f1b22debcb@cgp.ibs.re.kr SUMMARY:A characterization of complex hyperbolic Kleinian groups with trace fields contained in R II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonhyung Kim\n\nEvent: Seminar 2016\n\nAbstract: Let G < SU(2, 1) be a non-elementary complex hyperbolic Kleinian group. The trace field of G is the field generated by the traces of all the elements of G over the base field Q. In 1988, B. Maskit characterized non-elementary hyperbolic Kleinian groups of SL(2,C) whose trace fields are contained in R. After that, this theorem has been generalized in SU(n, 1) and Sp(n, 1) cases. In 2012, X. Fu, L. Li and X. Wang generalized this theorem in SU(2, 1) case and I generalized further in SU(3, 1) case (joint work with Sungwoon Kim) and Sp(2; 1) case.In this talk, I will explain previous results and present current results on most generel case, that is SU(n, 1) case for all n. This is a joint work with Sungwoon Kim. END:VEVENT BEGIN:VEVENT DTSTART:20161230T130000 DTEND:20161230T150000 DTSTAMP:20161229T150000Z UID:9d372fadfb725de8818fa991c81a9bbf@cgp.ibs.re.kr SUMMARY:Moduli spaces of quadratic rational maps with a marked periodic point of small order LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jung Kyu Canci\n\nEvent: Seminar 2016\n\nAbstract: I will present a joint work with J. Blanc and N. Elkies where we studied some surfaces that parametrize some objects of dynamical origin. It is conjectured that quadratic polynomial maps of the affine line, defined over the field of rational numbers, have no periodic point of order more than 3. So far it is proved that the periodicity can not be 4 and 5. I will describe the analogue case of quadratic endomorphisms of the projective line and explain why the situation is really different, by describing the set of points of periodicity 6. END:VEVENT BEGIN:VEVENT DTSTART:20161229T130000 DTEND:20161229T140000 DTSTAMP:20161228T150000Z UID:9c795eb503b881bd6147ed348f52f9d6@cgp.ibs.re.kr SUMMARY:Introduction to Wrapped Floer homology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Seminar 2016\n\nAbstract: We give an introductory lecture on Wrapped Floer homology END:VEVENT BEGIN:VEVENT DTSTART:20161230T160000 DTEND:20161230T180000 DTSTAMP:20161229T150000Z UID:31efcbfa7890988fc6db559728444b2b@cgp.ibs.re.kr SUMMARY:On the Homological mirror symmetry of punctured Riemann surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Seminar 2016\n\nAbstract: We first explain the recent work of Heather Lee on the homological mirror symmetry of a punctured Riemann surface and then explain a geometric construction of the mirror Landau-Ginzburg model, which is a toric Calabi-Yau manifold with a potential function. This is a joint work in progress with Hansol Hong and Siu-Cheong Lau. END:VEVENT BEGIN:VEVENT DTSTART:20170106T160000 DTEND:20170106T180000 DTSTAMP:20170105T150000Z UID:15dc8e02928c447807ae862ecb54dca7@cgp.ibs.re.kr SUMMARY:Real group orbits on complex infinite-dimensional flag varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mikhail Ignatyev\n\nEvent: CGP Seminar\n\nAbstract: Let Gn be a simple complex algebraic group, Pn be a parabolic subgroup of Gnand F`n = Gn=Pn be the corresponding flag variety. Denote by G0n a real form of Gn. Then G0n acts naturally on F`n. The G0n-orbit structure of F`n was described by J.A. Wolf. Now,let G be a classical simple infinite-dimensional algebraic ind-group, i.e., G is a direct limitlim !Gn of simple finite-dimensional groups, P be a (splitting) parabolic subgroup of G, andF` = G=P be the corresponding ind-variety of (generalized) flags. Denote by G0 a real formof G. Then G0 acts naturally on F`. I will discuss generalizations of J.A. Wolf’s results to thisinfinite-dimensional case. In particular, I will provide necessary and sufficient conditions for thefiniteness of the number of G0-orbits on F`, as well as for the existence of an open and a closedorbit. The talk is based on our joint work with I. Penkov and J.A. Wolf. END:VEVENT BEGIN:VEVENT DTSTART:20170214T160000 DTEND:20170214T180000 DTSTAMP:20170213T150000Z UID:bd0403a7074a12a446bcf150aeafedc6@cgp.ibs.re.kr SUMMARY:Persistent homology and symplectic/contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Zhang\n\nEvent: Seminar 2017\n\nAbstract: This is a talk on various applications of persistent homology on symplectic/contact topology. First, I will introduce the basic language of persistent homology, including the structure theorem and isometry theorem with keywords - interleaving, barcode and bottleneck distance. Second, I will briefly mention several set-ups and invariants mainly arising from (different flavors of) Floer theory in both symplectic and contact topology so that persistent homology can naturally fit in. Last but not least, as examples, several questions related with Hamiltonian dynamics or rigidity phenomena will be demonstrated and answered by using persistent homology. END:VEVENT BEGIN:VEVENT DTSTART:20170105T140000 DTEND:20170105T153000 DTSTAMP:20170104T150000Z UID:f0e90d607c504f55db936d36a030303d@cgp.ibs.re.kr SUMMARY:Symmetries and Critical Phenomena in Fluids LOCATION:CGP Main Hall DESCRIPTION:Speaker: In-Jee Jeong\n\nEvent: Seminar 2017\n\nAbstract: We consider basic incompressible fluid models in scaling critical spaces, and show that upon an appropriate symmetry condition, the systems are locally well-posed. This is in contrast with the recent ill-posedness results in critical spaces. As a special case, we obtain classes of scale invariant solutions, which are described by a respective system in one less dimension. Although these solutions have infinite energy, we demonstrate a way to obtain compactly supported solutions with the "same" dynamical properties. This is joint work with T. Elgindi. END:VEVENT BEGIN:VEVENT DTSTART:20170116T160000 DTEND:20170116T173000 DTSTAMP:20170115T150000Z UID:840b6faa4a6d11fef6adf9851911e82a@cgp.ibs.re.kr SUMMARY:Highest weight representations of Kac-Moody algebras and their crystal bases LOCATION:CGP Main Hall DESCRIPTION:Speaker: Uhi Rinn Suh\n\nEvent: Seminar 2017\n\nAbstract: There have been studied about combinatorial approaches to representation theories. For a highest weight representation of a Kac-Moody algebra, corresponding crystal basis and crystal graph show some connections between representations and combinatorics. In this talk, I will briefly introduce 1) integrable representations and highest weight representations of Kac-Moody algebras, 2) definitions of crystal bases and crystal graphs and their properties. I will mainly focus on finite dimensional Lie algebras (finite Kac-Moody algebras) cases. END:VEVENT BEGIN:VEVENT DTSTART:20170117T160000 DTEND:20170117T173000 DTSTAMP:20170116T150000Z UID:aa3a212b92a8a94094f86bc5cacb63ee@cgp.ibs.re.kr SUMMARY:On W-algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Uhi Rinn Suh\n\nEvent: Seminar 2017\n\nAbstract: A W-algebra is firstly introduced by physicists working on conformal field theory (CFT). In late 80's and early 90's, mathematicians found out a certain family of W-algebras which can be expressed mathematically. More precisely, for a given simple Lie algebra, we can define a related quantum W-algebra whose algebraic structure allows to describe a CFT. Moreover, a classical W-algebra (a classical limit of quantum W-algebras) and a finite W-algebras (finitization of a W-algebra) are widely studied in various fields of Mathematics. In this talk, I will introduce various kinds of W-algebras and explain why they are interesting. END:VEVENT BEGIN:VEVENT DTSTART:20170102T160000 DTEND:20170102T170000 DTSTAMP:20170101T150000Z UID:05d0a6019cc851a3aa5213c416fba7ad@cgp.ibs.re.kr SUMMARY:p-adic Hodge Theory in the Relative Case LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong Suk Moon\n\nEvent: Seminar 2017\n\nAbstract: We give an overview of p-adic Hodge theory in the relative case. We will explainthe construction of relative period rings and the properties of associated Dieudonnemodules, introduced in Brinon's paper \Representations p-adiques cristallines et dede Rham dans le cas relatif". END:VEVENT BEGIN:VEVENT DTSTART:20170103T160000 DTEND:20170103T170000 DTSTAMP:20170102T150000Z UID:7e82d02b0f3730f776fe02b422ab5408@cgp.ibs.re.kr SUMMARY:Rigidity of de Rham Representations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong Suk Moon\n\nEvent: Seminar 2017\n\nAbstract: In their paper \Rigidity and a Riemann-Hilbert correspondence for p-adic local sys-tems", Liu and Zhu constructed a functor from the category of p-adic etale localsystems on a smooth rigid analytic variety to the category of vector bundles with anintegrable connection. As a consequence, they proved that if the stalk of such a localsystem at one point is de Rham, then the stalk at every point is de Rham. This talkwill be a survey of the result. END:VEVENT BEGIN:VEVENT DTSTART:20170104T100000 DTEND:20170104T110000 DTSTAMP:20170103T150000Z UID:b037d1250d5decd4c3924a9bd91739ca@cgp.ibs.re.kr SUMMARY:Relative Crystalline Representations in the Unramied Case LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong Suk Moon\n\nEvent: Seminar 2017\n\nAbstract: In this talk, we will study the integral structure of relative crystalline representationsin the unramied case. We will show that when r < p 1, the locus of relativecrystalline representations whose Hodge-Tate weights lie in [0; r] cuts out a closedsubspace of the universal deformation ring. END:VEVENT BEGIN:VEVENT DTSTART:20170103T140000 DTEND:20170103T150000 DTSTAMP:20170102T150000Z UID:4d50e5d134ee9aca6ca23260e5ddce32@cgp.ibs.re.kr SUMMARY:de Rham Comparison Isomorphisms for Rigid-analytic Varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong Suk Moon\n\nEvent: Seminar 2017\n\nAbstract: Scholze proved de Rham comparison isomorphisms for rigid-analytic varieties withcoecients and in families, in his paper \p-adic Hodge theory for rigid-analytic vari-eties". In this talk, we will give a survey of Scholze's results. END:VEVENT BEGIN:VEVENT DTSTART:20170119T160000 DTEND:20170119T180000 DTSTAMP:20170118T150000Z UID:cb806441a118df9ccdb2939d179edf34@cgp.ibs.re.kr SUMMARY:Topology & Arithmetic of moduli space for elliptic Lefschetz fibrations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun-Yong Park (Univ. of Minnesota)\n\nEvent: CGP Seminar\n\nAbstract: We consider the moduli space $\mathcal{L}_{g, \mu}$ of holomorphic genus $g$ Lefschetz fibrations over $\mathbb{P}^{1}$ with $\mu$ number of singular fibers. After establishing a relationship between the moduli space $\mathcal{L}_{g, \mu}$ and the algebraic mapping stack of regular morphisms $Alg_{\mu}[\mathbb{P}^{1}, \overline{\mathcal{M}}_{g,n}]$ where $\overline{\mathcal{M}}_{g,n}$ is the Deligne--Mumford compactified stack of stable genus $g$ curves with $n$ markings, we examine the Deligne--Mumford stack $\mathcal{L}_{1, \mu}$ of moduli for holomorphic elliptic Lefschetz fibrations over $\mathbb{P}^{1}$ with $\mu = 12n$ number of irreducible singular fibers and a distinguished section. Looking at the moduli of weighted projective embeddings, we show that the cardinality of the set of $\mathbb{F}_q$--points with characteristic $\mathbb{F}_q \neq 2,3$ for $\mathcal{L}_{1, \mu}$ is bounded by $\frac{(q^{10\mu + 2}-q^{10\mu + 1})}{(q-1)} = q^{10\mu + 1} \le |\mathcal{L}_{1, {\mu} = 12n}(\mathbb{F}_q)| \le \frac{(q^{10{\mu} + 2}-1)}{(q-1)}$. In the end, we pass the acquired arithmetic invariant through the function fields $\&$ number fields analogy which renders conjectural asymptotic on $Z_{\mathbb{Q}}(X)$ the ordering of semistable elliptic curves with squarefree conductor $\mathcal{N}$. END:VEVENT BEGIN:VEVENT DTSTART:20170119T140000 DTEND:20170119T153000 DTSTAMP:20170118T150000Z UID:4633bb1465cc5dcc922b275678e29a85@cgp.ibs.re.kr SUMMARY:Stabilizing and Deforming LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rafael Bocklandt\n\nEvent: Seminar 2017\n\nAbstract: In this talk, I will explain how mirror symmetry conjectures a duality between Deformation theory and Stability theory in triangulated categories. We will illustrate how this works with examples coming from dimer models. END:VEVENT BEGIN:VEVENT DTSTART:20170117T140000 DTEND:20170117T153000 DTSTAMP:20170116T150000Z UID:aaea57d9596b6c05b309d1e5f10cbd92@cgp.ibs.re.kr SUMMARY:Wall-crossing on universal compactified Jacobians LOCATION:CGP Main Hall DESCRIPTION:Speaker: Nicola Pagani\n\nEvent: Seminar 2017\n\nAbstract: The last 20 years have seen huge develpoments in the enumerative geometry of the moduli spaces Mb_{g,n} of stable curves. In this talk, we will discuss the beginning of a similar programme for the universal Jacobian Jgn parameterizing line bundles on stable curves. The universal Jacobian admits many natural compactifications, each of which should play an important role in the enumerative geometry, thus giving rise to interesting wall-crossing phenomena. We will discuss our aims and our first results and applications of this research programme. We have an explicit picture of the combinatorics of the stability space and of the walls that govern all different compactifications, and we understand how the wall-crossing works for codimension-1cycles. END:VEVENT BEGIN:VEVENT DTSTART:20170207T160000 DTEND:20170207T180000 DTSTAMP:20170206T150000Z UID:ee5d6751ddecbd3ccf917ade07b4a174@cgp.ibs.re.kr SUMMARY:Real Gromov-Witten theory in all genera LOCATION:CGP Main Hall DESCRIPTION:Speaker: Penka Vasileva Georgieva\n\nEvent: Seminar 2017\n\nAbstract: We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces. This allows us to endow the uncompactified moduli spaces of real maps from symmetric surfaces of all topological types with natural orientations and to verify that they extend across the codimension-one boundaries of these spaces. In reasonably regular cases, these invariants can be used to obtain lower bounds for counts of real curves of arbitrary genus. Joint work with A. Zinger. END:VEVENT BEGIN:VEVENT DTSTART:20170321T160000 DTEND:20170321T180000 DTSTAMP:20170320T150000Z UID:2406daf3280e6af9bb817e154db64cbc@cgp.ibs.re.kr SUMMARY:Lagrangian fibrations on two-plane Grassmannians and mirror symmetry I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuichi Nohara\n\nEvent: Seminar 2017\n\nAbstract: For each triangulation of a convex polygon with n sides, one can associate a completely integrable system on the Grassmannian of 2-planes in an n-space, which we call a generalized Gelfand-Cetlin system.In these lectures we will study Floer theory for Lagrangian fibers of generalizes Gelfand-Cetlin systems and relation to mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20170322T160000 DTEND:20170322T180000 DTSTAMP:20170321T150000Z UID:c345fe423ed4a123169bc2e14081e443@cgp.ibs.re.kr SUMMARY:Lagrangian fibrations on two-plane Grassmannians and mirror symmetry II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuichi Nohara\n\nEvent: Seminar 2017\n\nAbstract: For each triangulation of a convex polygon with n sides, one can associate a completely integrable system on the Grassmannian of 2-planes in an n-space, which we call a generalized Gelfand-Cetlin system.In these lectures we will study Floer theory for Lagrangian fibers of generalizes Gelfand-Cetlin systems and relation to mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20170323T160000 DTEND:20170323T180000 DTSTAMP:20170322T150000Z UID:3cd75ea098a43ee384934bd3cb81e55b@cgp.ibs.re.kr SUMMARY:Potential functions on two-plane Grassmannians and cluster transformations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuichi Nohara\n\nEvent: CGP Seminar\n\nAbstract: For each triangulation of a convex polygon with n sides, one can associate a Lagrangian fibration on the Grassmannian of 2-planes in an n-space.In this talk, we discuss a relation between SYZ mirror symmetry for theses Lagrangian fibrations and the mirror Landau-Ginzburg model given by Marsh and Rietsch. END:VEVENT BEGIN:VEVENT DTSTART:20170324T160000 DTEND:20170324T180000 DTSTAMP:20170323T150000Z UID:8fc05d14ce2ac86b4f47dbc02a75b617@cgp.ibs.re.kr SUMMARY:Lagrangian fibrations on two-plane Grassmannians and mirror symmetry III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuichi Nohara\n\nEvent: Seminar 2017\n\nAbstract: For each triangulation of a convex polygon with n sides, one can associate a completely integrable system on the Grassmannian of 2-planes in an n-space, which we call a generalized Gelfand-Cetlin system.In these lectures we will study Floer theory for Lagrangian fibers of generalizes Gelfand-Cetlin systems and relation to mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20170206T160000 DTEND:20170206T180000 DTSTAMP:20170205T150000Z UID:9565a49313c48df46f2b5bc71b2228cd@cgp.ibs.re.kr SUMMARY:Vertex algebras and quantum master equation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Si