1) Under what conditions on 0 does $Alg_0$ present the “homotopically correct” category of algebras over an operad (e.g., in the sense of ∞-categories)?
2) Under what conditions on 0 does $Alg_0$ possess a model structure?
3) Under what conditions on 0 and 0' does a weak equivalence 0→0' inducea Quillen equivalence $Alg_0$→$Alg_0$'?
We provide a complete answer to 1) and 3) in terms of an if-and-only-ifcriterion that is easy to verify in practice,and we also give a sufficient condition for 2) that is applicable to all knownpractical examples.Our criteria work in abstract monoidal model categories,such as simplicial sets, chain complexes, motivic spectra, topologicalspaces, and many others.The above is joint work with Jakob Scholbach (Münster).If time permits, I will also discuss the case of coalgebras overoperads, as well as Leinster-style homotopy algebras over operads. END:VEVENT BEGIN:VEVENT DTSTART:20180823T090000 DTEND:20180823T120000 DTSTAMP:20180822T150000Z UID:69dc42cde2b5c715bb8c43d39fc6bda0@cgp.ibs.re.kr SUMMARY:Operads and moduli spaces of genus zero curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Clément Dupont\n\nEvent: Pohang Operadic Workshop\n\nAbstract: We will review classical and more recent work relating the algebro-geometric properties of moduli spaces of genus zero curves with operadic structures. In particular, we will give a Hodge-theoretic interpretation and a proof of the fact that Getzler’s gravity operad is free as a non-symmetric operad. This is joint with Bruno Vallette. END:VEVENT BEGIN:VEVENT DTSTART:20180821T090000 DTEND:20180821T120000 DTSTAMP:20180820T150000Z UID:7dbe3045a77bdde3727b3e933798b31f@cgp.ibs.re.kr SUMMARY:Homotopy theory of linear cogebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Brice Le Grignou\n\nEvent: Pohang Operadic Workshop\n\nAbstract: Cogebras appear in various areas in Mathematics, for instance in algebraic topology or in formal geometry. However, mathematicians often dualize them to get algebras since these ones are easier to handle. The goal of this talk is to provide tools to work directly with various types of differential graded cogebras : coassociative cogebras, cocommutative cogebras, Lie cogebras, etc. All of these are particular examples of cogebras over an operad. To understand the homotopy theories that govern such objects, we define the category of complete curved algebras over a coperad --- where the notion of quasi-isomorphims does not make sense --- and endow it with a model category structure, equivalent to that of the category of cogebras. END:VEVENT BEGIN:VEVENT DTSTART:20180820T090000 DTEND:20180820T120000 DTSTAMP:20180819T150000Z UID:86dafe13f803ff8f45bc55d4a4d32e3b@cgp.ibs.re.kr SUMMARY:Cyclic operads: syntactic, algebraic, categoried and combinatorial aspects LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jovana Obradović\n\nEvent: Pohang Operadic Workshop\n\nAbstract: In this talk, we set up theoretical grounds of syntactic, algebraic, categoried and combinatoral nature for cyclic operads of Getzler and Kapranov. In the syntactic treatment, we propose a λ-calculus-style formal language, called µ-syntax, as a lightweight representation of the entries-only cyclic operad structure. As opposed to the original exchangeable-output characterisation of cyclic operads, according to which the operations of a cyclic operad have inputs and an output that can be "exchanged" with one of the inputs, the entries-only cyclic operads have only entries (i.e. the output is put on the same level as the inputs). By employing the rewriting methods behind the formalism, we give a complete step-by-step proof of the equivalence between the unbiased and biased denitions of cyclic operads. Guided by the microcosm principle of Baez and Dolan and by the algebraic denitions of operads of Kelly and Fiore, in the algebraic approach we dene cyclic operads internally to the category of Joyal's species of structures. In this way, both the original exchangeable-output characterisation of Getzler and Kapranov, and the alternative entries-only characterisation of cyclic operads of Markl are epitomised as "monoid-like" objects in "monoidal-like" categories of species. Relying on a result of Lamarche on descent for species, we use these "monoid-like" denitions to prove the equivalence between the exchangeable-output and entries-only points of view on cyclic operads. We next establish a notion of categoried cyclic operad for set-based cyclic operads with symmetries, dened in terms of generators and relations. The categorications we introduce are obtained by replacing sets of operations with categories, by relaxing associativity and commutativity to isomorphisms, while leaving the equivariance strict, and by formulating coherence conditions for these isomorphisms. The coherence theorem that we prove has the form "all diagrams of canonical isomorphisms commute". For entries-only categoried cyclic operads, our proof is of syntactic nature and relies on the coherence of categoried operads established by Dosen and Petric. We prove the coherence of exchangeable-output categoried cyclic operads by "lifting to the categoried setting" the equivalence between entries-only and exchangeable-output cyclic operads, set up previously in the algebraic approach. We give an example of a categoried cyclic operad in the form of a generalisation of the structure of profunctors of Benabou. We then show how to exploit the coherence conditions of categoried cyclic operads in proving that the Feynman category for cyclic operads, introduced by Kaufmann and Ward, admits an odd version. We finish with combinatorial aspects of categoried cyclic operads, i.e. with their possible characterisations in convex and discrete geometry. This investigation aims at nding polytopes which describe the coherences of categoried cyclic operads, in the same was as the geometry of symmetric monoidal categories is demonstrated by permutoassociahedra, or the geometry of categoried operads by hypergraph polytopes. After appropriately adjusting the set of canonical isomorphisms of categoried cyclic operads, we show that cyclic operadic polytopes are associahedral, hemiassociahedral and permutohedral arrangements of hypercubes. END:VEVENT BEGIN:VEVENT DTSTART:20180814T153000 DTEND:20180814T180000 DTSTAMP:20180813T150000Z UID:9539ae00230a6ea9154b5d2ce5f11f42@cgp.ibs.re.kr SUMMARY:조별활동 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 조별활동\n\nEvent: 2018 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20180815T153000 DTEND:20180815T180000 DTSTAMP:20180814T150000Z UID:de87a657ece8084cd9e07c8ae36aa130@cgp.ibs.re.kr SUMMARY:조별활동 