Li\n\nEvent: Quantum Monday\n\nAbstract: We study the effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals and Maurer-Cartan equations for chiral vertex operators. The generating functions are proven to be almost holomorphic modular forms. As an application, we construct an exact solution of quantum B-model (BCOV theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on elliptic curves. The talk is based on arXiv: 1612.01292[math.QA] END:VEVENT BEGIN:VEVENT DTSTART:20170210T160000 DTEND:20170210T180000 DTSTAMP:20170209T150000Z UID:580bdcb226d630a15d81b1ab2f7f92ee@cgp.ibs.re.kr SUMMARY:Triangulated subcategories in derived categories of Fano orbifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar 2017\n\nAbstract: When a triangulated category is embedded in the derived category of a variety or stack then there are interesting relations between the category and geometry. I will discuss some examples of such situations. Then I will discuss which triangulated categories can be embedded in derived categories of Fano orbifolds. This is a joint work with Young-Hoon Kiem. END:VEVENT BEGIN:VEVENT DTSTART:20170215T160000 DTEND:20170215T180000 DTSTAMP:20170214T150000Z UID:33ed3a46061298e32f3b09a71b0cd0e7@cgp.ibs.re.kr SUMMARY:ACM bundles on some algebraic varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar 2017\n\nAbstract: Recently, there are lots of interests in ACM bundles on algebraic varieties. In this talks, I will discuss about basic properties, existence problem and moduli spaces of ACM bundles on some surfaces and Fano manifolds. Then I will discuss my recent joint work in progress with Yonghwa Cho and Yeongrak Kim. END:VEVENT BEGIN:VEVENT DTSTART:20170217T100000 DTEND:20170217T120000 DTSTAMP:20170216T150000Z UID:7fbb925d43b8784c8a42fbefbfb6b666@cgp.ibs.re.kr SUMMARY:ACM bundles on some algebraic varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar 2017\n\nAbstract: Recently, there are lots of interests in ACM bundles on algebraic varieties. In this talks, I will discuss about basic properties, existence problem and moduli spaces of ACM bundles on some surfaces and Fano manifolds. Then I will discuss my recent joint work in progress with Yonghwa Cho and Yeongrak Kim. END:VEVENT BEGIN:VEVENT DTSTART:20170223T160000 DTEND:20170223T180000 DTSTAMP:20170222T150000Z UID:fdcab4bfc311e6d45268c5e62f9d91cd@cgp.ibs.re.kr SUMMARY:Nilpotent orbits in variation of p-adic etale cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammad Reza Rahmati\n\nEvent: Seminar 2017\n\nAbstract: We formulate the analogue of the nilpotent orbits and nilpotent orbit theorem for variation of p-adic ´etale cohomology or crystalline cohomology with respect to the slope filtration. Specifically we show that any such orbit converges to semistable filtration. END:VEVENT BEGIN:VEVENT DTSTART:20170216T160000 DTEND:20170216T180000 DTSTAMP:20170215T150000Z UID:f766f0881945282eb96f3a9fc5181380@cgp.ibs.re.kr SUMMARY:The Green-Griffiths-Lang conjecture LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mohammad Reza Rahmati\n\nEvent: Seminar 2017\n\nAbstract: The Green-Griffiths-Lang conjecture states that for every projective variety X of general type over C, there exists a proper algebraic subvariety of X containing all non constant entire curves. I will first explain the strategy mainly developed by J. P. Demaily toward this conjecture and in the remainder of the time discuss some notions of D-module theory to complete the Demaily procedure. END:VEVENT BEGIN:VEVENT DTSTART:20170308T160000 DTEND:20170308T180000 DTSTAMP:20170307T150000Z UID:12f94e11981b60c703ab5869f8f5a5bf@cgp.ibs.re.kr SUMMARY:An introduction to quantum sheaf cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eric Sharpe\n\nEvent: Seminar 2017\n\nAbstract: In this talk I will review highlights of mathematical results and methods in `quantum sheaf cohomology,' a generalization of quantum cohomology that has currently been worked out for toric varieties and in part for Grassmannians, in work done in collaboration with S. Katz, R. Donagi, Z. Lu, and others. Quantum sheaf cohomology is defined on pairs (X, E), where X is a Kahler manifold (as above), and E --> X is a holomorphic vector bundle satisfying certain consistency conditions. In the special case that E=TX, quantum sheaf cohomology reduces to ordinary quantum cohomology of the underlying space. We will illustrate computations for the special case of P1xP1, and outline results for more general cases. If time permits, I may also outline how quantum sheaf cohomology arises from string theory. END:VEVENT BEGIN:VEVENT DTSTART:20170424T140000 DTEND:20170424T150000 DTSTAMP:20170423T150000Z UID:f13dc28f23c1740db1db0ffd50177128@cgp.ibs.re.kr SUMMARY:Alpha invariant for an existence of Kaehler-Einstein metric, constant scalar curvature Kaehler metric and K-stability for Fano varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Yau-Tian-Donaldson conjecture states that an existence of constant scalar curvature Kaehler metric for class c_1(A) is equivalent to K-polystability for ample divisor A. Now the conjecture is true for anticanonical divisors of Fano manifolds by Chen, Donaldson and Sun. Alpha invariant gives a sufficient condition to have such metrics and to be K-stable. We explain the technics, results and applications about alpha invariant for Fano varieties. END:VEVENT BEGIN:VEVENT DTSTART:20170426T140000 DTEND:20170426T150000 DTSTAMP:20170425T150000Z UID:0218d3b7d5db6a4b21d37f151a637955@cgp.ibs.re.kr SUMMARY:Alpha function and Cylidricity of Fano varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We extends concept of alpha invariant to alpha function to investigate an existence of cylinder structure of Fano varieties which is a cylinder-like open subset. It is closely related to an existence of additive group actions of affine cone over a certain Fano variety. END:VEVENT BEGIN:VEVENT DTSTART:20170427T140000 DTEND:20170427T150000 DTSTAMP:20170426T150000Z UID:72f1ed2dad62ebd6d0dbc7320a5763c9@cgp.ibs.re.kr SUMMARY:Beta, Gamma, Delta invariant for K-stability of Fano variety LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We introduce new invariants , Beta, Gamma, Delta invariant and discuss how these are good to show K-stability of Fano variety in practical way. END:VEVENT BEGIN:VEVENT DTSTART:20170619T140000 DTEND:20170619T150000 DTSTAMP:20170618T150000Z UID:720d44d4e4589d6316ac756f79e39187@cgp.ibs.re.kr SUMMARY:Topology of Gelfand-Cetlin fibers and its application to symplectic geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A Gelfand-Cetlin system is a completely integrable system on a partial flag manifold, which was introduced by Guillemin and Sternberg. First, we introduce combinatorial procedure playing with various blocks on the ladder diagrams in order to describe the diffeomorphic type of fibers and classify Lagrangian fibers on partial flag manifolds of various types. Adopting Gelfand-Cetlin systems as local models, we construct monotone Lagrangian tori on the cotangent bundles of spheres, unitary groups or their products. Also, we discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint works with Yunhyung Cho and Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20170621T140000 DTEND:20170621T150000 DTSTAMP:20170620T150000Z UID:91d91a3fca1e56de9eb571d7400402a7@cgp.ibs.re.kr SUMMARY:Topology of Gelfand-Cetlin fibers and its application to symplectic geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A Gelfand-Cetlin system is a completely integrable system on a partial flag manifold, which was introduced by Guillemin and Sternberg. First, we introduce combinatorial procedure playing with various blocks on the ladder diagrams in order to describe the diffeomorphic type of fibers and classify Lagrangian fibers on partial flag manifolds of various types. Adopting Gelfand-Cetlin systems as local models, we construct monotone Lagrangian tori on the cotangent bundles of spheres, unitary groups or their products. Also, we discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint works with Yunhyung Cho and Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20170623T140000 DTEND:20170623T150000 DTSTAMP:20170622T150000Z UID:fb139e3ce931de721f571f50656989c5@cgp.ibs.re.kr SUMMARY:Topology of Gelfand-Cetlin fibers and its application to symplectic geometry LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: A Gelfand-Cetlin system is a completely integrable system on a partial flag manifold, which was introduced by Guillemin and Sternberg. First, we introduce combinatorial procedure playing with various blocks on the ladder diagrams in order to describe the diffeomorphic type of fibers and classify Lagrangian fibers on partial flag manifolds of various types. Adopting Gelfand-Cetlin systems as local models, we construct monotone Lagrangian tori on the cotangent bundles of spheres, unitary groups or their products. Also, we discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint works with Yunhyung Cho and Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20170330T160000 DTEND:20170330T180000 DTSTAMP:20170329T150000Z UID:43667115c9e4954d44290b51883b31a5@cgp.ibs.re.kr SUMMARY:Homotopy theory of unital algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Brice Le Grignou\n\nEvent: CGP Seminar\n\nAbstract: In this talk, I will describe the homotopy theory of differential graded unital associative algebras. We already know that they are organized into a model category whose weak equivalences are quasi-isomorphisms. However, the computations of cofibrant resolutions of algebras make this framework unwieldy. I will show that the category of dg unital associative algebras may be embedded into the category of curved coalgebras whose homotopy theory is equivalent but more manageable. Then, I will generalize this method to the case of dg operads and to the case of algebras over an operad. END:VEVENT BEGIN:VEVENT DTSTART:20170314T130000 DTEND:20170314T150000 DTSTAMP:20170313T150000Z UID:4eb87004c2ac9a2d081121127d7948a6@cgp.ibs.re.kr SUMMARY:Derived Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Damien Lejay\n\nEvent: Derived Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20170407T103000 DTEND:20170407T120000 DTSTAMP:20170406T150000Z UID:21b53d9349477ac3fe744b743d5a52f8@cgp.ibs.re.kr SUMMARY:Old problem on weight multiplicities and new families of tableaux LOCATION:CGP Main Hall DESCRIPTION:Speaker: Se-jin Oh\n\nEvent: Seminar 2017\n\nAbstract: Computing the weight multiplicities of highest weight modules over finite dimensional simple Lie algebra is quite an old problem. Weyl's character formula and Freudenthal's formula provide ways to compute such weight multiplicities. However, it is hard to get practical closed formulas or to see properties of weight multiplicities.The crystal basis theory and it's related combinatorics, initiated by Kashiwara in the beginning of 1990, provide alternative ways to compute weight multiplicities. For example, by enumerating Kashiwara-Nakashima tableaux with a fixed weight, one can compute weight multiplicities. But the description of Kashiwara-Nakashima tableaux is somewhat complicated, and it is difficult to compute multiplicities by using Kashiwara-Nakashima tableaux in general.In a joint work with Kyu-Hwan Lee and Jangsoo Kim, we suggest new families of tableaux, called (spin) rigid tableaux, which are standard (skew) Young tableaux with some conditions and are equinumerous to weight multiplicities of certain infinite families of highest modules over finite dimensional simple Lie algebras of types B and D. Moreover, we can give explicit closed formulas for certain subfamilies. Interestingly, they form Pascal, Catalan, Motzkin, Riordan (newly defined by us) and Bessel triangular arrays. END:VEVENT BEGIN:VEVENT DTSTART:20170413T160000 DTEND:20170413T180000 DTSTAMP:20170412T150000Z UID:6e0b7ed39a3f690698143d8ade3893d6@cgp.ibs.re.kr SUMMARY:On Chain Groups LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: CGP Seminar\n\nAbstract: A chain group is the group generated by finitely many homeomorphisms of the real line, each of which is supported on an interval. After "minimalizing" the action, we prove that [G,G] is simple. We also prove that there are uncountably many distinct isomorphism types of such a group G. (Joint work with Yash Lodha and Thomas Koberda.) END:VEVENT BEGIN:VEVENT DTSTART:20170414T140000 DTEND:20170414T160000 DTSTAMP:20170413T150000Z UID:787910d8d850af4ef34451dc04ae9e71@cgp.ibs.re.kr SUMMARY:Morse theory and the stack of broken lines LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Seminar 2017\n\nAbstract: I will discuss how a stack of broken lines naturally recasts Morse theory as an example of a deformation problem. This is work in progress, and joint with Jacob Lurie. END:VEVENT BEGIN:VEVENT DTSTART:20170321T130000 DTEND:20170321T150000 DTSTAMP:20170320T150000Z UID:067da23b332be8ace51382ff1291c10a@cgp.ibs.re.kr SUMMARY:Derived Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel Drummond-Cole & Chang-Yeon Chough\n\nEvent: Derived Seminar\n\nAbstract: More information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170328T130000 DTEND:20170328T150000 DTSTAMP:20170327T150000Z UID:715a1f479e7512c478efcd984f6ac91a@cgp.ibs.re.kr SUMMARY:Motivation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seongjin Choi(POSTECH)& Morimishi Kawasaki(IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: More information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170404T130000 DTEND:20170404T150000 DTSTAMP:20170403T150000Z UID:5f65cd47da28dc837f68667b35ff78a7@cgp.ibs.re.kr SUMMARY:ᴅɢ-categories ɪ LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yoosik Kim(IBS-CGP) & Tae-Su Kim(SNU)\n\nEvent: Derived Seminar\n\nAbstract: More information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170620T130000 DTEND:20170620T150000 DTSTAMP:20170619T150000Z UID:cd973e7f7a57fe4364ec3fe9106febc2@cgp.ibs.re.kr SUMMARY:DG-categories III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Morimichi Kawasaki & Youngjin Bae (IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170418T130000 DTEND:20170418T150000 DTSTAMP:20170417T150000Z UID:b2b213822bbc841d8ffd0169b24a5c3c@cgp.ibs.re.kr SUMMARY:Model categories ɪɪ LOCATION:CGP Main Hall DESCRIPTION:Speaker: Damien Lejay & Mehdi Tavakol (IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170425T130000 DTEND:20170425T150000 DTSTAMP:20170424T150000Z UID:2ef4caffe0bc3ed33d540a17ebe82e8f@cgp.ibs.re.kr SUMMARY:Model Category III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170418T160000 DTEND:20170418T180000 DTSTAMP:20170417T150000Z UID:b8df20e1abfc873e6718883757f6c927@cgp.ibs.re.kr SUMMARY:The little discs operads, graph complexes, and Grothendieck-Teichmüller groups LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benoit Fresse\n\nEvent: CGP Seminar\n\nAbstract: The little discs operads were introduced by Boardman-Vogt and May for the study of iterated loop spaces. The study of the little cubes operads has been completely renewed during the last decade and new applications of these objects have been discovered in various fields of algebra and topology. To cite one application, one can prove that the spaces of compactly supported embeddings of Euclidean spaces modulo immersions have a description in terms of mapping spaces associated to the little discs operads. This result represents the outcome of a series of works by Sinha, Arone-Turchin, Dwyer-Hess and Boavida-Weiss on the Goodwillie-Weiss calculus of functors. In another direction, the second generation of proofs of the existence of deformation-quantizations for Poisson manifolds, by Tamarkin and Kontsevich, relies on an interpretation of Drinfeld's associators in terms of formality quasi-isomorphism for the little 2-discs operad. This new approach has hinted the existence of an action of the Grothendieck-Teichmüller group on the moduli space of deformation quantization.The goal of my lecture is to explain that the rational homotopy of mapping spaces associated to the little discs operads can be determined by graph complexes. This computation can also be performed for the spaces of homotopy automorphisms of the little discs operads, and can be used to retrieve that the Grothendieck-Teichmüller group represents the group of homotopy automorphisms of the little 2-discs operad. The proof of these results relies on a study of the rational homotopy of the little discs operads which I will also explain in my lecture. END:VEVENT BEGIN:VEVENT DTSTART:20170622T160000 DTEND:20170622T180000 DTSTAMP:20170621T150000Z UID:5de53bdc81d5d1dea6d138a7c38db0e1@cgp.ibs.re.kr SUMMARY:Examples of stability for complexes of coherent sheaves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chieh-Cheng Lo (Jason Lo)\n\nEvent: CGP