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 조별활동\n\nEvent: 2018 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20180816T153000 DTEND:20180816T180000 DTSTAMP:20180815T150000Z UID:d06edd6b3cb7193ef7efb1a6d9d15fbf@cgp.ibs.re.kr SUMMARY:조별활동 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 조별활동\n\nEvent: 2018 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20180816T103000 DTEND:20180816T120000 DTSTAMP:20180815T150000Z UID:65ef4f19c54de5c5251dfad7d1072d17@cgp.ibs.re.kr SUMMARY:조별활동 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 조별활동\n\nEvent: 2018 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20180816T140000 DTEND:20180816T150000 DTSTAMP:20180815T150000Z UID:7a3cd3f3d1b19ee5b7276b3dde3f1b90@cgp.ibs.re.kr SUMMARY:조별활동 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: 조별활동\n\nEvent: 2018 IBS-CGP Mathematics Festival\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20180830T100000 DTEND:20180830T120000 DTSTAMP:20180829T150000Z UID:e09736610da67c9e7f9a63207028485b@cgp.ibs.re.kr SUMMARY:On the topology of real toric manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Suyoung Choi\n\nEvent: Seminar\n\nAbstract: One of the most important classes in toric geometry is a class of non-singular complete toric varieties, simply called a toric manifold.Another important object in toric geometry is the real locus of a toric manifold $X$, denoted by $X^{\mathbb{R}}$. We simply call $X^{\mathbb{R}}$ a real toric manifold. It is known that $X^{\mathbb{R}}$ is a real variety and a smooth manifold.From the viewpoint of topologists, the topology of $X^{\mathbb{R}}$ is more complicated than the topology of $X$.For instance, $X$ is simply connected whereas $X^{\mathbb{R}}$ is never simply connected, and the integral cohomology ring of $X$ can be described beautifully as a quotient of the polynomial rings whereas the integral cohomology ring of $X^{\mathbb{R}}$ remains unknown.Indeed, although the cohomology formula of toric manifolds has been well-established since the late 1970s due to Jurkiewicz and Danilov, only partial results of cohomology of $X^{\mathbb{R}}$ have been obtained.Recently, the speaker and his collaborators have developed the fundamental framework of real toric spaces.In the lecture, I will introduce the recent progress on the topology and combinatorics of real toric spaces, and propose several "challengeable" open problems. END:VEVENT BEGIN:VEVENT DTSTART:20180904T160000 DTEND:20180904T180000 DTSTAMP:20180903T150000Z UID:56e013415f48c7b2dac13326ba57a961@cgp.ibs.re.kr SUMMARY:Le Potier's strange duality and universal formulas LOCATION:CGP Main Hall DESCRIPTION:Speaker: Thomas Goller\n\nEvent: Seminar\n\nAbstract: Le Potier's strange duality is a conjectured duality between the global sections of certain line bundles on moduli spaces of sheaves on algebraic surfaces. I will give a non-technical introduction to strange duality. One can arrange the dimensions of these vector spaces of global sections into power series. I will explain how strange duality and algebraic cobordism relate to universal formulas for these power series. END:VEVENT BEGIN:VEVENT DTSTART:20180904T130000 DTEND:20180904T150000 DTSTAMP:20180903T150000Z UID:47ae9779a778959d651ccb1cfe39e34c@cgp.ibs.re.kr SUMMARY:Superrigidity of smooth Fano hypersurfaces of index 1 LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The aim of this talk is to explain a proof of the birational superrigidity and non-rationality of smooth Fano hypersurfaces of index 1. This Talk is based on the recent article "The rigidity theorem of Fano-Segre-Iskovskikh-Manin-Corti-Pukhlikov-Cheltsov-de Fernex-Ein-Mustaţă-Zhuang" written by János Kollár. END:VEVENT BEGIN:VEVENT DTSTART:20180911T160000 DTEND:20180911T180000 DTSTAMP:20180910T150000Z UID:0fe611f370bbf82e4edb3db8f4a18797@cgp.ibs.re.kr SUMMARY:Multiplicity bounds and non-canonical centers LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: This is a continuation of my previous talk "Superrigidity of smooth Fano hypersurfaces of index 1". To prove the (weak) superrigidity of smooth Fano hypersurfaces of index 1, I will explain that a subvariety of a smooth hypersurface cannot be unexpectedly singular along a large dimensional subset, and estimating the multiplicity of a linear system is useful to decide whether a pair of a variety and a linear system is canonical or log canonical. This talk is based on the recent article "The rigidity theorem of Fano-Segre-Iskovskikh-Manin-Corti-Pukhlikov-Cheltsov-de Fernex-Ein-Mustaţă-Zhuang" written by János Kollár. END:VEVENT BEGIN:VEVENT DTSTART:20180918T160000 DTEND:20180918T180000 DTSTAMP:20180917T150000Z UID:580862a376440ebb3accb406f70966ab@cgp.ibs.re.kr SUMMARY:Global sections from isolated log canonical singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: This is a continuation of my previous two talks "Superrigidity of smooth Fano hypersurfaces of index 1" and "Multiplicity bounds and non-canonical centers". After recalling the Bertini type theorems and inversion of adjunction, I will deduce that these results imply the Doubling a linear system and the Cutting down to isolated centers. The Zhuang's new observation leads to the result that the space of global sections associated to an ample divisor with isolated log canonical singularities grows exponentially with the dimension by focusing on multiplier ideals of a linear system. This talk is based on the recent article "The rigidity theorem of Fano-Segre-Iskovskikh-Manin-Corti-Pukhlikov-Cheltsov-de Fernex-Ein-Mustaţă-Zhuang" written by János Kollár. END:VEVENT BEGIN:VEVENT DTSTART:20180920T160000 DTEND:20180920T180000 DTSTAMP:20180919T150000Z UID:149cbf8ecd22aa74150729c57c1b5102@cgp.ibs.re.kr SUMMARY:A Galois action on the space of knots LOCATION:CGP Main Hall DESCRIPTION:Speaker: Geoffroy Horel\n\nEvent: CGP Seminar\n\nAbstract: Vassiliev and Goodwillie-Weiss have produced a tower of approximation of the space of knots. This tower induces a spectral sequence that tries to compute the homology of the space of knots. If we tensor it with the field of rational numbers, this spectral sequence is well-understood. It collapses at the $E^2$-page and this page has a purely combinatorial description. The integral situation is a lot more mysterious. In joint work with Pedro Boavida de Brito, we construct an intersting action of the absolute Galois group of the rational numbers on this spectral sequence. This allows us to obtain some integral vanishing results on the differentials. END:VEVENT BEGIN:VEVENT DTSTART:20181008T110000 DTEND:20181008T120000 DTSTAMP:20181007T150000Z UID:cfe24fac907da018412a6429ca3e7939@cgp.ibs.re.kr