Seminar\n\nAbstract: In constructing a moduli space of coherent sheaves or complexes of coherent sheaves on a variety, we often begin with a notion of `slope', which determines the objects to be parametrised by the moduli space. In this talk, I will discuss common notions of slope, and the stable objects they give rise to. Examples will include the usual Gieseker stability for coherent sheaves (which give DT invariants), and a polynomial stability in the sense of Bayer (which give PT invariants). END:VEVENT BEGIN:VEVENT DTSTART:20170629T160000 DTEND:20170629T180000 DTSTAMP:20170628T150000Z UID:a40a96d442c9ff6631c36676e951fc88@cgp.ibs.re.kr SUMMARY:Stable objects under a Fourier-Mukai transform on the product elliptic threefold LOCATION:CGP Main Hall DESCRIPTION:Speaker: Chieh-Cheng Lo (Jason Lo)\n\nEvent: CGP Seminar\n\nAbstract: A Fourier-Mukai transform from the derived category of coherent sheaves on a variety to itself is an autoequivalence of the derived category. A natural question to ask is, what happens to various stable objects under this autoequivalence? Answers to this question have implications on the birational properties of the moduli spaces as well as symmetries in counting invariants. In this talk, I will consider this question for slope-stable torsion-free sheaves on the product elliptic threefold. If time permits, I will also discuss this question for Gieseker stable 1-dimensional sheaves. END:VEVENT BEGIN:VEVENT DTSTART:20170410T160000 DTEND:20170410T180000 DTSTAMP:20170409T150000Z UID:d6ece93d224d7d715775cb9aa7200932@cgp.ibs.re.kr SUMMARY:Classiﬁcation of smooth Schubert varieties of the rational homogeneous manifold (F4, α4) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Minhyuk Kwon\n\nEvent: Seminar 2017\n\nAbstract: Let G be a complex simple Lie group and B be a Borel subgroup of G.For a parabolic subgroup P of G containing B, a rational homogeneous manifold S = G/P can be written as a disjoint union of ﬁnite B-orbits. We call the closure of each B-orbit a Schubert variety of S.If S is of Picard number one, then S is associated to one simple root, say α. For this reason, we express S as the Dynkin diagram of G with the marking at α, or as the pair (type of G, α) simply. When S is associated to a long root, J. Hong and N. Mok proved that every smooth Schubert variety of S corresponds to a subdiagram of the marked Dynkin diagram of S. On the other hands, this result is not true for a short root case anymore. When S is associated to a short root, the classiﬁcation of smooth Schubert varieties of S is done except for S = (F4, α3) and (F4, α4).In this talk, we classify smooth Schubert varieties of S = (F4, α4). To do this, we ﬁrst introduce the way to regard the complex simple Lie groups of type E6 and F4 as subgroups of GL(27, C) and the relation between the the Cayley plane (E6, α1) and S. After describing the generating elements of Schubert varieties explicitely, we ﬁnd the geometric relation between Schubert varieties of the Cayley plane and those of S, and then we classify all of the smooth Schubert varieties of S of lower dimensions. To distinguish singular Schubert varieties of higher dimension, we compute a lower bound of the dimension of the Zariski tangent space of each of them at a base point. END:VEVENT BEGIN:VEVENT DTSTART:20170419T140000 DTEND:20170419T153000 DTSTAMP:20170418T150000Z UID:2ecb6accef4ad82d2453ee0a6dbe8172@cgp.ibs.re.kr SUMMARY:Yang-Baxter sigma-models, conformal twists and noncommutative Yang-Mills LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eoin O. Colgain (APCTP)\n\nEvent: Seminar 2017\n\nAbstract: Over the last 3 years, we have witnessed the emergence of a correspondence between r-matrix solutions to the classical Yang-Baxter equation and integrable deformations of string theory geometries. In this talk, we provide a new perspective by showing that all the information in the deformation is encoded in the noncommutative (NC) parameter of open string theory. We conjecture that the deformed geometries are AdS/CFT dual to NC deformations of Yang-Mills, a statement we support by showing that the NC parameter from the field theory and geometry agree. END:VEVENT BEGIN:VEVENT DTSTART:20170420T160000 DTEND:20170420T180000 DTSTAMP:20170419T150000Z UID:7a6423631d68ce0353ced51738279dca@cgp.ibs.re.kr SUMMARY:The little discs operads, graph complexes, and Grothendieck-Teichmüller groups II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benoit Fresse\n\nEvent: Seminar 2017\n\nAbstract: The little discs operads were introduced by Boardman-Vogt and May for the study of iterated loop spaces. The study of the little cubes operads has been completely renewed during the last decade and new applications of these objects have been discovered in various fields of algebra and topology. To cite one application, one can prove that the spaces of compactly supported embeddings of Euclidean spaces modulo immersions have a description in terms of mapping spaces associated to the little discs operads. This result represents the outcome of a series of works by Sinha, Arone-Turchin, Dwyer-Hess and Boavida-Weiss on the Goodwillie-Weiss calculus of functors. In another direction, the second generation of proofs of the existence of deformation-quantizations for Poisson manifolds, by Tamarkin and Kontsevich, relies on an interpretation of Drinfeld's associators in terms of formality quasi-isomorphism for the little 2-discs operad. This new approach has hinted the existence of an action of the Grothendieck-Teichmüller group on the moduli space of deformation quantization. The goal of my lecture is to explain that the rational homotopy of mapping spaces associated to the little discs operads can be determined by graph complexes. This computation can also be performed for the spaces of homotopy automorphisms of the little discs operads, and can be used to retrieve that the Grothendieck-Teichmüller group represents the group of homotopy automorphisms of the little 2-discs operad. The proof of these results relies on a study of the rational homotopy of the little discs operads which I will also explain in my lecture. END:VEVENT BEGIN:VEVENT DTSTART:20170421T160000 DTEND:20170421T180000 DTSTAMP:20170420T150000Z UID:8612be8c03c5b31ed8abb809ded1597a@cgp.ibs.re.kr SUMMARY:The little discs operads, graph complexes, and Grothendieck-Teichmüller groups III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benoit Fresse\n\nEvent: Seminar 2017\n\nAbstract: AbstractThe little discs operads were introduced by Boardman-Vogt and May for the study of iterated loop spaces. The study of the little cubes operads has been completely renewed during the last decade and new applications of these objects have been discovered in various fields of algebra and topology. To cite one application, one can prove that the spaces of compactly supported embeddings of Euclidean spaces modulo immersions have a description in terms of mapping spaces associated to the little discs operads. This result represents the outcome of a series of works by Sinha, Arone-Turchin, Dwyer-Hess and Boavida-Weiss on the Goodwillie-Weiss calculus of functors. In another direction, the second generation of proofs of the existence of deformation-quantizations for Poisson manifolds, by Tamarkin and Kontsevich, relies on an interpretation of Drinfeld's associators in terms of formality quasi-isomorphism for the little 2-discs operad. This new approach has hinted the existence of an action of the Grothendieck-Teichmüller group on the moduli space of deformation quantization. The goal of my lecture is to explain that the rational homotopy of mapping spaces associated to the little discs operads can be determined by graph complexes. This computation can also be performed for the spaces of homotopy automorphisms of the little discs operads, and can be used to retrieve that the Grothendieck-Teichmüller group represents the group of homotopy automorphisms of the little 2-discs operad. The proof of these results relies on a study of the rational homotopy of the little discs operads which I will also explain in my lecture. END:VEVENT BEGIN:VEVENT DTSTART:20170523T160000 DTEND:20170523T180000 DTSTAMP:20170522T150000Z UID:0be1a7182f38797debc08127dd88668d@cgp.ibs.re.kr SUMMARY:The Homfly polynomial, Floer homology, and contact structures LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tamas Kalman\n\nEvent: Seminar 2017\n\nAbstract: I will report on a formula that expresses certain extremal coefficients in the Homfly polynomial of a special alternating link from the Seifert graph G of the link (with an automatic extension to homogeneous links). This happens in a combinatorially novel way, using the so-called interior polynomial I(G). There is an intermediate step in the computation of I(G) where we consider a particular set of vectors that I call ‘hypertrees’. It turns out that hypertrees can be identified with spin-c structures that support a certain sutured Floer homology group. Hence in effect we are computing Homfly coefficients from Floer theory. But hypertrees also represent, faithfully, the tight contact structures on the same sutured manifold (through their Euler classes). Thus we also get a contact topological interpretation of the same coefficients. I plan to mention joint results with A. Juhasz, D. Mathews, H. Murakami, A. Postnikov, and J. Rasmussen. END:VEVENT BEGIN:VEVENT DTSTART:20170516T140000 DTEND:20170516T151500 DTSTAMP:20170515T150000Z UID:0e81925702f0f8d4feae1b1c71b4e4d7@cgp.ibs.re.kr SUMMARY:Introduction to matrix models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Introduction to matrix models\n\nAbstract: In this series of lectures I will give a brief introduction to matrix models and related topics. We will focus on the two most important examples of the matrix models, namely the Hermitianmatrix model and the Kontsevich matrix model. In particular, we will discuss the Virasoro constraints, relations to the enumerative geometry problems and to the integrable hierarchies. END:VEVENT BEGIN:VEVENT DTSTART:20170523T140000 DTEND:20170523T151500 DTSTAMP:20170522T150000Z UID:ae51ae060e103f757aa01bdb77a98b0b@cgp.ibs.re.kr SUMMARY:Introduction to matrix models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Introduction to matrix models\n\nAbstract: In this series of lectures I will give a brief introduction to matrix models and related topics. We will focus on the two most important examples of the matrix models, namely the Hermitianmatrix model and the Kontsevich matrix model. In particular, we will discuss the Virasoro constraints, relations to the enumerative geometry problems and to the integrable hierarchies. END:VEVENT BEGIN:VEVENT DTSTART:20170530T140000 DTEND:20170530T151500 DTSTAMP:20170529T150000Z UID:9a6918b3f661bcb4d3028fbf109cf56c@cgp.ibs.re.kr SUMMARY:Introduction to matrix models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Introduction to matrix models\n\nAbstract: In this series of lectures I will give a brief introduction to matrix models and related topics. We will focus on the two most important examples of the matrix models, namely the Hermitianmatrix model and the Kontsevich matrix model. In particular, we will discuss the Virasoro constraints, relations to the enumerative geometry problems and to the integrable hierarchies. END:VEVENT BEGIN:VEVENT DTSTART:20170605T140000 DTEND:20170605T151500 DTSTAMP:20170604T150000Z UID:a360ad578ffbad30bcc2c5334b34ba3e@cgp.ibs.re.kr SUMMARY:Introduction to matrix models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Introduction to matrix models\n\nAbstract: In this series of lectures I will give a brief introduction to matrix models and related topics. We will focus on the two most important examples of the matrix models, namely the Hermitianmatrix model and the Kontsevich matrix model. In particular, we will discuss the Virasoro constraints, relations to the enumerative geometry problems and to the integrable hierarchies. END:VEVENT BEGIN:VEVENT DTSTART:20170613T140000 DTEND:20170613T151500 DTSTAMP:20170612T150000Z UID:545058af3aeed41181d56f1c97167d0c@cgp.ibs.re.kr SUMMARY:Introduction to matrix models LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Introduction to matrix models\n\nAbstract: In this series of lectures I will give a brief introduction to matrix models and related topics. We will focus on the two most important examples of the matrix models, namely the Hermitianmatrix model and the Kontsevich matrix model. In particular, we will discuss the Virasoro constraints, relations to the enumerative geometry problems and to the integrable hierarchies. END:VEVENT BEGIN:VEVENT DTSTART:20170515T160000 DTEND:20170515T180000 DTSTAMP:20170514T150000Z UID:7742f52f6bec48ecdcf508552aca5d8b@cgp.ibs.re.kr SUMMARY:Deformations of quadratic Poisson algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Xiaojun Chen\n\nEvent: Quantum Monday\n\nAbstract: In this talk, we study the deformations of a quadratic Poisson algebra and the ones of its Koszul dual. If the Poisson structure is unimodular, we show that the Poisson cohomology of these two algebras are isomorphic as Batalin-Vilkovisky algebras, which are further isomorphic to the Hochschild cohomology of their deformation quantizations. END:VEVENT BEGIN:VEVENT DTSTART:20170529T160000 DTEND:20170529T180000 DTSTAMP:20170528T150000Z UID:2dde67f1c18c77b1121f00d99862f31f@cgp.ibs.re.kr SUMMARY:Quantization of Rational Homotopy Theory I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday\n\nAbstract: I am going to summarize my research on mathematics of quantum field theory at CGP via a concrete example, which treats certain derived version of the rational homotopy theory of Chen-Quillen-Sullivan as a classical field theory.I will begin the first talk with an introduction to affine dg group scheme before characterizing its linear representations via twisting cochains and establishing a Riemann-Hilbert type correspondence. Then I will construct unipotent dg group scheme $p^W_1$ from any augmented homotopy commutative algebra $W$ over a field k of characteristic zero such that the real points of $p^W_1$, after a completion, is isomorphic to the pro-unipotent fundamental group of based smooth manifold $M$ if $W$, over the reals, is quasi-isomorphic to the algebra of smooth differential forms on $M$. This setup, in general, can be used define a pro-unipotent fundamental affine dg scheme over the rationals to any topological space $X$ from Sullivan’s CDGA of polynomial differential forms on $X$ with rational coefficients and study its representations, etc, leading to derived rational homotopy theory. The second talk is a quantization of the first talk. END:VEVENT BEGIN:VEVENT DTSTART:20170605T160000 DTEND:20170605T180000 DTSTAMP:20170604T150000Z UID:bd335bd91a9f703514e8014694867e9c@cgp.ibs.re.kr SUMMARY:Quantization of Rational Homotopy Theory II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: Quantum Monday\n\nAbstract: I am going to summarize my research on mathematics of quantum field theory at CGP via a concrete example, which treats certain derived version of the rational homotopy theory of Chen-Quillen-Sullivan as a classical field theory.I will begin the first talk with an introduction to affine dg group scheme before characterizing its linear representations via twisting cochains and establishing a Riemann-Hilbert type correspondence. Then I will construct unipotent dg group scheme $p^W_1$ from any augmented homotopy commutative algebra $W$ over a field k of characteristic zero such that the real points of $p^W_1$, after a completion, is isomorphic to the pro-unipotent fundamental group of based smooth manifold $M$ if $W$, over the reals, is quasi-isomorphic to the algebra of smooth differential forms on $M$. This setup, in general, can be used define a pro-unipotent fundamental affine dg scheme over the rationals to any topological space $X$ from Sullivan’s CDGA of polynomial differential forms on $X$ with rational coefficients and study its representations, etc, leading to derived rational homotopy theory. The second talk is a quantization of the first talk. END:VEVENT BEGIN:VEVENT DTSTART:20170615T160000 DTEND:20170615T180000 DTSTAMP:20170614T150000Z UID:d3959f543ccc69bb7fd604f586c21bb7@cgp.ibs.re.kr SUMMARY:An analog of the Dubrovin's conjecture LOCATION:CGP Main Hall DESCRIPTION:Speaker: Fumihiko Sanda\n\nEvent: CGP Seminar\n\nAbstract: B. Dubrovin conjectured the equivalence between the semi-simplicity of the quantum cohomology of a Fano manifold and the existence of a full exceptional collection in the derived category of coherent sheaves on it. He also conjectured the Stokes matrix of the quantum D-module can be described by the Euler pairings of the full exceptional collection. Recently, the later statement is refined as Gamma conjecture by Galkin-Golyshev-Iritani. In this talk, I will speak about an analogue of Dubrovin's conjecture for the case that the quantum cohomology is not necessarily semi-simple. This is a joint work with Y. Shamoto. END:VEVENT BEGIN:VEVENT DTSTART:20170621T160000 DTEND:20170621T180000 DTSTAMP:20170620T150000Z UID:349ce86c948e307d69f0116214ba4868@cgp.ibs.re.kr SUMMARY:Configuration spaces of products LOCATION:CGP Main Hall DESCRIPTION:Speaker: Benjamin Knudsen\n\nEvent: Seminar 2017\n\nAbstract: According to the additivity theorem of Dunn, the configuration spaces of a product of Euclidean spaces may be recovered (up to homotopy) from the configuration spaces of the factors, together with some algebraic structure. I will discuss joint work in progress with Bill Dwyer and Kathryn Hess extending this local result to more general manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20170612T130000 DTEND:20170612T150000 DTSTAMP:20170611T150000Z UID:bb7dbe8f28bc099af44edd3a184fb7ac@cgp.ibs.re.kr SUMMARY:DG categories II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh & Kyoung-Seog Lee (IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170411T130000 DTEND:20170411T150000 DTSTAMP:20170410T150000Z UID:3f60b6dd20c434bc4cd179c7d59a9d2d@cgp.ibs.re.kr SUMMARY:Model categories ɪ LOCATION:CGP Main Hall DESCRIPTION:Speaker: Wanmin Liu &Cheolgyu Lee (IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170616T150000 DTEND:20170616T154500 DTSTAMP:20170615T150000Z UID:5336ab17397ad371602f82706ae7fd28@cgp.ibs.re.kr SUMMARY:Disk complexes, mapping class groups, and 2-bridge knots II LOCATION:Korea University DESCRIPTION:Speaker: Sangbum Cho\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: We describe the combinatorial structure of the disk complex of a genus-2 handlebody. In particular, when the handlebody is one of the handlebodies of a reducible genus-2 Heegaard splitting, the disk complex admits an interesting subcomplex, called the primitive disk complex. As applications of a study of the primitive disk complexes, first we provide a finite presentation of the mapping class group of each of the reducible genus-2 Heegaard splittings, and next we give an alternative proof of a result of Kobayashi and Saeki that every (1, 1)-position of a non-trivial 2-bridge knot is a stabilization of its 2-bridge position. This is a joint work with Yuya Koda. END:VEVENT BEGIN:VEVENT DTSTART:20170616T140000 DTEND:20170616T144500 DTSTAMP:20170615T150000Z UID:6e25678a06068f2f31e093c32ef0d4f8@cgp.ibs.re.kr SUMMARY:Disk complexes, mapping class groups, and 2-bridge knots I LOCATION:Korea University DESCRIPTION:Speaker: Sangbum Cho\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: We describe the combinatorial structure of the disk complex of a genus-2 handlebody. In particular, when the handlebody is one of the handlebodies of a reducible genus-2 Heegaard splitting, the disk complex admits an interesting subcomplex, called the primitive disk complex. As applications of a study of the primitive disk complexes, first we provide a finite presentation of the mapping class group of each of the reducible genus-2 Heegaard splittings, and next we give an alternative proof of a result of Kobayashi and Saeki that every (1, 1)-position of a non-trivial 2-bridge knot is a stabilization of its 2-bridge position. This is a joint work with Yuya Koda. END:VEVENT BEGIN:VEVENT DTSTART:20170616T161500 DTEND:20170616T170000 DTSTAMP:20170615T150000Z UID:7a04e641d5e2d736d76e25ad60cc94eb@cgp.ibs.re.kr SUMMARY:Heegaard Floer correction terms, definite 4-manifolds, and Dehn surgery I LOCATION:Korea University DESCRIPTION:Speaker: Kyungbae Park\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: Heegaard Floer correction term is a rational-valued invariant for closed, oriented 3-manifolds equipped with torsion spincspinc structures, introduced by Ozsváth and Szabó using the absolute grading of Heegaard Floer homology. In particular, it is known that the invariant gives constraints on definite smooth 4-manifolds bounded by a give 3-manifold. In this talk, we discuss the construction and the formal properties of the correction term, and introduce two applications of it. First, we present infinitely many examples of closed, oriented, irreducible 3-manifolds MM such that b1(M)=1b1(M)=1 and π1(M)π1(M) has weight 1, but MM is not the result of Dehn surgery along a knot in the 3-sphere. This is a joint work with Matt Hedden and Min Hoon Kim. Secondly, we show if a rational homology 3-sphere YY bounds a positive definite smooth 4-manifold, then there are only finitely many intersection forms of negative definite smooth 4-manifolds bounded by YY. This is a joint work with Dong Heon Choe. END:VEVENT BEGIN:VEVENT DTSTART:20170616T171500 DTEND:20170616T180000 DTSTAMP:20170615T150000Z UID:d656b86403cbf89ae6e4391ec3136ad2@cgp.ibs.re.kr SUMMARY:Heegaard Floer correction terms, definite 4-manifolds, and Dehn surgery II LOCATION:Korea University DESCRIPTION:Speaker: Kyungbae Park\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: Heegaard Floer correction term is a rational-valued invariant for closed, oriented 3-manifolds equipped with torsion spincspinc structures, introduced by Ozsváth and Szabó using the absolute grading of Heegaard Floer homology. In particular, it is known that the invariant gives constraints on definite smooth 4-manifolds bounded by a give 3-manifold. In this talk, we discuss the construction and the formal properties of the correction term, and introduce two applications of it. First, we present infinitely many examples of closed, oriented, irreducible 3-manifolds MM such that b1(M)=1b1(M)=1 and π1(M)π1(M) has weight 1, but MM is not the result of Dehn surgery along a knot in the 3-sphere. This is a joint work with Matt Hedden and Min Hoon Kim. Secondly, we show if a rational homology 3-sphere YY bounds a positive definite smooth 4-manifold, then there are only finitely many intersection forms of negative definite smooth 4-manifolds bounded by YY. This is a joint work with Dong Heon Choe. END:VEVENT BEGIN:VEVENT DTSTART:20170617T093000 DTEND:20170617T101500 DTSTAMP:20170616T150000Z UID:0a7f16ddb99af7e16ee1d21b7610659b@cgp.ibs.re.kr SUMMARY:Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex LOCATION:Korea University DESCRIPTION:Speaker: Hyunshik Shin\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: Let MM be a hyperbolic fibered 3-manifold with b1(M)≥2b1(M)≥2 and let SS be a fiber with pseudo-Anosov monodromy ψψ. We show that there exists a sequence (Rn,ψn)(Rn,ψn) of fibers contained in the fibered cone of (S,ψ)(S,ψ) such that the asymptotic translation length of ψnψn on the curve complex (Rn)C(Rn) behaves asymptotically like 1/|χ(Rn)|21/|χ(Rn)|2. As an application, we can reprove the previous result by Gadre--Tsai that the minimal asymptotic translation lengths of a closed surface of genus gg are bounded below and above by C/g2C/g2 and D/g2D/g2 for some positive constants CC and DD, respectively. We also show that this also holds for the cases of hyperelliptic mapping class group and hyperelliptic handlebody group. END:VEVENT BEGIN:VEVENT DTSTART:20170617T104500 DTEND:20170617T113000 DTSTAMP:20170616T150000Z UID:1245e70e71189819cab122ab06afbd5b@cgp.ibs.re.kr SUMMARY:Introduction to trisection and bridge trisection LOCATION:Korea University DESCRIPTION:Speaker: Bo-hyun Kwon\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: In this talk, we introduce the Trisection of closed, smooth 4-manifolds which was developed by Gay and Kirby and the Bridge Trisection of knotted surfaces in S4S4 which is introduced by Meier and Zupan. Also, I would give some interesting open problems about these topics. END:VEVENT BEGIN:VEVENT DTSTART:20170617T114500 DTEND:20170617T123000 DTSTAMP:20170616T150000Z UID:1ca47e9a4bd5a17d6bfe1f5ab69d97b3@cgp.ibs.re.kr SUMMARY:Partially abelian PSL(2,C) representations of knot groups LOCATION:Korea University DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: The 3rd Mini Workshop on Knot theory\n\nAbstract: Octahedral developings of knot complement are inspired by Volume conjecture. These are parametrized by several ways using complex variables related to cross-ratios, in particular segment variables and region variables. We will see a condition if there is a missing representation in a solution set of gluing equation and introduce the notion of partially abelian representation, which is also related to a PSL(2,C) representation of virtually knot group. END:VEVENT BEGIN:VEVENT DTSTART:20170627T130000 DTEND:20170627T150000 DTSTAMP:20170626T150000Z UID:24c1f503b74393c93dc0a49623db4882@cgp.ibs.re.kr SUMMARY:DG Categories IV LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tae-Su Kim & Gabriel Drummond-Cole\n\nEvent: Derived Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20170704T130000 DTEND:20170704T150000 DTSTAMP:20170703T150000Z UID:524b6da59c309ab0d193f9fad67cf961@cgp.ibs.re.kr SUMMARY:DG Categories V LOCATION:CGP Main Hall DESCRIPTION:Speaker: Wanmim Liu & Yong-Geun Oh (IBS-CGP)\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20170710T160000 DTEND:20170710T173000 DTSTAMP:20170709T150000Z UID:31bc83657ab6e2d7f7226ba7054c764b@cgp.ibs.re.kr SUMMARY:Stability conditions on derived categories of varieties I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hathurusinghege Dulip Bandara Piyaratne\n\nEvent: Seminar 2017\n\nAbstract: The aim of this series of talks is to discuss about Bridgeland stability conditions on smooth projective varieties with special emphasis on threefolds. I will start by recalling some important notions associated to derived categories of varieties and stability conditions. In particular, I will discuss about stability conditions on curves and surfaces. Then I will explain how the conjectural construction introduced by Bayer, Macri and Toda gives rise to stability conditions on some threefolds. END:VEVENT BEGIN:VEVENT DTSTART:20170712T160000 DTEND:20170712T173000 DTSTAMP:20170711T150000Z UID:e7357159efe38def111ea43545d1f0ee@cgp.ibs.re.kr SUMMARY:Stability conditions on derived categories of varieties II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hathurusinghege Dulip Bandara Piyaratne\n\nEvent: Seminar 2017\n\nAbstract: The aim of this series of talks is to discuss about Bridgeland stability conditions on smooth projective varieties with special emphasis on threefolds. I will start by recalling some important notions associated to derived categories of varieties and stability conditions. In particular, I will discuss about stability conditions on curves and surfaces. Then I will explain how the conjectural construction introduced by Bayer, Macri and Toda gives rise to stability conditions on some threefolds. END:VEVENT BEGIN:VEVENT DTSTART:20170714T160000 DTEND:20170714T173000 DTSTAMP:20170713T150000Z UID:e71666fb2dfe1e59b99c56d4abfd4411@cgp.ibs.re.kr SUMMARY:Stability conditions on derived categories of varieties III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hathurusinghege Dulip Bandara Piyaratne\n\nEvent: Seminar 2017\n\nAbstract: The aim of this series of talks is to discuss about Bridgeland stability conditions on smooth projective varieties with special emphasis on threefolds. I will start by recalling some important notions associated to derived categories of varieties and stability conditions. In particular, I will discuss about stability conditions on curves and surfaces. Then I will explain how the conjectural construction introduced by Bayer, Macri and Toda gives rise to stability conditions on some threefolds. END:VEVENT BEGIN:VEVENT DTSTART:20170731T100000 DTEND:20170731T110000 DTSTAMP:20170730T150000Z UID:0ed4eb64da64b2b1fc481a31f9c7ca03@cgp.ibs.re.kr SUMMARY:Stability of a polarized manifold and coercivity of the K-energy functional LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Tomoyuki Hisamoto\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: I would like to survey our joint work with S. Boucksom and M. Jonsson. We study the uniform K-stability condition for a polarized manifold. This stronger stability in fact holds for the Kähler-Einstein case and corresponds to the certain growth condition for Mabuchi's K-energy functional. END:VEVENT BEGIN:VEVENT DTSTART:20170731T111500 DTEND:20170731T121500 DTSTAMP:20170730T150000Z UID:b72ce6d63c2c2a6f088ef9a0f028fa06@cgp.ibs.re.kr SUMMARY:Pseudoconcavity of flag domains LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Jaehyun Hong\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: In this talk we investigate the Levi geometry of flag domains. A flag domain is pseudoconvex if and only if there is a nontrivial equivariant holomorphic map to a Hermitian symmetric space of noncompact type. It is conjectured that if a flag domain is not pseudoconvex, then it is pseudoconcave. We prove this conjecture by relating it to the ampleness of the normal bundle of the base cycle. This is joint work with A. Huckleberry and A. Seo. END:VEVENT BEGIN:VEVENT DTSTART:20170731T140000 DTEND:20170731T150000 DTSTAMP:20170730T150000Z UID:c0d5fea8c18cf88ff86e4837b05c0772@cgp.ibs.re.kr SUMMARY:Geodesics in the space of Kahler cone metrics and constant scalar curvature Kahler cone metrics LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Kai Zheng\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: We would present the construction and asymptotic analysis of geodesics in the space of Kahler metrics with cone singularities. As geometric application, we would also discuss recent progress in the constant scalar curvature Kahler metrics with cone singularities. END:VEVENT BEGIN:VEVENT DTSTART:20170731T153000 DTEND:20170731T163000 DTSTAMP:20170730T150000Z UID:6503c77571bf408485ba216855b1ff77@cgp.ibs.re.kr SUMMARY:The positive mass theorem on the three-dimensional CR manifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Pak Tung Ho\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: In this talk, I will try to explain the p-mass which is defined on the three-dimensional asymptotically flat pseudohermitian manifold, and the CR positive mass theorem proved by Cheng-Malchiodi-Yang.And I will talk about the proof of a conformal version of the CR positive mass theorem. END:VEVENT BEGIN:VEVENT DTSTART:20170801T100000 DTEND:20170801T110000 DTSTAMP:20170731T150000Z UID:0053e9d572e94f14f0328e7ecee6adca@cgp.ibs.re.kr SUMMARY:Periodic plane tropical curves and holomorphic curves on tori LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Takeo Nishinou\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: Tropical curves are combinatorial object satisfying certain harmonicity condition. They reflect properties of holomorphic curves, and a few precise correspondence is known between tropical curves in real affine spaces and holomorphic curves in toric varieties. A natural question is whether there is a correspondence between periodic tropical curves and holomorphic curves on complex tori. The two dimensional case can be solved in a satisfactory manner, but the situation is rather different from the non-periodic case. This is a joint work with Tony Yue Yu. END:VEVENT BEGIN:VEVENT DTSTART:20170801T111500 DTEND:20170801T121500 DTSTAMP:20170731T150000Z UID:c76d5f510ad37b94f21b905c76cc0e90@cgp.ibs.re.kr SUMMARY:Monotone Lagrangian tori in cotangent bundles LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: As an attempt to classify Lagrangian submanifolds and due to their importance in Floer theory, monotone Lagrangian tori have been got attention. In this talk, we provide a way producing monotone Lagrangian tori in the cotangent bundles of some manifolds including spheres and unitary groups. The construction is based on the classification of Lagrangian fibers of a certain completely integrable system on a partial flag manifold of various types. We then discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint works with Yunhyung Cho and Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20170801T140000 DTEND:20170801T150000 DTSTAMP:20170731T150000Z UID:6e42216e9f91cefd0375e5d4a3bb369e@cgp.ibs.re.kr SUMMARY:The extension problem of mean curvature flow in $R^3$ LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Haozhao Li\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: In this talk, I will show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in $R^3$. This is joint work with Bing Wang. END:VEVENT BEGIN:VEVENT DTSTART:20170801T153000 DTEND:20170801T163000 DTSTAMP:20170731T150000Z UID:ad55a37f0432716a394e34d7c632303b@cgp.ibs.re.kr SUMMARY:The extension of holomorphic functions on a non-pluriharmonic locus LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Yusaku Tiba\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: Hartogs extension theorem shows that there exists a subdomain such that any holomorphic