SUMMARY:Arithmetic of the moduli of fibered algebraic surfaces with heuristics for counting curves over global fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The first half of the talk will give the construction of the moduli of semistable elliptic surfaces based on the stack of morphisms $\mathcal{L}_{1,12n} \cong \mathrm{Hom}_n(\mathbb{P}^{1}, \overline{\mathcal{M}}_{1,1})$ where $\overline{\mathcal{M}}_{1,1}$ is the Deligne-Mumford stack of stable elliptic curves and $K$ is any field of characteristic not equal to $2, 3$. I would like to make it as self-contained as possible. The rest of the talk will be devoted to the application of the Grothendieck ring of K–stacks to acquire the motive of the moduli stack $\mathcal{L}_{1,12n}$ is $\mathbb{L}^{10n + 1}-\mathbb{L}^{10n - 1}$ which implies that the cardinality of the set of weighted $\mathbb{F}_q$--points to be $\#_q(\mathcal{L}_{1,12n}) = q^{10n + 1}-q^{10n - 1}$. I want to present example of passing the acquired arithmetic invariant through the global fields analogy which renders a new heuristic of $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$ for counting the semistable elliptic curves over Q by the bounded height of discriminant $\Delta$ END:VEVENT BEGIN:VEVENT DTSTART:20181012T110000 DTEND:20181012T120000 DTSTAMP:20181011T150000Z UID:fdfa12dcebadcaf030ce25fc83418877@cgp.ibs.re.kr SUMMARY:Arithmetic of the moduli of fibered algebraic surfaces with heuristics for counting curves over global fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The first half of the talk will give the construction of the moduli of semistable elliptic surfaces based on the stack of morphisms $\mathcal{L}_{1,12n} \cong \mathrm{Hom}_n(\mathbb{P}^{1}, \overline{\mathcal{M}}_{1,1})$ where $\overline{\mathcal{M}}_{1,1}$ is the Deligne-Mumford stack of stable elliptic curves and $K$ is any field of characteristic not equal to $2, 3$. I would like to make it as self-contained as possible. The rest of the talk will be devoted to the application of the Grothendieck ring of K–stacks to acquire the motive of the moduli stack $\mathcal{L}_{1,12n}$ is $\mathbb{L}^{10n + 1}-\mathbb{L}^{10n - 1}$ which implies that the cardinality of the set of weighted $\mathbb{F}_q$--points to be $\#_q(\mathcal{L}_{1,12n}) = q^{10n + 1}-q^{10n - 1}$. I want to present example of passing the acquired arithmetic invariant through the global fields analogy which renders a new heuristic of $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$ for counting the semistable elliptic curves over Q by the bounded height of discriminant $\Delta$ END:VEVENT BEGIN:VEVENT DTSTART:20181015T110000 DTEND:20181015T120000 DTSTAMP:20181014T150000Z UID:8a597e08e60c085086ecb7a09b705e63@cgp.ibs.re.kr SUMMARY:Arithmetic of the moduli of fibered algebraic surfaces with heuristics for counting curves over global fields LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The first half of the talk will give the construction of the moduli of semistable elliptic surfaces based on the stack of morphisms $\mathcal{L}_{1,12n} \cong \mathrm{Hom}_n(\mathbb{P}^{1}, \overline{\mathcal{M}}_{1,1})$ where $\overline{\mathcal{M}}_{1,1}$ is the Deligne-Mumford stack of stable elliptic curves and $K$ is any field of characteristic not equal to $2, 3$. I would like to make it as self-contained as possible. The rest of the talk will be devoted to the application of the Grothendieck ring of K–stacks to acquire the motive of the moduli stack $\mathcal{L}_{1,12n}$ is $\mathbb{L}^{10n + 1}-\mathbb{L}^{10n - 1}$ which implies that the cardinality of the set of weighted $\mathbb{F}_q$--points to be $\#_q(\mathcal{L}_{1,12n}) = q^{10n + 1}-q^{10n - 1}$. I want to present example of passing the acquired arithmetic invariant through the global fields analogy which renders a new heuristic of $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$ for counting the semistable elliptic curves over Q by the bounded height of discriminant $\Delta$ END:VEVENT BEGIN:VEVENT DTSTART:20181016T160000 DTEND:20181016T180000 DTSTAMP:20181015T150000Z UID:07cfd5331f69c5d5040b8e363ce87e0b@cgp.ibs.re.kr SUMMARY:Smooth plane quartic curves and del Pezzo 3-folds of degree 1 with 28 nodes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jihun Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will explain how to construct a del Pezzo 3-fold of degree 1 with 28 nodes from a given smooth plane quartic curve. The construction is based on a j-invariant function defined by the given plane quartic curve. In the construction, the 28 bitangent lines of the smooth quartic curve yield 28 nodes on the del Pezzo 3-fold, which result from 21 lines and 7 twist cubic curves determined by 7 points of $\mathbb{P}^3$ in general position. END:VEVENT BEGIN:VEVENT DTSTART:20181018T160000 DTEND:20181018T180000 DTSTAMP:20181017T150000Z UID:f8a8e2b360a0fb893a6ce69a3fdf9d60@cgp.ibs.re.kr SUMMARY:Riemann-Hilbert correspondence and Fukaya category LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: CGP Seminar\n\nAbstract: Riemann-Hilbert correspondence translates differential equations into some topological data. For irregular singularities, the topological data is called Stokes structure. Some years ago, D'Agnolo-Kashiwara proposed a formalism treating all the Stokes structures simultaneously and proved Riemann-Hilbert correspondence for irregular singularities. In this talk, I will talk about a modified version of this formalism and also discuss a relationship with Fukaya category. END:VEVENT BEGIN:VEVENT DTSTART:20181108T160000 DTEND:20181108T180000 DTSTAMP:20181107T150000Z UID:738d0e9a17b3150f9ee3aa0a40e172b1@cgp.ibs.re.kr SUMMARY:Vertex algebras and applications to algebraic geometry and number theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Alexander Zuevsky\n\nEvent: CGP Seminar\n\nAbstract: In the first part we recall the notion of vertex algebras, their modules, construction of characters on Riemann surfaces of various genus, and their relations to modular forms. The second part will be devoted to algebraic methods of computation of correlation functions for corresponding Conformal Field Theories (Heisenberg and free fermionic vertex operator algebras). We provide also pplications in algebraic geometry (Szego kernel), differential geometry (construction of associated foliations of smooth manifolds), and number theory identities for modular forms. END:VEVENT BEGIN:VEVENT DTSTART:20181112T160000 DTEND:20181112T180000 DTSTAMP:20181111T150000Z UID:fcd8333d91f8636ca0f9cd9decfabd6c@cgp.ibs.re.kr SUMMARY:Mapping class group invariants via geometric recursion LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gaëtan