function on the subdomain can be extended to the entire domain. This is one of the major difference between the theory of one and several complex variables. In this talk, we show a new extension theorem of holomorphic functions. Our main result is the following: Let $n\ge 4$ and let $\Omega$ be a bounded hyperconvex domain in $C^n$. Let $\phi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. Then any holomorphic function defined on a connected open neighborhood of the support of $(i\partial\dot\partial\phi)^{n-3}$ can be extended to the holomorphic functionon on $\Omega$. END:VEVENT BEGIN:VEVENT DTSTART:20170802T093000 DTEND:20170802T103000 DTSTAMP:20170801T150000Z UID:9082d9c6bd92ce20b28334376bce9962@cgp.ibs.re.kr SUMMARY:Barcodes and Hamiltonian diffeomorphisms LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Egor Shelukhin\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: We discuss applications of the theory of persistence modules to questions on Hamiltonian diffeomorphisms of closed symplectic manifolds. This talk is primarily based on joint works with Leonid Polterovich and Vukasin Stojisavljevic. END:VEVENT BEGIN:VEVENT DTSTART:20170802T104500 DTEND:20170802T114500 DTSTAMP:20170801T150000Z UID:2f5219cff46df3a872ced128af316b9d@cgp.ibs.re.kr SUMMARY:The wall-crossing formula and Lagrangian mutations LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Dmitry Tonkonog\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: The simplest open Gromov-Witten invariant is the Landau-Ginzburg superpotential of a monotone Lagrangian submanifold: it enumerates holomorphic Maslov index 2 disks. I will explain the general notion of mutation, a method of constructing new monotone Lagrangian submanifolds out of old ones, and the wall-crossing formula which relates their superpotentials. I will then talk about mutations of Lagrangian tori, in dimension 4 and higher. This is joint work with James Pascaleff. END:VEVENT BEGIN:VEVENT DTSTART:20170803T100000 DTEND:20170803T110000 DTSTAMP:20170802T150000Z UID:ccb62b8ec1808bd3535a03d2f8c0c22c@cgp.ibs.re.kr SUMMARY:Positivity of direct images of fiberwise Ricci-flat metrics on Calabi-Yau fibrations LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Young-Jun Choi\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: Let $p : X \to Y$ be a surjective holomorphic submersion between complex manifolds such that every fiber $X_y := p^{-1}(y)$ for $y \in Y$ , is a Calabi-Yau manifold, i.e., a compact Kahler manifold with trivial canonical line bundle. This is called a family of Calabi-Yau manifolds or a Calabi-Yau fibration. If $(X, \omega)$ is a Kahler manifold, then every fiber $X_y$ has a unique Ricci-flat Kahler metric whose associated Kahler form belongs to the fixed Kahler class $[\omega|]$ by Yau ‘s theorem. This family of Ricci-flat metrics induces the fiberwise Ricci-flat metric on a Calabi-Yau fibration.In this talk, we discuss positivity of direct images of fiberwise Ricci-flat metrics on the base $Y$. This positivity gives a lower bound of the fiberwise Ricci-flat metric on the total space $X$. END:VEVENT BEGIN:VEVENT DTSTART:20170803T111500 DTEND:20170803T121500 DTSTAMP:20170802T150000Z UID:e46aaaa6e9153a15b3652a8a7834ab87@cgp.ibs.re.kr SUMMARY:Bergman kernel and hyperconvexity index LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Bo-Yong Chen\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: It is well-known that the Bergman kernel is $L^2$. We prove that the Bergman kernel is $L^p$ for some $p > 2$ provided that the hyperconvexity index of the domain is positive. We also give an off-diagonal upper bound of the Bergman kernel in terms of the Monge-Ampere capacity. Various applications are given. END:VEVENT BEGIN:VEVENT DTSTART:20170803T140000 DTEND:20170803T152000 DTSTAMP:20170802T150000Z UID:7cb9fa7462404979408a7280ea2a8362@cgp.ibs.re.kr SUMMARY:Log geometric techniques for open invariants in mirror symmetry LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Nuromur Hulya Arguz\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: We will discuss an algebraic-geometric approach to the symplectic Fukaya category via log Gromov-Witten theory and tropical geometry. Our main object of study will be the degeneration of elliptic curves, namely the Tate curve. We will also discuss a construction of a split-generating set of real Lagrangians using log geometric techniques. This is joint work with Bernd Siebert, with general ideas based on discussions of Bernd Siebert and Mohammed Abouzaid. The symplectic aspects we will overview is joint work in progress with Dmitry Tonkonog. END:VEVENT BEGIN:VEVENT DTSTART:20170803T153000 DTEND:20170803T163000 DTSTAMP:20170802T150000Z UID:8ee98e8eefa6f364706291ace25736d1@cgp.ibs.re.kr SUMMARY:Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Bin Zhou\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: In this talk, we discuss the regularity of plurisubharmonic envelopes on compact Hermitian manifolds. We confirm a conjecture of Berman on the optimal $C^{1,1}$-regularity. The main ingredients are a priori estimates for a family of complex Monge-Ampere equations. We also present examples to show this regularity is sharp. It is a joint work with Jianchun Chu. END:VEVENT BEGIN:VEVENT DTSTART:20170804T093000 DTEND:20170804T103000 DTSTAMP:20170803T150000Z UID:ad238e08b4e9d31facd290d8893cf3dc@cgp.ibs.re.kr SUMMARY:Equidistribution of positive closed currents LOCATION:POSTECH Information Research Laboratories 122 DESCRIPTION:Speaker: Taeyong Ahn\n\nEvent: Pacific Rim Complex-Symplectic Geometry Conference\n\nAbstract: In this talk, we first discuss the asymptotic behavior of the inverse images of an analytic subset under a holomorphic endomorphisms of a complex manifold. Next, we discuss related equidistribution problems of positive closed currents of bidegree (p,p) with 1

2, with the condition d>2g-2, are induced by automorphisms of the curve. This is joint work with Indranil Biswas. END:VEVENT BEGIN:VEVENT DTSTART:20171101T140000 DTEND:20171101T180000 DTSTAMP:20171031T150000Z UID:6ca18cc5d5264ffc3a7c18286711d24b@cgp.ibs.re.kr SUMMARY:Free afternoon LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Free afternoon\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171102T100000 DTEND:20171102T110000 DTSTAMP:20171101T150000Z UID:eecf810d6d6981634e2f38e3cf457f84@cgp.ibs.re.kr SUMMARY:Constructions of EPW hyperkahler manifolds and their analogues LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Atanas Iliev\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: In the paper EPW cubes arXiv:1505.02389 (common with M. and G. Kapustka and K.Ranestad) we construct a complete family hyperkahler 6-folds - the double EPW cubes, which is a higher-dimensional analogue of the O'Grady's family of hyperkahler 4-folds - the double EPW sextics (or the double EPW squares). The two constructions are based on the existence of two symplectic vector bundles - respectively on the Grassmannian G(3,C^6) and on the projective space P(C^6) - both related to the symplectic vector space structure on \wedge^3 C^6. In this talk I will state in brief the two constructions (of EPW squares and of EPW cubes) from the point of view of some results from our earlier paper arXiv:0907.2781 with Laurent Manivel, and will discuss the question to describe analogues of the EPW manifolds for other symplectic vector bundles. END:VEVENT BEGIN:VEVENT DTSTART:20171102T111500 DTEND:20171102T121500 DTSTAMP:20171101T150000Z UID:f0eca80d96a178751d7f19e39f390f27@cgp.ibs.re.kr SUMMARY:Orbital degeneracy loci LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Laurent Manivel\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: Zero loci of sections of vector bundles, more generally, degeneracy loci of morphisms between vector bundles, are ubiquitous in algebraic geometry. Orbital degeneracy loci provide a vast generalization of those, modeled on orbits closures of algebraic groups in their linear representations. This is a very flexible tool, that allows in particular to construct new projective varieties with trivial canonical bundles. (Joint with V. Benedetti, S. Filippini, F. Tanturri.) END:VEVENT BEGIN:VEVENT DTSTART:20171103T111500 DTEND:20171103T121500 DTSTAMP:20171102T150000Z UID:b29f50e77cfa3b6b8778c63bdb47ffca@cgp.ibs.re.kr SUMMARY:Finite generation of the algebra of type A conformal blocks via birational geometry LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sang-Bum Yoo\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: We study birational geometry of the moduli space of parabolic bundles over a projective line, in the framework of Mori's program. We show that the moduli space is a Mori dream space. As a onsequence, we obtain the finite generation of the algebra of type A conformal blocks. Furthermore, we compute the H-representation of the effective cone which was previously obtained by Belkale. For each big divisor, the associated birational model is described in terms of moduli space of parabolic bundles. This is a joint work with Dr. Han-Bom Moon. END:VEVENT BEGIN:VEVENT DTSTART:20171102T153000 DTEND:20171102T180000 DTSTAMP:20171101T150000Z UID:67ad4d184db446fea62c83d96477f982@cgp.ibs.re.kr SUMMARY:Free discussion LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Free discussion\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171103T140000 DTEND:20171103T150000 DTSTAMP:20171102T150000Z UID:f42c9273882ea4dada6ad7d675ea7f6b@cgp.ibs.re.kr SUMMARY:Instantons and Nekrasov partition functions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jaeyoo Choy\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: For any compact simple Lie group of type A, B, C or D, the Hilbert series of the instanton space turns out to be the K-theoretic Nekrasov partition function proposed by Nekrasov-Shadchin. Using quiver descriptions, we also give the Hilbert series of moduli spaces of instantons invariant under subgroups of $SU(2)$ acting on the base $S^4$ and instantons over other base spaces, e.g. $S^1\times B^3$. END:VEVENT BEGIN:VEVENT DTSTART:20171102T140000 DTEND:20171102T150000 DTSTAMP:20171101T150000Z UID:64f599247177f05bbeb4a86a5966d596@cgp.ibs.re.kr SUMMARY:On Harder-Narasimhan stratifications of moduli stacks of coherent sheaves and of principal bundles LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Nitin Nitsure\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: We define a notion of relative Harder-Narasimhan filtrations and relative canonical parabolic reductions for families of coherent sheaves and of principal bundles on a projective variety. We show that this gives a stratification of the corresponding moduli stacks by locally closed substacks, which are the moduli stacks for sheaves or bundles of the given Harder-Narasimhan types. (This includes joint work with Sudarshan Gurjar). END:VEVENT BEGIN:VEVENT DTSTART:20171103T100000 DTEND:20171103T110000 DTSTAMP:20171102T150000Z UID:8709e7c7897d2113d1512455e57e7566@cgp.ibs.re.kr SUMMARY:aCM sheaves on multiple planes LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sukmoon Huh\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: Roughly speaking, an arithmetically Cohen-Macaulay sheaf on a projective scheme is a coherent sheaf without intermediate cohomology. There have been many works to show its existence and give its classification on various varieties. In this talk, we report our recent result on existence/classification of aCM sheaves on hyperplanes with multiplicity. We start from suggesting a conditional existence theorem of aCM vector bundle on any configuration of hyperplanes with multiplicities. Then we focus on the double plane. We show that any aCM vector bundle of rank two on the double plane splits, while this assertion is not extended to higher rank by a counterexample. Then we give the classification of aCM sheaves on the double plane up to rank 3/2. If time permits, we give a brief explanation about Ulrich sheaves on the double plane. This is a joint work with E. Ballico, F. Malaspina and J. Pons-Llopis. END:VEVENT BEGIN:VEVENT DTSTART:20171103T153000 DTEND:20171103T180000 DTSTAMP:20171102T150000Z UID:6bba5ed73fb9a89ab6ed417c9cc0838a@cgp.ibs.re.kr SUMMARY:Free discussion LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Free discussion\n\nEvent: Vector bundles on algebraic varieties\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171106T160000 DTEND:20171106T180000 DTSTAMP:20171105T150000Z UID:bd8ff9d6dc645b167de3a77254cfe7f2@cgp.ibs.re.kr SUMMARY:Lyusternik-Schnirelmann category and Localization Formula LOCATION:CGP Main Hall DESCRIPTION:Speaker: Marine Fontaine\n\nEvent: Seminar 2017\n\nAbstract: The LS-category of a topological space is a homotopical invariant, introduced originally in a course on the global calculus of variations by Lyusternik and Schnirelmann, to estimate the number of ritical points of a smooth function. When the topological space is a smooth manifold equipped with a proper smooth action of a Lie group, we give a localization formula to calculate the equivariant nalogue of this category in terms of the minimal orbit-type strata. The formula holds provided that the manifold admits a specific cover. We show that such a cover exists on every symplectic toric anifold. The known result stating that the LS-category of a symplectic toric manifold is equal to the number of fixed points of the torus action follows from our localization formula. END:VEVENT BEGIN:VEVENT DTSTART:20171108T160000 DTEND:20171108T180000 DTSTAMP:20171107T150000Z UID:ce30f7570060046da0dbc12d4b4218fb@cgp.ibs.re.kr SUMMARY:Asphericity, Eilenberg-MacLane spaces and periodic orbits in Hamiltonian dynamics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Ryuma Orita\n\nEvent: Seminar 2017\n\nAbstract: In the talk, we will deal with periodic orbits in Hamiltonian dynamics. Especially, we will show that if a Hamiltonian on a certain class of symplectic manifolds has a non-contractible orbit, then the Hamiltonian must have infinitely many non-contractible orbits. Here we note that if we don't stick to the existence of "non-contractible" orbits, then the Conley conjecture, which is proven for many symplectic manifolds, already implies the existence of infinitely many (not necessarily non-contractible) orbits. The proof uses the Floer homology and the Eilenberg-MacLane spaces. END:VEVENT BEGIN:VEVENT DTSTART:20171109T130000 DTEND:20171109T150000 DTSTAMP:20171108T150000Z UID:6e523f13819509a3ba939941a75675a7@cgp.ibs.re.kr SUMMARY:Wrapped floer homology and volume growth in the component of fibered twists LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joontae Kim\n\nEvent: CGP Seminar\n\nAbstract: Fibered twists are compactly supported symplectomorphisms that can be deﬁned on a Liouville domain whose boundary has a periodic Reeb ﬂow. We investigate an entropy-type invariant, called the slow volume growth, of the component of ﬁbered twists and give a uniform lower bound of the growth using wrapped Floer homology. We apply our results to ﬁbered twists coming from the Milnor ﬁbers of Ak-singularities and complements of a symplectic hypersurface in a real symplectic manifold. They admit so-called real Lagrangians, and we can explicitly compute wrapped Floer homology using a version of Morse-Bott spectral sequences. This is joint work with Myeonggi Kwon and Junyoung Lee. END:VEVENT BEGIN:VEVENT DTSTART:20171109T160000 DTEND:20171109T180000 DTSTAMP:20171108T150000Z UID:6bb00c4aa668c6d57adf28bf37fa727a@cgp.ibs.re.kr SUMMARY:On a Riemannian 4-manifold with a harmonic 2-form of constant length LOCATION:CGP Main Hall DESCRIPTION:Speaker: Inyoung Kim\n\nEvent: CGP Seminar\n\nAbstract: We consider a 4-dimensional Riemannian manifold (M, g) of positive sectional curvature which has a harmonic 2-form of constant length. W. Seaman proved that the intersection form of such a manifold is definite. By relating with an almost-kahler structure, we show that M is diffeomorphic of CP2. We discuss the existence of such metrics near the Fubini-Study metric on CP2 and give examples of conditions which can be added further in order to get the Fubini-Study metric on CP2 up to diffeomorphisms and rescaling. END:VEVENT BEGIN:VEVENT DTSTART:20171113T160000 DTEND:20171113T180000 DTSTAMP:20171112T150000Z UID:4ec433193266a4fab4dc4c91cd49f81d@cgp.ibs.re.kr SUMMARY:Classification results on fixed points of symplectic and Hamiltonian circle actions LOCATION:CGP Main Hall DESCRIPTION:Speaker: Donghoon Jang\n\nEvent: Seminar 2017\n\nAbstract: During this talk, we discuss classification results on symplectic and Hamiltonian circle actions, when there are fixed points. First, we begin with small numbers of fixed points. Second, we begin with low dimensions. Third, we discuss under which conditions a symplectic action with a fixed point must be Hamiltonian. END:VEVENT BEGIN:VEVENT DTSTART:20171218T143000 DTEND:20171218T153000 DTSTAMP:20171217T150000Z UID:703918073fa81da8eb8c79f6ea17e967@cgp.ibs.re.kr SUMMARY:Some topics on birational geometry in positive characteristic LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yifei Chen\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will introduce my observations of birational geometry in positive characteristic, including subadditivity of Kodaira dimension, canonical bundle formula and semi-positivity based on my joint work with Caucher Birkar, Lei Zhang and Yi Gu. END:VEVENT BEGIN:VEVENT DTSTART:20171219T160000 DTEND:20171219T170000 DTSTAMP:20171218T150000Z UID:62015e55104f6feac6f94a31c14615fc@cgp.ibs.re.kr SUMMARY:Geometric Rieman Roch for categories LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ludmil Katzarkov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: We will introduce a noncommutative version of Gromov Whitten invariants.Applications will be considered. END:VEVENT BEGIN:VEVENT DTSTART:20171221T160000 DTEND:20171221T170000 DTSTAMP:20171220T150000Z UID:9a742d1b3e6039b16287131386923b69@cgp.ibs.re.kr SUMMARY:Stability over rings and good models of del Pezzo fibrations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Igor Krylov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: This talk is motivated by the following problem, given a three-dimensional Mori fiber space, can we find a birational to it model with nice singularities? Sarkisov proved that for a cubic bundles there exists a smooth model. For del Pezzo fibrations smooth model may not exist in case degree <4. Corti has shown that there are Gorenstein (resp. 2-Gorenstein) models for del Pezzo fibrations of degree 3 (resp. 2). He proved it by constructing explicit birational maps improving singularities. Kollar improved his result in degree 3 using GIT. I discuss what are the issues in adapting Kollar's approach for degrees 1 and 2 and how to work around them. END:VEVENT BEGIN:VEVENT DTSTART:20171220T113000 DTEND:20171220T123000 DTSTAMP:20171219T150000Z UID:bf72c6d3fee65aa1b2bb1f5eab50cb8d@cgp.ibs.re.kr SUMMARY:Finite collineation groups and birationally rigidity LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will report on my recent work with Shramov on equivariant birational geometry of the projective space. END:VEVENT BEGIN:VEVENT DTSTART:20171220T143000 DTEND:20171220T153000 DTSTAMP:20171219T150000Z UID:c7c06863eea97c06e2b3f34f250845c2@cgp.ibs.re.kr SUMMARY:Compactification of the moduli space of certain K3 surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jesus Martinez Garcia\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: We study the moduli space of K3 surfaces obtained as minimal resolutions of double covers of the plane branched at the union of a quartic curve and two distinct lines. We construct and describe such a compactification using Geometric Invariant Theory. Then, we show that our compactification is isomorphic to the Baily-Borel compactification of the arithmetic quotient of the period domain of such K3 surfaces by certain arithmetic group. END:VEVENT BEGIN:VEVENT DTSTART:20171220T100000 DTEND:20171220T110000 DTSTAMP:20171219T150000Z UID:f6b884e77eb26e025981c0cf973cfaef@cgp.ibs.re.kr SUMMARY:Degenerations of del Pezzo surfaces in Q-Gorenstein families LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I am going to discuss log canonical surface singularities admitting smoothings in Q-Gorenstein families. As an application I present the classification of log canonical surfaces of Picard rank 1 which are Q-Gorenstein degenerations of smooth del Pezzo. END:VEVENT BEGIN:VEVENT DTSTART:20171220T160000 DTEND:20171220T170000 DTSTAMP:20171219T150000Z UID:1631576d16b4246db83be52c7c7a5e47@cgp.ibs.re.kr SUMMARY:Some properties of (almost) invertible rational maps LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ilya Karzhemanov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will present, old and new, families of rational self-maps of Pn, including surjective ones and those arising from homaloidal polynomials. I will discuss some, old and new, properties of these maps. END:VEVENT BEGIN:VEVENT DTSTART:20171116T160000 DTEND:20171116T180000 DTSTAMP:20171115T150000Z UID:f6de8b55bf202a58e3b0e6753ead07ea@cgp.ibs.re.kr SUMMARY:Cubical categories and nerve functors LOCATION:CGP Main Hall DESCRIPTION:Speaker: Brice Le Grignou\n\nEvent: CGP Seminar\n\nAbstract: This talk will deal with enriched categories. I will first described categories enriched in cubical sets (cubical categories). They form a model for infinity-categories as well as simplicial categories. However, they are much more easily linked to other kinds of enriched categories. Moreover, every known nerve functor from some kind of enriched categories to simplicial sets factorises through cubical categories. Then, we will described differential graded categories where the tools used in the cubical case have an interpretation in terms of A-infinity categories. END:VEVENT BEGIN:VEVENT DTSTART:20171114T160000 DTEND:20171114T180000 DTSTAMP:20171113T150000Z UID:4d7a80111193530d9da2381feea0aeff@cgp.ibs.re.kr SUMMARY:Conformally related Riemannian metrics with non-generic holonomy LOCATION:CGP Main Hall DESCRIPTION:Speaker: Andrei Moroianu\n\nEvent: Seminar 2017\n\nAbstract: We classify compact connected $n$-dimensional manifold $M$ has a conformal class containing two non-homothetic metrics $g$ and $\tilde g=e^{2f}g$ with non-generic holonomy. The proof is based on a new result concerning conformally product mectrics, and on several previous results like the classification of locally conformally Kähler manifolds with special holonomy (with F. Madani and M. Pilca), and the study of conformal Killing forms on manifolds with special holonomy (with F. Belgun and U. Semmelmann). END:VEVENT BEGIN:VEVENT DTSTART:20171107T130000 DTEND:20171107T150000 DTSTAMP:20171106T150000Z UID:612ee21979e14e41f36dada0cf3e89e5@cgp.ibs.re.kr SUMMARY:Homotopy algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Christophe Wacheux\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20171121T163000 DTEND:20171121T180000 DTSTAMP:20171120T150000Z UID:a571cea57537ef8733b5219fc0a97aef@cgp.ibs.re.kr SUMMARY:Aspects of twisted and differential refinements of K-theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byungdo Park\n\nEvent: Seminar 2017\n\nAbstract: Differential generalized cohomology is a construction on a smooth manifold combining topological and differential geometric data of a manifold in a homotopy theoretic way. It has interesting applications in Wess-Zumino-Witten terms, geometric string structures, study of conformal immersions, and classifications of Ramond-Ramond fields in string theory to list a few. In this talk, we shall focus on differential refinements of complex K-theory and give a construction of a twisted refinement of differential K-theory using Cech-type model of twisted K-theory. END:VEVENT BEGIN:VEVENT DTSTART:20171114T130000 DTEND:20171114T150000 DTSTAMP:20171113T150000Z UID:f4ab0abcf9405a4b7bcc65632c7fc1df@cgp.ibs.re.kr SUMMARY:Homotopy algebras II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Christophe Wacheux\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20171121T130000 DTEND:20171121T150000 DTSTAMP:20171120T150000Z UID:eb95a152d44730f5d6a181d7cad95376@cgp.ibs.re.kr SUMMARY:Model structure of DG-algebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Weonmo Lee\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20171208T093000 DTEND:20171208T120000 DTSTAMP:20171207T150000Z UID:855911b7114de0fc35069ae362ee8967@cgp.ibs.re.kr SUMMARY:Townhall Meeting (CGP Members only) LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Townhall Meeting\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171208T140000 DTEND:20171208T144500 DTSTAMP:20171207T150000Z UID:148bb44efd22a0203f4d0b6c79fc7341@cgp.ibs.re.kr SUMMARY:Monotone Lagrangians in flag varieties LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: According to the recent work by Cho-Kim- Oh, a Gelfand-Cetlin system on a partial flag manifold $X$ always admits infinitely many non-torus Lagrangian fibers unless $X$ is a projective space. In this talk, we classify all monotone Lagrangian Gelfand-Cetlin fibers. A key ingredient will bea certain Maslov index formula for a holomorphic disc bounded by an$S^1$ - invariant Lagrangian having constant energy in a Hamiltonian $S^1$-space. END:VEVENT BEGIN:VEVENT DTSTART:20171208T150000 DTEND:20171208T154500 DTSTAMP:20171207T150000Z UID:5e338ef9e544f345223d5a41f226465b@cgp.ibs.re.kr SUMMARY:Convexity of the base space of almost-toric Lagrangian fibration LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Christophe Wacheux\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: On a symplectic manifold $(M^{2n},\omega)$, toric systems are integrable Hamiltonian systems whose time-1 flow yields a $T^n$-action. The Atiyah - Guillemin & Sternberg theorem [Ati82], [GS82], [GS84] uses the affine structure of the base space of the associated Lagrangian fibration to prove that the image the moment map is a convex polytope in $\mathbb{R}^n$.In almost-toric systems, one allows so-called focus-focus singularities to occur, which in turn destroys some of the $S^1$-actions. For these almost-toric systems, the affine structure becomes singular and the image of the moment map is not a convex polytope of Rn in general. We will discuss the notion of intrinsic convexity of the base space with respect to its (singular) affine structure and give local and global convexity results for the base space, as well as counter-examples.This is a joint project with Tudor Ratiu and Nguyen Tien Zung.References[Ati82] M.F. Atiyah. Convexity and commuting Hamiltonians. Bulletin of the London Mathematical Society 14 (1982), no. 1, 1–15.[GS82] V. Guillemin and S. Sternberg. Convexity properties of the moment mapping. Inventiones Mathematicae 67 (1982), 491–513, doi:10.1007/BF01398933.[GS84] V. Guillemin and S. Sternberg. Convexity properties of the moment mapping. ii. Inventiones Mathematicae 77 (1984), 533–546, doi:10.1007/BF01388837. END:VEVENT BEGIN:VEVENT DTSTART:20171208T161500 DTEND:20171208T170000 DTSTAMP:20171207T150000Z UID:b65bfe162cc9a3adf4b0679b2b98f2b2@cgp.ibs.re.kr SUMMARY:Euclidean quantum gravity and applications of instantons LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Dong-Han Yeom\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: In this presentation, I would like to briefly review topics in Euclidean quantum gravity and applications of instantons. First, I comment on the framework of Euclidean path-integral approach. This path-integral will be approximated by instantons. Second, I show several important examples of instantons, including `the creation ofthe universe from nothing', `a bubble nucleation', `Hawking radiation', and `the Bekenstein-Hawking entropy'. END:VEVENT BEGIN:VEVENT DTSTART:20171209T100000 DTEND:20171209T104500 DTSTAMP:20171208T150000Z UID:5704f17d43460b569fe1cec42f4d3cf5@cgp.ibs.re.kr SUMMARY:BV algebras and the inverse value of the modular j-function LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Jeehoon Park\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: Jae-Suk Park and the speaker attached a BV(Battalion-Vilkovisky) algebra toa smooth projective hypersurface $X$, whose cohomology is the primitive middle dimensional cohomology of $X$.Then Yesule Kim and the speaker developed a deformation theory for the period matrices of $X$based on the BV algebra structure. The goal of this talk is to apply this deformation idea to the elliptic curves and the modular $j$-invarint to get an explicit algorithm to compute the inverse value of the modular $j$-function. The modular $j$-invariant is a modular function of weight 0, which plays an important role in many areas of number theory. This is a joint work with Kwanghyun Kim and Yesule Kim. END:VEVENT BEGIN:VEVENT DTSTART:20171209T111500 DTEND:20171209T120000 DTSTAMP:20171208T150000Z UID:3737b30f2f3b1596ad6df82182e02ea2@cgp.ibs.re.kr SUMMARY:Modular curves, Hecke operators and their actions LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Taekyung Kim\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: The modular curve $X_0(N)$ is the coarse moduli scheme parametrizing the elliptic curves together with cyclic subgroups of order $N$ contained in the curve. In order to study the arithmetic of $X_0(N)$, we embed the curve into $J_0(N)$, the Jacobian of the curve $X_0(N)$. Hecke operators are certain endomorphisms of $J_0(N)$. We are interested in the actions of Hecke operators on reductions of $J_0(N)$ modulo various primes. In this talk, I will introduce these concepts more deeply. More specifically, I will pay much attention to the Deligne--Rapoport model of the reduction of $J_0(N)$ modulo $p$, i.e., the special fibre $J_0(N)_p$ over $p$ of the Néron model of $J_0(N)$ where $p$ exactly divides $N$. After giving some previous result about the Hecke action of the component group of $J_0(N)_p$, I will also explain our recent result studied jointly with Dr. Hwajong Yoo. END:VEVENT BEGIN:VEVENT DTSTART:20171209T140000 DTEND:20171209T144500 DTSTAMP:20171208T150000Z UID:30b8b4d08e8801b0760539f0e9e7add8@cgp.ibs.re.kr SUMMARY:Slicing knots and gropes in 4-space LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Taehee Kim\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: A knot is a smooth simple closed curve in 3-space. A knot bounding a disk in 4-space is called a sliceknot, and slice knots play a key role in classifying topological 4-manifolds. We can measure how close a knot is to being slice using gropes in 4-space, which are certain 2-complexesobtained by stacking up surfaces with a single boundary component. In this talk, I will give a brief review of thissubject and talk about distinguishing knots using gropes in 4-space. END:VEVENT BEGIN:VEVENT DTSTART:20171209T150000 DTEND:20171209T154500 DTSTAMP:20171208T150000Z UID:5a9fb6e49b40af7c4f043fdbda3a81f9@cgp.ibs.re.kr SUMMARY:Volumes of hyperbolic manifolds LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: BoGwang Jeon\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: In this talk, I will give an general overview about the volumes of hyperbolic manifolds.Some fundamental results and properties of them will be discussed, and I will alsomention about several conjectures and their connections with other areas ofmathematics. END:VEVENT BEGIN:VEVENT DTSTART:20171209T161500 DTEND:20171209T170000 DTSTAMP:20171208T150000Z UID:9d3aef78e886b404dce23c0ba80bd7c7@cgp.ibs.re.kr SUMMARY:New Horizons in Asia Pacific Physics Community LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Woo-Sung Jung\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: Asia-Pacific Center for Theoretical Physics (APCTP), which was established in 1996 to be a leader in world physics research, to facilitate international collaboration, and to train young scientists in the Asia-Pacific region. The Center was relocated to the POSTECH campus in 2001. We celebrated the Center’s 21st anniversary with 16 member countries this year.The Center now runs numerous research programs: Junior Research Group (JRG), which promotes young scientists in leadership roles; Young Scientist Training, which provides post-doctoral positions; and the Visitors Program, which allows short and long-term visits of researchers from across the Asia-Pacific region. END:VEVENT BEGIN:VEVENT DTSTART:20171210T100000 DTEND:20171210T104500 DTSTAMP:20171209T150000Z UID:0261e82d6469e87402a0ddbc55c1aa0d@cgp.ibs.re.kr SUMMARY:On the Bishop-Phelps-Bollobás type theorems LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Sheldon Miriel Gil Dantas\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: In 1970, Bollobás proved that whenever$$|x^*(x)|>1-\frac{\epsilon^2}4,$$where $x^*$ is a norm-one functional and $x$ is a norm-one vector, there are a new norm-onefunctional $y^*$ and a new norm-one vector $y \in S_X$ satisfying the following$$|y^*(y)|=1,\quad \|y − x\| < \epsilon\quad \text{and}\quad \|y^*− x^*\| < \epsilon.