Borot\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will present a general mechanism called "geometric recursion" (GR), whose aim is to construction mapping class group invariants for surfaces of arbitrary topologies, from a small amount of initial data, by summing over homotopy classes of pairs of pants decompositions. I will mainly focus on the instance of this construction taking values in continuous functions over the Teichmuller space. The celebrated generalization of McShane identity by Mirzakhani shows that the constant function 1 can be obtained by GR. We generalize Mirzakhani identity by a twisting procedure: it shows that linear statistics of hyperbolic lengths of simple multicurves, seen as functions on the Teichmuller space, can also be obtained by GR.Integration of functions obtained by GR against the Weil-Petersson volume form over the moduli space of bordered Riemann surfaces automatically satisfy a topological recursion (TR). We will give several examples governed by this GR/TR, including correlation functions of semi-simple cohomological field theories. The twisting procedure can be seen as a lift to hyperbolic geometry of the action of a subgroup of the Givental group originally defined in the context of cohomological field theories. Based on joint work with Jorgen Andersen and Nicolas Orantin. END:VEVENT BEGIN:VEVENT DTSTART:20181029T100000 DTEND:20181029T110000 DTSTAMP:20181028T150000Z UID:3607b3b0aa10f2a3856a36207dd1ac90@cgp.ibs.re.kr SUMMARY:Open intersection numbers, matrix models and integrability LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: From the seminal papers of Witten and Kontsevich we know that the intersection theory on the moduli spaces of complex curves is described by a tau-function of the KdV integrable hierarchy. Moreover, this tau-function is given by a matrix integral and satisfies the Virasoro constraints. Recently, in the work of R. Pandharipande, J. Solomon, and R. Tessler, an open version of this intersection theory was introduced. In my talk I will show that the generating function for this open version can be described very similar to the closed one. In particular, it is given by a tau-function of the integrable hierarchy. Moreover, it's W-constraints can be naturally described in terms of two free bosonic fields. END:VEVENT BEGIN:VEVENT DTSTART:20181029T111500 DTEND:20181029T121500 DTSTAMP:20181028T150000Z UID:009cf0b1da45ed6b13dc3513f7344a1c@cgp.ibs.re.kr SUMMARY:Modularity and holomorphic anomaly equations of GW invariants for toric CY 3-folds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Bohan Fang\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: I will describe the set-up of holomorphic anomaly equations (HAE) for toric CY 3-folds. The remodeling conjecture (theorem) directly implies such HAE. I will also explain how it implies the modularity property of GW invariants. Together we can obtain the Yamaguchi-Yau type modular anomaly equations for GW invariants. This talk is based on the joint work with C.-C. M. Liu and Z. Zong, and with Y. Ruan, Y. Zhang and J. Zhou. END:VEVENT BEGIN:VEVENT DTSTART:20181029T143000 DTEND:20181029T153000 DTSTAMP:20181028T150000Z UID:735892f788c0c7aa27cd6f022853f726@cgp.ibs.re.kr SUMMARY:Tropical counting from Maurer-Cartan equations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kwokwai Chan\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: I will explain a recent joint work (arXiv:1807.08159) with Ziming Ma where we show how Maurer-Cartan elements of the extended deformation theory of the mirror Landau-Ginzburg model $(\check{X}, W)$ of a toric surface $X$ give rise to tropical disks and hence a perturbation of $W$. We will also see that the jumping, or wall-crossing, of the perturbed potential across the edges of a scattering diagram (due to Gross when $X = \mathbb{P}^2$) can be explained as a gauge equivalence. END:VEVENT BEGIN:VEVENT DTSTART:20181029T160000 DTEND:20181029T170000 DTSTAMP:20181028T150000Z UID:b677e18eda4c9aa82cdfa12e0d973984@cgp.ibs.re.kr SUMMARY:Wall-crossing formulas for Lagrangian mutations and their quantization LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: James Pascaleff\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: In this talk I will discuss several versions of the wall-crossing phenomenon that arise in Floer theory. The first is the interpretation of the wall-crossing formula as a coordinate change between charts on the moduli space of compact exact Lagrangian objects in the Fukaya category of an exact symplectic manifold M, and the second is the behavior of superpotentials of those same Lagrangians when M is replaced by a partial compactification X. By relating the Fukaya categories of M and X, Dmitry Tonkonog and I showed how the latter is determined by the former in a general context. This allows us to derive new wall-crossing formulas in complex dimension greater than two. A third aspect is the way that the same algebra governs also the ring structure on the wrapped Floer cohomology of certain non-compact Lagrangians. This perspective also gives us a way to develop the non-commutative deformation of the wall-crossing formula (joint work with Nick Sheridan). END:VEVENT BEGIN:VEVENT DTSTART:20181030T100000 DTEND:20181030T110000 DTSTAMP:20181029T150000Z UID:7d11cbfc5d464f6f3fea1e25e0c4956c@cgp.ibs.re.kr SUMMARY:Fukaya A-infinity algebras of Lagrangian Lie groups LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jake Solomon\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: I will explain a criterion for the Fukaya A-infinity algebra of a Lagrangian Lie group to be quasi-isomorphic to the de Rham cohomology algebra. More generally, the criterion applies to Lagrangian gamma spaces. It follows from this criterion that the Lagrangian tori appearing in the SYZ conjecture are unobstructed. Also, the moduli space of bounding chains and Floer cohomology of such tori have the expected form. END:VEVENT BEGIN:VEVENT DTSTART:20181030T111500 DTEND:20181030T121500 DTSTAMP:20181029T150000Z UID:e196e1648a81189d5119ddd5860df185@cgp.ibs.re.kr SUMMARY:Completing the SYZ mirrors by Lagrangian immersions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Siu-Cheong Lau\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: The SYZ program asserts a geometric way to construct mirrors and derive HMS via duality of special Lagrangian torus fibrations. Singular fiber is the key difficulty in realizing the SYZ program. The resulting mirror merely constructed from regular fibers has missing points. In this talk, I will explain how to glue in the singular fibers, thereby obtaining a complete