$$This shows, in particular, the Bishop-Phelps theorem which says that the functionals thatattain their norms is dense in $X^∗$. Lindenstrauss showed that Bollobás' result is no longertrue for bounded linear operators and for that reason Acosta, Aron, García and Maestreintroduced the Bishop-Phelps-Bollobás property (the BPBp, for short) in order to getBollobás type theorems for operators.In this talk is we present the Bishop-Phelps-Bollobás property in different contexts.We give a historical resume with a motivation behind this property and very recent resultson this topic. END:VEVENT BEGIN:VEVENT DTSTART:20171210T111500 DTEND:20171210T120000 DTSTAMP:20171209T150000Z UID:c8fbb0505daf2e2d1331d002ba40d499@cgp.ibs.re.kr SUMMARY:Recurrence and ergodic averages LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Younghwan Son\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: In this talk we will discuss connection between recurrence in dynamical systems, the limiting behavior of ergodic averages and arithmetic structures in densely large integer sets. In particular we will present Furstenberg's ergodic approach to Szemeredi's theorem and its generalizations. END:VEVENT BEGIN:VEVENT DTSTART:20171209T104500 DTEND:20171209T111500 DTSTAMP:20171208T150000Z UID:f293de1cc6b3404d024daf195ee0fc18@cgp.ibs.re.kr SUMMARY:Coffee Break LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Coffee Break\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171210T104500 DTEND:20171210T111500 DTSTAMP:20171209T150000Z UID:f1975aec2c6b8f7e177c642e6dd64b94@cgp.ibs.re.kr SUMMARY:Coffee Break LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Coffee Break\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171208T154500 DTEND:20171208T161500 DTSTAMP:20171207T150000Z UID:6ef632ca0b564ee86fb924630e80ac9e@cgp.ibs.re.kr SUMMARY:Coffee Break LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Coffee Break\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171209T154500 DTEND:20171209T161500 DTSTAMP:20171208T150000Z UID:1d20eba78610f1876649ef0172849645@cgp.ibs.re.kr SUMMARY:Coffee Break LOCATION:RAMADA Hotel, Jeonju DESCRIPTION:Speaker: Coffee Break\n\nEvent: 2017 Pohang Mathematics Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20171128T160000 DTEND:20171128T180000 DTSTAMP:20171127T150000Z UID:35bcaa6bade49499beece6829e4d555f@cgp.ibs.re.kr SUMMARY:Newton-Okounkov Bodies of Bott-Samelson Varieties, and Beyond LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Seminar 2017\n\nAbstract: Let $G$ be a simply-connected semisimple algebraic group over $\mathbb{C}$. A Bott-Samelson variety $Z$ is an iterated sequence of $\mathbb{C} P^1$-bundles which has an action of the Borel subgroup $B\subset G$. For a given holomorphic line bundle $\mathcal L$ over $Z$, the set of holomorphic sections $H^0(Z,\mathcal L)$ is a $B$-module, called a generalized Demazure module. This gives a fruitful connection between representation theory and algebraic geometry: a character formula of $B$-modules, the standard monomial theory, and moreover the theory of Newton-Okounkov bodies. In this talk, we give an overview of this connection, especially, the theory of Newton-Okounkov bodies. And we introduce flag Bott-Samelson variety, which is a generalization of both Bott-Samelson variety and full flag variety. Furthermore we study Newton-Okounkov bodies of flag Bott-Samelson varieties. This talk is based on an on-going project with Naoki Fujita and Dong Youp Suh. END:VEVENT BEGIN:VEVENT DTSTART:20171128T130000 DTEND:20171128T150000 DTSTAMP:20171127T150000Z UID:a48a6216cf16751a24ea83e96d589f35@cgp.ibs.re.kr SUMMARY:The Bar adjunction LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20171204T160000 DTEND:20171204T180000 DTSTAMP:20171203T150000Z UID:192b68a56e0f361e652ab6f1feee703d@cgp.ibs.re.kr SUMMARY:Moduli of second fundamental forms of a nonsingular intersection of two quadrics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yewon Jeong\n\nEvent: Seminar 2017\n\nAbstract: In 1979, Griffiths and Harris raised a question on the moduli of second fundamental forms of a projective complex submanifold of codimension two. We will report on our study of the question for complete intersections of two quadrics. END:VEVENT BEGIN:VEVENT DTSTART:20171211T160000 DTEND:20171211T180000 DTSTAMP:20171210T150000Z UID:d3a7e7cfa56813740977674afd3a3a19@cgp.ibs.re.kr SUMMARY:Cauchy problems in modern collisional kinetic theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The goal of this lecture series is to provide the audience with an introduction to the modern mathematical theory of collision processes in gases and plasmas as a branch of kinetic theory. We will start with discussing the varied Cauchy problems for the Boltzmann and Landau equations. We will also consider Boltzmann's celebrated H-theorem and entropy dissipation whose roles are crucial for the discussion of the trend to equlibrium. The last lecture bears on the brief introduction to the relativistic Boltzmann equation, which is a relativistic variant for the description of relativistic hydrodynamics. A relativistic analogue of the cancellation lemma for the classical Boltzmann collision operator will also be given during the last lecture. END:VEVENT BEGIN:VEVENT DTSTART:20171213T160000 DTEND:20171213T180000 DTSTAMP:20171212T150000Z UID:5dab4a66ccccf7909d1db4058b27cc6a@cgp.ibs.re.kr SUMMARY:Boltzmann H-theorem and entropy dissipation LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The goal of this lecture series is to provide the audience with an introduction to the modern mathematical theory of collision processes in gases and plasmas as a branch of kinetic theory. We will start with discussing the varied Cauchy problems for the Boltzmann and Landau equations. We will also consider Boltzmann's celebrated H-theorem and entropy dissipation whose roles are crucial for the discussion of the trend to equlibrium. The last lecture bears on the brief introduction to the relativistic Boltzmann equation, which is a relativistic variant for the description of relativistic hydrodynamics. A relativistic analogue of the cancellation lemma for the classical Boltzmann collision operator will also be given during the last lecture. END:VEVENT BEGIN:VEVENT DTSTART:20171215T160000 DTEND:20171215T180000 DTSTAMP:20171214T150000Z UID:7890e2c485c27e54df4877336a8fb735@cgp.ibs.re.kr SUMMARY:The relativistic Boltzmann equation and a cancellation lemma LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The goal of this lecture series is to provide the audience with an introduction to the modern mathematical theory of collision processes in gases and plasmas as a branch of kinetic theory. We will start with discussing the varied Cauchy problems for the Boltzmann and Landau equations. We will also consider Boltzmann's celebrated H-theorem and entropy dissipation whose roles are crucial for the discussion of the trend to equlibrium. The last lecture bears on the brief introduction to the relativistic Boltzmann equation, which is a relativistic variant for the description of relativistic hydrodynamics. A relativistic analogue of the cancellation lemma for the classical Boltzmann collision operator will also be given during the last lecture. END:VEVENT BEGIN:VEVENT DTSTART:20171201T151500 DTEND:20171201T161500 DTSTAMP:20171130T150000Z UID:bbb1b71b114a8bbaa5d17ba71a6499db@cgp.ibs.re.kr SUMMARY:Prounipotent Fundamental Affine DG Group Scheme of a Space and Its Quantization LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jae-Suk Park\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: Singular cohomology of a path connected, based and finite type space X with the rational coefficient has a structure of homotopy commutative algebra such that the rational homotopy equivalence of spaces induces quasi-isomorphism of the algebras. For any homotopy commutative algebra over a field k of characteristic zero, I will construct a representable functor from the homotopy category of dg commutative algebras over k to the category of groups (an affine dg group scheme) such that a quasi-isomorphism of homotopy commutative algebras is a natural isomorphism of the functors. These construction lead to a definition of pro-unipotent affine dg group scheme $G_X$ of X, such that $G_X(C)$ is isomorphic to the pro-unipotent fundamental group of X, as well as a higher homotopy generalization of Chen-Sullivan $\pi_1$ de Rham theorem. A program of quantization of $G_X$ will be sketched, whose starting point is deformation quantization of a homotopy commutative algebra over k to a topologically free homotopy associative algebra over k[[h]]. Such a quantization may lead to a construction of Frobenius manifold structure on the C-rational homotopy group of symplectic manifold. END:VEVENT BEGIN:VEVENT DTSTART:20171201T163000 DTEND:20171201T173000 DTSTAMP:20171130T150000Z UID:186a584c457a7df0c9427a15c936e209@cgp.ibs.re.kr SUMMARY:Mori’s program of the moduli space of parabolic bundles over a projective line LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sang-Bum Yoo\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: We study birational geometry of the moduli space of parabolic bundles over a projective line,in the framework of Mori’s program. We show that the moduli space is a Mori dream space. As aconsequence, we obtain the finite generation of the algebra of type A conformal blocks. Furthermore,we compute the H-representation of the effective cone which was previously obtained by Belkale. Foreach big divisor, the associated birational model is described in terms of moduli space of parabolicbundles. In this talk, we focus on the H-representation of the effective cone and descriptions ofbirational models of the moduli space. This is a joint work with Dr. Han-Bom Moon. END:VEVENT BEGIN:VEVENT DTSTART:20171202T110000 DTEND:20171202T120000 DTSTAMP:20171201T150000Z UID:ac9e5b5cd399e4fbf020a4cfc4db7b86@cgp.ibs.re.kr SUMMARY:Toward a GIT construction for a moduli space of commuting nilpotents LOCATION:CGP Main Hall DESCRIPTION:Speaker: Donghoon Hyeon\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: I will describe how a moduli space of commuting nilpotents may be constructed via GIT and how non-reductive GIT can make things much simpler. END:VEVENT BEGIN:VEVENT DTSTART:20171202T140000 DTEND:20171202T150000 DTSTAMP:20171201T150000Z UID:5656bd9e972b637ebe175189d3bcb2b9@cgp.ibs.re.kr SUMMARY:Virtual cycles via two-periodic localized Chern characters LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bumsig Kim\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: The localized Chern character of a bounded complex of vector bundles is a bivariant classdefined by Baum, Fulton, and MacPherson. They used such classes to prove a general Riemann-Roch theorem for singular varieties. For a two-periodic complex of vector bundles, Polishchuk andVaintrob have constructed its localized Chern character, which is a generalization of the usual one.We discuss some properties of PV’s localized Chern characters. In particular, the cosectionlocalization defined by Kiem and Li can be expressed as a localized Chern character operation. Thisresult is a generalization of the related work by Chang, Li, and Li. The talk is based on joint work withJeongseok Oh. END:VEVENT BEGIN:VEVENT DTSTART:20171202T151500 DTEND:20171202T161500 DTSTAMP:20171201T150000Z UID:88f8f53f7451d568d9af1ce591518679@cgp.ibs.re.kr SUMMARY:Fano contact manifolds and contact prolongations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun-Muk Hwang\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: It has been conjectured that a Fano manifold with a contact structure is homogeneous. Oneapproach to this conjecture is by studying the varieties of minimal rational tangents of contact lines onsuch a Fano manifold. We introduce a new ingredient in this approach using the notion of contactprolongations from the theory of contact G-structures. By characterizing subadjoint varieties in termsof contact prolongations, we prove that a Fano contact manifold is homogeneous if its varieties ofminimal rational tangents form a locally trivial fibration outside a set of codimension 2. END:VEVENT BEGIN:VEVENT DTSTART:20171202T163000 DTEND:20171202T173000 DTSTAMP:20171201T150000Z UID:4bdeb3c8a43e38858a9065f5f5b20f1f@cgp.ibs.re.kr SUMMARY:Equations of a fake projective plane LOCATION:CGP Main Hall DESCRIPTION:Speaker: JongHae Keum\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: We present explicit equations of a fake projective plane in ite bicanonical embedding in $P^9$. This is a joint work with Lev Borisov. END:VEVENT BEGIN:VEVENT DTSTART:20171202T174500 DTEND:20171202T181500 DTSTAMP:20171201T150000Z UID:8ec99fab8962e05cc711f714633073d5@cgp.ibs.re.kr SUMMARY:TBA LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jaeyoo Choy\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20171203T110000 DTEND:20171203T120000 DTSTAMP:20171202T150000Z UID:3c094d4ca35bb329e85f4556ad4b74c9@cgp.ibs.re.kr SUMMARY:$O_X$ regularity for smooth case and singular case. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sijong Kwak\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: In this talk, we explain why $O_X$ regularity conjecture is true for smooth case and why it isnot true in the singular case. For the smooth case, the semi ampleness of the double point divisorinduced by general inner projection is important and we can compute it for scroll cases. On the otherhand, for the singular case, there are counterexamples for the $O_X$ regularity conjecture. We explainthese for threefolds in $P^5$. END:VEVENT BEGIN:VEVENT DTSTART:20171203T094500 DTEND:20171203T104500 DTSTAMP:20171202T150000Z UID:4bac49c5ad4083f340b3a6cfaa77f18b@cgp.ibs.re.kr SUMMARY:Moduli of sheaves on del Pezzo surface LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinwon Choi\n\nEvent: The 3rd Yeongnam workshop on algebraic geometry\n\nAbstract: We explore the geometry of the moduli spaces of one-dimensional sheaves, which is closelyrelated to the curve-counting invariants. We propose a new integer invariant defined from the logCalabi-Yau geometry of the surface with a smooth anticanonical divisor. We study their conjecturalrelationship to the moduli of sheaves and the BPS invariants. This talk is based on joint work withMichel van Garrel, Sheldon Katz and Nobuyoshi Takahashi. END:VEVENT BEGIN:VEVENT DTSTART:20171214T160000 DTEND:20171214T180000 DTSTAMP:20171213T150000Z UID:066e069a6b8b5ea0278a81d6e2eceb2f@cgp.ibs.re.kr SUMMARY:Openness results for uniform K-stability LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kento Fujita\n\nEvent: CGP Seminar\n\nAbstract: It is expected that several "openness" results holds for uniform K-stability of polarized varieties. In this talk, I will discuss certain partial results for this problem. END:VEVENT BEGIN:VEVENT DTSTART:20171205T160000 DTEND:20171205T180000 DTSTAMP:20171204T150000Z UID:53e22c1c3521f46adcf49f112d1774ca@cgp.ibs.re.kr SUMMARY:Curves, sheaves, and cycles on K3 surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Qizheng Yin\n\nEvent: Seminar 2017\n\nAbstract: The story begins with the pioneer work of Beauville and Voisin, who showed remarkable properties of algebraic cycles on K3 surfaces. In my talks I will recall the Beauville-Voisin theorem, and discuss generalizations in two different directions. One concerns cycles on families of K3 surfaces. Ideas and techniques from Gromov-Witten theory are applied to this setting, which eventually lead to the solution of the Marian-Oprea-Pandharipande conjecture on the tautological ring of the moduli spaces of K3 surfaces. The other connects curves and sheaves on K3 surfaces, bringing together the derived categories of K3 surfaces, cycles on K3 surfaces, and cycles on the moduli spaces of objects in the derived categories. Results in this direction include the proof of O’Grady’s conjecture, and applications to the Beauville-Voisin conjecture on the cycle ring of holomorphic symplectic varieties. The talks are based on joint work with Rahul Pandharipande, Junliang Shen, and Xiaolei Zhao. END:VEVENT BEGIN:VEVENT DTSTART:20171214T130000 DTEND:20171214T150000 DTSTAMP:20171213T150000Z UID:d3b05cd287d9a347df59ba763dbdc610@cgp.ibs.re.kr SUMMARY:Bihamiltonian Structures of Evolutionary PDEs and their Classification LOCATION:CGP Main Hall DESCRIPTION:Speaker: Si-Qi Liu\n\nEvent: CGP Seminar\n\nAbstract: The classificatioin problem of evolutionary PDEs that possess bihamiltonian structures play an important role in modern mathematical physics. In this talk, I will introduce our results on this problem, including the quasi-triviality theorem, the uniqueness theorem, and the existence theorem (proved by Carlet, Posthuma, and Shadrin). I will also talk about some open problems. END:VEVENT BEGIN:VEVENT DTSTART:20171212T160000 DTEND:20171212T180000 DTSTAMP:20171211T150000Z UID:5514ac92075684c63f57725cb518c94e@cgp.ibs.re.kr SUMMARY:1. Derived equivalence and Grothendieck ring of varieties 2. Projective reconstruction in algebraic vision LOCATION:CGP Main Hall DESCRIPTION:Speaker: Makoto Miura\n\nEvent: Seminar 2017\n\nAbstract: I would like to include two kinds of talks on different subject.In the first half, I will talk on some examples of Calabi--Yau manifolds in (generalized) Grassmannians. Through these examples, we will be led to one naive problem on a relationship between derived equivalence of varieties