mirror. It consists of joint works with Cheol-Hyun Cho, Hansol Hong and Yoosik Kim. END:VEVENT BEGIN:VEVENT DTSTART:20181030T143000 DTEND:20181030T153000 DTSTAMP:20181029T150000Z UID:5e9da4efb81a7d0fba267103fe39b86e@cgp.ibs.re.kr SUMMARY:Mirror construction of Grassmannians via Lagrangian deformations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: A partial flag manifold carries a completely integrable system, so-called a Gelfand-Cetlin system. The image of the system is a polytope and every fiber over its interior is a Lagrangian torus as in the toric case. However, non-toric Lagrangian fibers can appear at boundary strata. In this talk, I will explain how to locate non-toric Lagrangian fibers and understand their topology. We then produce immersed Lagrangians replacing non-toric Lagrangians and glue mirror spaces of Lagrangians Floer-theoretically to obtain an SYZ mirror. END:VEVENT BEGIN:VEVENT DTSTART:20181031T104500 DTEND:20181031T114500 DTSTAMP:20181030T150000Z UID:0f1ac048f591bbe96ccbff8324c71d69@cgp.ibs.re.kr SUMMARY:Pairing structures in mirror symmetry between symplectic manifolds and Landau-Ginzburg B-models LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin-Li pairing of the mirror Landau-Ginzburg model under localized mirror functor. Such a relation follows from multi-crescent Cardy identity, which is a generalized form of Cardy identity. There is an interesting conformal factor between these two pairings, which can be described as a ratio of Floer volume class and classical volume class. We also introduce a new kind of invariants of Lagrangian Floer cohomology with values in Jacobian ring of the mirror potential function. As an application, we discuss the case of general toric manifold, and the relation to the work of Fukaya-Oh-Ohta-Ono and their Z-invariant. Also, we compute the conformal factor for an elliptic curve quotient which is expected to be related to the choice of a primitive form. This is a joint work with Cheol-hyun Cho and Hyung-Seok Shin. END:VEVENT BEGIN:VEVENT DTSTART:20181031T120000 DTEND:20181031T130000 DTSTAMP:20181030T150000Z UID:b28ce2129e5fb6664e90d37fad7ca6a3@cgp.ibs.re.kr SUMMARY:Relative Gromov-Witten theory in symplectic side LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: I want to report my joint work with A. Daemi on the study of Lagrangian Floer theory of Symplectic manifold with Divosor. I may talk about its equivariant version and possible application to gauge theory. END:VEVENT BEGIN:VEVENT DTSTART:20181031T093000 DTEND:20181031T103000 DTSTAMP:20181030T150000Z UID:f31bf04842b0c6d2a03cec8a4a222395@cgp.ibs.re.kr SUMMARY:Kernels for Grassmann flops LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Matthew Ballard\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: I will discuss joint work with Nitin Chidambaram, David Favero, Patrick McFaddin, and Rovert Vandermolen which implements, in a specific example, a general method described by the speaker, Diemer, and Favero for manufacturing integral kernels associated to birational maps. One result is an explicit Fourier-Mukai kernel for a family of flops studied originally by Donovan and Segal. END:VEVENT BEGIN:VEVENT DTSTART:20181030T160000 DTEND:20181030T170000 DTSTAMP:20181029T150000Z UID:4937eb9c479e641bb3d6ae7f603cedf1@cgp.ibs.re.kr SUMMARY:Geometry of symplectic flux and lagrangian torus fibrations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Renato Vianna\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: Symplectic flux measures the areas of cylinders swept in theprocess of a Lagrangian isotopy. We call the shape of a symplectic manifold $X$ relative to a Lagrangian submanifold $L$, $Sh_L(X) \subset H^1(L; \mathbb{R})$ the set of fluxesof Lagrangian isotopies starting at $L$. A more interesting symplectic invariant of $L \subset X$ is the star-shape $Sh_L^\star(X) \subset Sh_L(X) \subset H^1(L;\mathbb{R})$, where we impose the extra conditionon the isotopy the its flux evolves linearly.We study flux via a numerical invariant of aLagrangian submanifold that we define using its Fukaya algebra. The maingeometric feature of the invariant is its concavity over isotopies with linearflux. Besides new computation of shapes and star-shapes, this tool allows us toderive constraints on flux, Weinstein neighbourhood embeddings and holomorphicdisk potentials for Gelfand-Cetlin fibres on Fano varieties in terms oftheir polytopes. We show that Calabi-Yau SYZ fibres have unobstructed Floertheory under a general assumption. We also describe the space of fibresof almost toric fibrations on the complex projective plane up to Hamiltonianisotopy, and provide other applications. END:VEVENT BEGIN:VEVENT DTSTART:20181029T121500 DTEND:20181029T143000 DTSTAMP:20181028T150000Z UID:59423a487697f442f6f2c211f803c2b2@cgp.ibs.re.kr SUMMARY:Break LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Lunch\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: Lunch END:VEVENT BEGIN:VEVENT DTSTART:20181030T121500 DTEND:20181030T143000 DTSTAMP:20181029T150000Z UID:92e0be517ccb77bb64172f380626ca5e@cgp.ibs.re.kr SUMMARY:Break LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Lunch\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: Lunch END:VEVENT BEGIN:VEVENT DTSTART:20181030T183000 DTEND:20181030T090000 DTSTAMP:20181029T150000Z UID:1cd3268ea82c24006a2498bb90cd66c0@cgp.ibs.re.kr SUMMARY:Banquet LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Banquet\n\nEvent: Wall-crossing formula, open Gromov-Witten invariants and related areas\n\nAbstract: Banquet END:VEVENT BEGIN:VEVENT DTSTART:20181114T160000 DTEND:20181114T180000 DTSTAMP:20181113T150000Z UID:d6be11f84664477d7dd527d22762ce36@cgp.ibs.re.kr SUMMARY:K-theory, endomorphisms, and Witt vectors LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: David Gepner\n\nEvent: CGP Seminar\n\nAbstract: K-theory is a deep and difficult invariant of algebraic objects such as rings and varieties with numerous applications to number theory and geometry. We will begin with an introduction to K-theory and various related functors, such as Hochschild homology and cyclic K-theory. By a theorem of Almkvist, the cyclic K-theory of a commutative ring is closely related to its ring of Witt vectors (actually a dense subring known as the rational Witt vectors). In addition to the usual Witt vector operations, such as Frobenius and Verschiebung, K-theory allows us to classify all natural operations on rational Witt vectors. END:VEVENT BEGIN:VEVENT DTSTART:20181119T160000 DTEND:20181119T180000 DTSTAMP:20181118T150000Z UID:9add636b41a668383d08f677b4a43cf7@cgp.ibs.re.kr SUMMARY:Introduction to generalized SYZ mirror