and the Grothendieck ring of varieties. This talk is mainly based on a joint work with Atsushi Ito, Shinnosuke Okawa and Kazushi Ueda.In the second half, our topic is somehow closer to an application of algebraic geometry. I will give an overview on the connection between multi-view geometry in computer vision and algebraic geometry, and introduce recent developments of them. This talk is based on a joint work with Atsushi Ito and Kazushi Ueda. END:VEVENT BEGIN:VEVENT DTSTART:20171222T100000 DTEND:20171222T110000 DTSTAMP:20171221T150000Z UID:e12a8ded1694f7a68fe867c7fdd2cb0d@cgp.ibs.re.kr SUMMARY:On function fields of general hypersurface sections of Fano 3-folds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yongnam Lee\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will present on my recent work with Gian Pietro Pirola on dominant rational maps from generalhypersurface sections of Fano 3-folds. END:VEVENT BEGIN:VEVENT DTSTART:20171219T100000 DTEND:20171219T110000 DTSTAMP:20171218T150000Z UID:515a0690218f241bb08fb7357de59187@cgp.ibs.re.kr SUMMARY:ADE moduli of surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Valery Alexeev\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: In a joint work with Alan Thompson, we construct compact moduli spaces corresponding to the ADEroot lattices. END:VEVENT BEGIN:VEVENT DTSTART:20171221T100000 DTEND:20171221T110000 DTSTAMP:20171220T150000Z UID:45214a05d0b0abc72ba87a482b372586@cgp.ibs.re.kr SUMMARY:Recognizing G/P by its varieties of minimal rational tangents LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jun-Muk Hwang\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: Let $G/P$ be a rational homogeneous space of Picard number 1 and let $X$ be a Fano manifold of Picardnumber 1. The question we are interested in is: if the variety of minimal rational tangents at a general point of $X$ is isomorphic to that of $G/P$, is $X$ biholomorphic to $G/P$? An affirmative answer is given for $G/P$ associated with a long root in the works of Mok and Hong-Hwang in 2008. In these cases, Tanaka theory for parabolic geometry was used to handle the underlying differential geometric structures. The question has been open for the other $G/P$, i.e., symplectic Grassmannians or two cases of $F_4$-homogeneous spaces. The main difficulty in the remaining cases is that the underlying geometric structure is no longer a parabolic geometry and certain degenerate structures may occur. In a collaboration with Qifeng Li, we overcome this difficulty by constructing a Cartan connection associated to the geometric structure under the assumption that certain vector bundles arising from Spencer complexes do not have nonzero sections. Using this construction, we settle the case of symplectic Grassmannians. END:VEVENT BEGIN:VEVENT DTSTART:20171218T113000 DTEND:20171218T123000 DTSTAMP:20171217T150000Z UID:81af8d8e324ae516d45f8e3af3463e4f@cgp.ibs.re.kr SUMMARY:Canonical rings of NC varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Florin Ambro\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will discuss the finite generation, and the existence of minimal models, for projective varieties withat most normal crossings singularities. Based on joint work with J. Kollar. END:VEVENT BEGIN:VEVENT DTSTART:20171218T100000 DTEND:20171218T110000 DTSTAMP:20171217T150000Z UID:1f4e3ab41f4f044515345323d158fce3@cgp.ibs.re.kr SUMMARY:Some problems in birational geometry LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Caucher Birkar\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: Singularities play a fundamental role in modern birational geometry as they naturally appear in manycontexts. In this talk I will discuss some problems in birational geometry focusing on singularities and theirinteraction with global geometry. END:VEVENT BEGIN:VEVENT DTSTART:20171218T160000 DTEND:20171218T170000 DTSTAMP:20171217T150000Z UID:c7b56d52e943c66657e5cf97c60900ed@cgp.ibs.re.kr SUMMARY:Log canonical pairs with boundaries containing ample divisors LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Zhengyu Hu\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: Let $(X,B)$ be a projective log canonical pair. Assume that $B \geq A$ for some ample divisor $A \geq0$. We prove that $(X,B)$ has a good minimal model or a Mori fiber space. As an application we prove that alog Fano type variety $X$ with $\mathbb{Q}$-factorial log canonical singularities is a Mori dream space. END:VEVENT BEGIN:VEVENT DTSTART:20171219T143000 DTEND:20171219T153000 DTSTAMP:20171218T150000Z UID:2c66c84a3c5987c2f775c7d7c0094325@cgp.ibs.re.kr SUMMARY:A Weak Fano Threefold Arising as a Blowup of a Curve of Genus 5 and Degree 8 on P^3 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joseph Cutrone\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: This article constructs the smooth weak Fano threefold of Picard number two with small anti-canonical map that arises as a blowup of a smooth curve of genus 5 and degree 8 independent of priorclassification results. END:VEVENT BEGIN:VEVENT DTSTART:20171221T113000 DTEND:20171221T123000 DTSTAMP:20171220T150000Z UID:361f130430bdda3d47c40ce5f2085ca9@cgp.ibs.re.kr SUMMARY:Flexible open subsets of del Pezzo fibrations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Adrien Dubouloz\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: By the work of Pukhlikov, "most" three-dimensional fibrations in del Pezzo surfaces of degree lower than or equal to 3 have non rational total spaces. In this talk, I will discuss special del Pezzo fibrations which in contrast contain many affine cylinders over a rational base, some of these even arising as projective completions of the affine 3-space. (Joint work with T. Kishimoto, Saitama Univ.) END:VEVENT BEGIN:VEVENT DTSTART:20171222T113000 DTEND:20171222T123000 DTSTAMP:20171221T150000Z UID:9d73497e7b4c15f5d5657a309d9a2065@cgp.ibs.re.kr SUMMARY:Complements, log adjunction and mld's. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Vyacheslav Shokurov\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will explain that the complement conjecture follows from some other standart conjectures andalready nonconjectures. In particular, the complemt conjecture holds in dimension 2 and in dimension 3 itfollows from the acc of mld's near 1. END:VEVENT BEGIN:VEVENT DTSTART:20171219T113000 DTEND:20171219T123000 DTSTAMP:20171218T150000Z UID:4dc29fab207cb6d5d0950b9a18c2b062@cgp.ibs.re.kr SUMMARY:Okounkov bodies of pseudoeffectieve divisors LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: I will survey our recent results on Okounkov bodies obtained through the collaboration with Y.Hyun, J.Park, and J.Won. After introducing the constructions of Okounkov bodies for pseudoeffective divisors, I will explain how various positivity properties of divisors are encoded in the Okounkov bodies. END:VEVENT BEGIN:VEVENT DTSTART:20171221T143000 DTEND:20171221T153000 DTSTAMP:20171220T150000Z UID:81d6e26d8296deb1c07e457d8a79a483@cgp.ibs.re.kr SUMMARY:K-stability for smooth del Pezzo surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: The Shokurovs : workshop for birationalists\n\nAbstract: We introduce some invariants for K-stability of Fano varieties then show how we can estimate the invariants to determine K-stability of smooth del Pezzo surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20171218T173000 DTEND:20171218T190000 DTSTAMP:20171217T150000Z UID:40f9e0f4eb2442b636c48475d53947ad@cgp.ibs.re.kr SUMMARY:Proper holomorphic maps between reducible bounded symmetric domains LOCATION:CGP Main Hall DESCRIPTION:Speaker: Aeryeong Seo\n\nEvent: Seminar 2017\n\nAbstract: In this talk, I will present proper holomorphic maps between bounded symmetric domains when the source domain is not irreducible. More precisely, we provide sufficient conditions for semi-product proper holomorphic maps to be product proper. As an application we characterize proper holomorphic maps between equidimensional bounded symmetric domains. END:VEVENT BEGIN:VEVENT DTSTART:20180117T160000 DTEND:20180117T180000 DTSTAMP:20180116T150000Z UID:48ef85486585c43f6286e1d18b0c3158@cgp.ibs.re.kr SUMMARY:SYZ transforms for immersed Lagrangian multi-sections LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: We study the geometry of the SYZ transform on a semi-flat Lagrangian torus fibration. Our starting point is an investigation on the relation between Lagrangian surgery of a pair of straight lines in a symplectic 2-torus and extension of holomorphic vector bundles over the mirror elliptic curve, via the SYZ transform for immersed Lagrangian multi-sections. This study leads us to a new notion of equivalence between objects in the immersed Fukaya category of a general compact symplectic manifold M, under which the immersed Floer cohomology is invariant; in particular, this provides an answer to a question of Akaho-Joyce, which concerning non-Hamiltonian invariant property of the immersed Floer cohomology. Furthermore, if M admits a Lagrangian torus fibration over an integral affine manifold, we prove that, under some additional assumptions, this new equivalence is mirror to isomorphism between holomorphic vector bundles over the dual torus fibration via the SYZ transform. END:VEVENT BEGIN:VEVENT DTSTART:20180115T160000 DTEND:20180115T180000 DTSTAMP:20180114T150000Z UID:352abd7c8567d7f9da0a82bfb3fd14be@cgp.ibs.re.kr SUMMARY:Localizations of the category of $A_\infty$ categories: geometric applications LOCATION:CGP Main Hall DESCRIPTION:Speaker: Paolo Stellari\n\nEvent: Seminar\n\nAbstract: In this talk, I will compare the localization of the category of (small) dg categories with respect to quasi-equivalences to various localizations of the category of $A_\infty$ categories. In particular, I will provide a simple and complete proof of results which are claimed in the existing literature but whose proofs are partially missing. The applications that will be discussed concern the uniqueness of higher categorical enhancements of 'geometric' triangulated categories and internal Homs of dg categories. The talk is based on joint work with A. Canonaco and joint work in progress with A. Canonaco and M. Ornaghi. END:VEVENT BEGIN:VEVENT DTSTART:20180118T160000 DTEND:20180118T180000 DTSTAMP:20180117T150000Z UID:c81a99227644b9ede76751176b4dc034@cgp.ibs.re.kr SUMMARY:Ergodic approach to combinatorial number theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Younghwan Son\n\nEvent: CGP Seminar\n\nAbstract: At first we will discuss some recurrence results in ergodic theory, which are connected to some cobinatorial results such as Sarkozy Theorem and Szemeredi Theorem. Then we will present some ideas in the ergodic proof of recurrence theorems. END:VEVENT BEGIN:VEVENT DTSTART:20180116T130000 DTEND:20180116T150000 DTSTAMP:20180115T150000Z UID:c4ac41b2e4538e50dc927b90274f1fed@cgp.ibs.re.kr SUMMARY:The Bar adjunction II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Derived Seminar\n\nAbstract: more information at https://paracompact.space/derived-seminar END:VEVENT BEGIN:VEVENT DTSTART:20180131T133000 DTEND:20180131T153000 DTSTAMP:20180130T150000Z UID:1ce011201ba3d3f0ad448e4eb079ad26@cgp.ibs.re.kr SUMMARY:Wall-crossing formula LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of talks, we hope to discuss various aspect of Kontsevich-Soibelman's wall crossing formula. I will start with discussing about the wall crossing formula arising from the mutation of Landau-Ginzburg potential and its application to construction of Vianna's exotic monotone Lagrangian tori. Talks on different aspect shall follow by talks hopefully given by other audience. END:VEVENT BEGIN:VEVENT DTSTART:20180316T100000 DTEND:20180316T120000 DTSTAMP:20180315T150000Z UID:9944e0d344b9c60587f1313b5178d2fd@cgp.ibs.re.kr SUMMARY:Newton-Okounkov polytopes and representation theory I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Seminar\n\nAbstract: The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Kaveh (resp., the speaker and Naito) proved that Berenstein-Littelmann-Zelevinsky's string polytope (resp., Nakashima-Zelevinsky's polyhedral realization of a highest weight crystal basis) is identical to the Newton-Okounkov polytope of a Schubert variety associated with a specific valuation.In this series of talks, after reviewing the theory of Newton-Okounkov polytopes and Kaveh's result on string polytopes, we see how these polytopes are related to polyhedral realizations of crystal bases. In addition, we discuss generalizations to Bott-Samelson varieties. This series of talks is based on the following papers:(1) N. Fujita, Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules, preprint 2015, arXiv:1503.08916v2.(2) N. Fujita and S. Naito, Newton-Okounkov convex bodies of Schubert varieties and polyhedral realizations of crystal bases, Math. Z. 285 (2017), 325-352.* Plan of this series of talks: 1st talk: Introduction to Newton-Okounkov polytopes We overview the theory of Newton-Okounkov polytopes and related topics.2nd talk: Relation with representation theory We see relations among Newton-Okounkov polytopes of Schubert varieties, string polytopes, and polyhedral realizations of crystal bases.3rd talk: Generalizations to Bott-Samelson varietiesThe 3rd talk is devoted to explaining the theory of generalized string polytopes. We also see how Kaveh's result is generalized to Bott-Samelson varieties via generalized string polytopes. END:VEVENT BEGIN:VEVENT DTSTART:20180316T133000 DTEND:20180316T153000 DTSTAMP:20180315T150000Z UID:b097dd947692853ffb907f7f847a41d3@cgp.ibs.re.kr SUMMARY:Newton-Okounkov polytopes and representation theory II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Seminar\n\nAbstract: The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Kaveh (resp., the speaker and Naito) proved that Berenstein-Littelmann-Zelevinsky's string polytope (resp., Nakashima-Zelevinsky's polyhedral realization of a highest weight crystal basis) is identical to the Newton-Okounkov polytope of a Schubert variety associated with a specific valuation.In this series of talks, after reviewing the theory of Newton-Okounkov polytopes and Kaveh's result on string polytopes, we see how these polytopes are related to polyhedral realizations of crystal bases. In addition, we discuss generalizations to Bott-Samelson varieties. This series of talks is based on the following papers:(1) N. Fujita, Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules, preprint 2015, arXiv:1503.08916v2.(2) N. Fujita and S. Naito, Newton-Okounkov convex bodies of Schubert varieties and polyhedral realizations of crystal bases, Math. Z. 285 (2017), 325-352.* Plan of this series of talks: 1st talk: Introduction to Newton-Okounkov polytopes We overview the theory of Newton-Okounkov polytopes and related topics.2nd talk: Relation with representation theory We see relations among Newton-Okounkov polytopes of Schubert varieties, string polytopes, and polyhedral realizations of crystal bases.3rd talk: Generalizations to Bott-Samelson varietiesThe 3rd talk is devoted to explaining the theory of generalized string polytopes. We also see how Kaveh's result is generalized to Bott-Samelson varieties via generalized string polytopes. END:VEVENT BEGIN:VEVENT DTSTART:20180319T093000 DTEND:20180319T113000 DTSTAMP:20180318T150000Z UID:cf2622413cf7544f5c640d0c661915f8@cgp.ibs.re.kr SUMMARY:Newton-Okounkov polytopes and representation theory III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Seminar\n\nAbstract: The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Kaveh (resp., the speaker and Naito) proved that Berenstein-Littelmann-Zelevinsky's string polytope (resp., Nakashima-Zelevinsky's polyhedral realization of a highest weight crystal basis) is identical to the Newton-Okounkov polytope of a Schubert variety associated with a specific valuation.In this series of talks, after reviewing the theory of Newton-Okounkov polytopes and Kaveh's result on string polytopes, we see how these polytopes are related to polyhedral realizations of crystal bases. In addition, we discuss generalizations to Bott-Samelson varieties. This series of talks is based on the following papers:(1) N. Fujita, Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules, preprint 2015, arXiv:1503.08916v2.(2) N. Fujita and S. Naito, Newton-Okounkov convex bodies of Schubert varieties and polyhedral realizations of crystal bases, Math. Z. 285 (2017), 325-352.* Plan of this series of talks: 1st talk: Introduction to Newton-Okounkov polytopes We overview the theory of Newton-Okounkov polytopes and related topics.2nd talk: Relation with representation theory We see relations among Newton-Okounkov polytopes of Schubert varieties, string polytopes, and polyhedral realizations of crystal bases.3rd talk: Generalizations to Bott-S