symmetry LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The famous SYZ conjecture is proposed by Strominger, Yau and Zaslow, in order to study the geometry of mirror symmetry. The conjecture suggested that one can construct the mirror of a symplectic manifold by consider the (quantum) moduli space of special Lagrangian torus. Recently, Cho, Hong and Lau applied the idea of SYZ to immersed Lagrangian to construct mirror space and prove homological mirror symmetry. The resulting mirror space is what they called a generalized SYZ mirror. In this lecture, I will give an introduction to generalized SYZ mirror construction. I will start by reviewing the immersed Floer theory introduced by Akaho and Joyce. Then I will discuss how generalized SYZ mirror construction are applied to a single Lagrangian immersion, which should be regarded as the local model. Finally, I will talk about how to glue these local pieces by the so called pseudo-isomorphism. END:VEVENT BEGIN:VEVENT DTSTART:20181123T140000 DTEND:20181123T144500 DTSTAMP:20181122T150000Z UID:a637636a7a3b5b7282c296e4bee16d11@cgp.ibs.re.kr SUMMARY:Geometric quantization via SYZ transforms LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: The so-called quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this talk, I will explain how SYZ transforms are used to solve the quantization problem. END:VEVENT BEGIN:VEVENT DTSTART:20181123T150000 DTEND:20181123T154500 DTSTAMP:20181122T150000Z UID:d065b5b78973067095622586813c26f1@cgp.ibs.re.kr SUMMARY:Mirror isomorphisms from mirror functors LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: We show how to construct an isomorphism between mirror closed states under the presence of Yoneda type mirror functor(as called as a localized mirror functor). Then we will see that this construction is equivalent to the Kodaira-Spencer isomorphism due to Fukaya-Oh-Ohta-Ono. END:VEVENT BEGIN:VEVENT DTSTART:20181123T161500 DTEND:20181123T170000 DTSTAMP:20181122T150000Z UID:6755c4a0fe970cd99bd5e89ba60ac5fa@cgp.ibs.re.kr SUMMARY:An IMO problem, and fusion ring computations LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Chul-hee Lee\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: Problem 3 of the International Mathematical Olympiad in 1986 is as follows :To each vertex of a regular pentagon an integer is assigned in such a way that the sum of all five numbers is positive. If three consecutive vertices are assigned the numbers x,y,z respectively and y<0 then the following operation is allowed: the numbers x,y,z are replaced by x+y,-y,z+y respectively. Such an operation is performed repeatedly as long as at least one of the five numbers is negative. Determine whether this procedure necessarily comes to an end after a finite number of steps. I will explain this algorithm using the Coxeter groups and how to use it for computations with the affine fusion rings that arise from conformal field theory. END:VEVENT BEGIN:VEVENT DTSTART:20181124T100000 DTEND:20181124T104500 DTSTAMP:20181123T150000Z UID:cd364d06f599524e89113a02f59f6282@cgp.ibs.re.kr SUMMARY:A construction of multiplicity class from Hesselink stratification LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Cheolgyu Lee\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: In this talk, we will define the multiplicity class of hypersurfaces and construct it from the Hesselink stratification of a Hilbert scheme. END:VEVENT BEGIN:VEVENT DTSTART:20181124T111500 DTEND:20181124T120000 DTSTAMP:20181123T150000Z UID:2b2d095a26dda6f60ca8b7a1b6d2c21a@cgp.ibs.re.kr SUMMARY:Topology of the moduli of semistable elliptic surfaces LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: We derive the $l$-adic étale cohomology of $\mathrm{Hom}_n(\mathbb{P}^1,\mathcal{P}(a,b))$, where $\mathcal{P}(a,b)$ is a 1-dimensional $(a,b)$ weighted projective stack, together with its eigenvalues of the geometric Frobenius morphism when $K$ is any field of characteristic not dividing $a,b,l$. We achieve this by using the quotient stack structure of $\mathrm{Hom}_n(\mathbb{P}^1,\mathcal{P}(a,b)) = [T/\mathbb{G}_m]$ and the motive class $\mathbb{L}^{(a+b)n+1}-\mathbb{L}^{(a+b)n-1}$ in the Grothendieck ring of $K$--stacks worked out previously by Han and Park as well as the Behrend-Grothendieck-Lefschetz-Hopf trace formula. We show that the moduli is rational homotopically $S^3$ and its étale cohomology is Tate type but not pure. We also show that there is \'etale homological stability for $\mathrm{Hom}_n(\mathbb{P}^1,\mathcal{P}(a,b))$ that is independent of degree $n$ and the weight $(a,b)$. As a corollary, we acquire Galois representations of the moduli of nonsingular semistable elliptic fibrations over $\mathbb{P}^{1}$, also known as semistable elliptic surfaces, with $12n$ nodal singular fibers and a distinguished section. END:VEVENT BEGIN:VEVENT DTSTART:20181124T140000 DTEND:20181124T144500 DTSTAMP:20181123T150000Z UID:1649ca471668fc695fd96bf554063abe@cgp.ibs.re.kr SUMMARY:On higher secant varieties of smooth projective curves LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: Consider a smooth projective complex curve (=a compact Riemann surface) embedded by the complete linear system of a line bundle of sufficiently large degree. Castelnuovo, Mumford, Saint-Donat, Fujita proved that it is arithmetically Cohen-Macaulay and the defining ideal is generated by quadrics. In this talk, I give a generalization of this classical result to higher secant varieties of the curve. This is joint work with Lawrence Ein and Wenbo Niu. END:VEVENT BEGIN:VEVENT DTSTART:20181124T150000 DTEND:20181124T154500 DTSTAMP:20181123T150000Z UID:b4e947ff3ae88e672d9df76babe0f7e5@cgp.ibs.re.kr SUMMARY:On graph coloring and induced subgraphs LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Ringi Kim\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: A coloring of a graph $G$ is a coloring of vertices of $G$ in such a way that no adjacent vertices receive the same color. The minimum number of colors needed for a coloring of $G$ is called the chromatic number of $G$. There are many results and conjectures regarding classes of graphs which can be obtained by forbidding a certain family of graphs and have bounded chromatic number. For example, a celebrated conjecture by Gyárfá s and Sumner is a long-standing open problem dealing with such classes of graphs.A tournament is a digraph whose underlying graph is a complete graph. A coloring of a tournament $T$ is a coloring of vertices of $T$ such that no monochromatic subtournament contains a directed cycle, and the chromatic number of $T$ is defined as the minimum number of colors needed for a coloring of $T$. Motivated by the Gyárfás-Sumner conjecture, we propose a similar question for tournaments. This talk will consist of a survey of results and open problems on the Gyárfás-Sumner conjecture for graphs and tournaments. END:VEVENT BEGIN:VEVENT DTSTART:20181124T161500 DTEND:20181124T170000 DTSTAMP:20181123T150000Z UID:5d26ca385eb230ede2c4bcb4342af58f@cgp.ibs.re.kr SUMMARY:Vertex-minors and pivot-minors of graphs LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Sang-il Oum\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: For a vertex v of a graph G, the local complementation at v is an operation to obtain a new graph denoted by G*v from G such that two distinct vertices x, y are adjacent in G*v if and only if both x, y are neighbors of v and x, y are non-adjacent, or at least one of x, y is not a neighbor of v and x, y are adjacent. For an edge xy of G, pivoting xy in G is an operation to obtain G*x*y*x from G. A graph H is a vertex-minor of a graph G if H is obtained from G by a sequence of local complementation and vertex deletions. A graph H is a pivot-minor of a graph G if H is obtained from G by a sequence of pivoting and vertex deletions.Motivated by the big success of the graph minor structure theory developed deeply by Robertson and Seymour since 1980s, we propose a similar theory for vertex-minors and pivot-minors. This talk will illustrate similarities between graph minors and graph pivot-/vertex-minors and give a survey of known theorems and open problems on vertex-minors and pivot-minors of graphs. END:VEVENT BEGIN:VEVENT DTSTART:20181125T100000 DTEND:20181125T104500 DTSTAMP:20181124T150000Z UID:30fe02028330e0a1cf4614a271e796ad@cgp.ibs.re.kr SUMMARY:Invariants of the homology cobordism group of homology cylinders LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Minkyoung Song\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: The homology cobordism group of homology cylinders is an enlargement of both the mapping class group and the concordance group of string links. In this talk, I introduce extended Milnor invariants and Hirzebruch-type invariants from iterated p-covers for homology cylinders. We observe structures of the group of homology cylinders via those invariants. END:VEVENT BEGIN:VEVENT DTSTART:20181125T111500 DTEND:20181125T120000 DTSTAMP:20181124T150000Z UID:47adc76434a16ecafd3b650f945ec6a5@cgp.ibs.re.kr SUMMARY:Gain of regularity for the relativistic collision operator LOCATION:The Ocean Hotel, Yeosu DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: 2018 Pohang Mathematics Workshop\n\nAbstract: In this talk we study a regularity property for the gain part of the relativistic Boltzmann collision operator when the collisional cross-section covers the full-range of generic hard and soft potentials with angular cut-off. The aim of this talk is to present two different proofs based on the Fourier transform. END:VEVENT BEGIN:VEVENT DTSTART:20181126T093000 DTEND:20181126T103000 DTSTAMP:20181125T150000Z UID:94d0124b59b76c2d00fc79c5020b06a0@cgp.ibs.re.kr SUMMARY:Counting Lagrangian subbundles via Gromov--Witten invariants LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Insong Choe\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: In this talk, I would like to answer the following question: given a general stable symplectic bundle over an algebraic curve, what is the number of Lagrangian subbundles of maximal degree? I'll discuss a link between this problem and certain Gromov--Witten invariants. As an important technical lemma to get this link, we need the irreducibility of certain Lagrangian Quot schemes. This is a joint work with Daewoong Cheong and George H. Hitching. END:VEVENT BEGIN:VEVENT DTSTART:20181126T110000 DTEND:20181126T120000 DTSTAMP:20181125T150000Z UID:a47db79a0bb2ada0330bcf3a39406173@cgp.ibs.re.kr SUMMARY:Schematic Harder-Narasimhan stratification LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sudarshan Gurjar\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: Around 1975, Harder-Narasimhan defined a canonical filtration of a vector bundle which proved to be of central importance to the subject. A natural question is to understand the variation of this filtration in families. Associated to such a filtration, one can define a ''type'' which is a measure of the non-semistability of the vector bundle. We show thatthis type varies upper-semicontinuously for families of vector bundles. Furthermore, for each type, we define a locally-closed subscheme structure on the subset of the parameter space, consisting of points corresponding to this type and show that it satisfies the universal property that a base-change admits a relative Harder-Narasimhan filtration if and only if the base-change factors through that stratum. As a consequence we show that vector bundles of a fixed Harder-Narasimhan type form an Artin stack which is a locally-closed substack of the stack of all vector bundles. These results hold more generally for Principal Bundles with a reductive structure group over higher dimensional varieties as well but I will mostly stick to vector bundles in the talk, making some comments about Principal Bundles in the end. END:VEVENT BEGIN:VEVENT DTSTART:20181128T143000 DTEND:20181128T153000 DTSTAMP:20181127T150000Z UID:b587bf8637b34635af4c09438b7afc2f@cgp.ibs.re.kr SUMMARY:Finite generation of the algebra of type a conformal blocks over arbitrary stable curves of any genus LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sang-Bum Yoo\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: We show finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application we construct a flat family of irreducible normal projective varieties over the moduli stack of stable pointed curves, whose fiber over a smooth curve is a moduli space of semistable parabolic bundles. This generalizes a construction of a degeneration of the moduli space of vector bundles done in a recent work of Belkale and Gibney. This is a joint work with Han-Bom Moon. END:VEVENT BEGIN:VEVENT DTSTART:20181127T093000 DTEND:20181127T103000 DTSTAMP:20181126T150000Z UID:99da0bb747176cf4e8e8f37c8c901259@cgp.ibs.re.kr SUMMARY:Strange duality via quiver representations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yao Yuan\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: Strange duality is a conjecture formulated in 1990s, which asserts a duality between the global section spaces of determinant line bundles over two moduli spaces of semistable sheaves over a smooth projective scheme $X$. When $X$ is a curve, this conjecture has been proved around 2007. When $X$ is a surface, there is so far no general set-up for this conjecture; but under some assumption the conjecture can be extended. There is not much known for surfaces on the conjecture. In this talk, I will talk about some results on this conjecture when $X$ is the projective plan, especially the latest one I obtained by applying some theorems in quiver representation theory. END:VEVENT BEGIN:VEVENT DTSTART:20181127T110000 DTEND:20181127T120000 DTSTAMP:20181126T150000Z UID:4a98227e3592e6fb2353b5fcff6a1adf@cgp.ibs.re.kr SUMMARY:Counting points of Quot schemes LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Thomas Goller\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: I will discuss some examples of finite Quot schemes and attempts to enumerate their points. This work is motivated by strange duality for curves and Le Potier's strange duality conjecture for surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20181128T110000 DTEND:20181128T120000 DTSTAMP:20181127T150000Z UID:7f64eeeee18eae6a6ba40ae17f1434c1@cgp.ibs.re.kr SUMMARY:Picard group of the moduli space of sheaves LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yinbang Lin\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: In this talk, I will review a few existing results about Picard groups of moduli spaces of sheaves over curves, as well as the rank 2 case over surfaces. Based on the related methods, I will discuss how to obtain similar results for high rank cases over surfaces. This is work in progress, conducted jointly with Jun Li, Howard Nuer and Xiaolei Zhao. END:VEVENT BEGIN:VEVENT DTSTART:20181128T093000 DTEND:20181128T103000 DTSTAMP:20181127T150000Z UID:6decfa52d6b60bd40d78e9c06fc9be62@cgp.ibs.re.kr SUMMARY:Intersection cohomology of the moduli space of sheaves on local CY 3-fold via Kirwan's desingularization LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kiryong Chung\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: Let $\mathbf{M}_0$ be the space of twisted ideal sheaves $\mathcal{I}_{L,Q}(1)$ where $Q$ is a rank $4$ quardric hypersurface in $\mathbb{P}^r$ and $L$ is a linear subspace of dimension $r-2$. The Simpson compactification $\mathbf{M}$ of $\mathbf{M}_0$ has been studied in different view points: The homological mirror symmetry and the log minimal model program. In the second perspective, it was proved that Kirwan's partial desingularization of $\mathbf{M}$ is isomorphic to the moduli space of degree $2$ stable maps in Grassmannian $\mathrm{Gr}(r-1,r+1)$. In this talk, by applying Kirwan's method, we obtain the intersection Hodge-Deligne (IHD) polynomial of $\mathbf{M}$. As a direct consequence, we obtain the IHD-polynomial of the moduli space of pure sheaves on the total space of the canonical line bundle of del-Pezzo surfaces. We also calculate the IHD-polynomial of some open cones which naturally comes from the microlocal geometric structure of $\mathbf{M}$. This is joint work with Y. Yoon. END:VEVENT BEGIN:VEVENT DTSTART:20181127T143000 DTEND:20181127T153000 DTSTAMP:20181126T150000Z UID:8a9c36d5c9b6a779e1fe6c4b48e1eb75@cgp.ibs.re.kr SUMMARY:Hilbert scheme of twisted cubics as simple wall-crossings LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Bingyu Xia\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: Hilbert scheme is introduced by Grothendieck and it played an important role in algebraic geometry. Hilbert scheme of twisted cubics in the projective space P^3 is one of the easiest but nontrivial Hilbert scheme, its geometric structure was first described by Piene and Schlessinger in 1985. In this talk, I will introduce Bridgeland stability conditions on the derived category of the projective space P^3, and use wall-crossing phenomena of stability conditions to reprove Piene and Schlessinger's result. END:VEVENT BEGIN:VEVENT DTSTART:20181129T093000 DTEND:20181129T103000 DTSTAMP:20181128T150000Z UID:e3d3ca005e58124a11a98e0784a64442@cgp.ibs.re.kr SUMMARY:Automorphism group of the moduli space of parabolic vector bundles LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Tomas L. Gomez\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking the dual, and Hecke transforms (using the filtrations given by the parabolic structure). A Torelli theorem for parabolic bundles with arbitrary rank and generic weights is also obtained. These results are extended to the classification of birational equivalences which are defined over "big" open subsets (3-birational maps). Joint work with David Alfaya. END:VEVENT BEGIN:VEVENT DTSTART:20181129T110000 DTEND:20181129T120000 DTSTAMP:20181128T150000Z UID:9a134afd31902d64baff86d79425e725@cgp.ibs.re.kr SUMMARY:Quantum singularity theory via cosection localization LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Workshop on Moduli theory & Derived category\n\nAbstract: I will discuss a recent joint work (arXiv:1806.00116) with Jun Li in which we generalize the cosection localization to intersection homology and Borel-Moore homology that provides us with a purely topological construction of FJRW invariants and some GLSM invariants for both broad and narrow sectors. END:VEVENT BEGIN:VEVENT DTSTART:20181204T160000 DTEND:20181204T180000 DTSTAMP:20181203T150000Z UID:bcb56029be7eacb3d7e7b74e7cf48119@cgp.ibs.re.kr SUMMARY:A tutorial on Tom and Jerry LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Miles Reid\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The talk is a first introduction to unprojection methods, and more specifically to Tom and Jerry unprojections.These two harmless tricks deserve to be better known, since they answer many questions about constructing Gorenstein schemes in codimension 4, including many QQ-Fano 3-folds. In particular, I treat the two smoothing components of the graded anticanonical cover over the weighted projective space PP(1,2,3). This is joint work with Gavin Brown and Jan Stevens. END:VEVENT BEGIN:VEVENT DTSTART:20181203T160000 DTEND:20181203T180000 DTSTAMP:20181202T150000Z UID:22de7c081e2c558c79f87210790a8cfb@cgp.ibs.re.kr SUMMARY:Introduction to generalized SYZ mirror symmetry II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The famous SYZ conjecture is proposed by Strominger, Yau and Zaslow, in order to study the geometry of mirror symmetry. The conjecture suggested that one can construct the mirror of a symplectic manifold by consider the (quantum) moduli space of special Lagrangian torus. Recently, Cho, Hong and Lau applied the idea of SYZ to immersed Lagrangian to construct mirror space and prove homological mirror symmetry. The resulting mirror space is what they called a generalized SYZ mirror. In this lecture, I will give an introduction to generalized SYZ mirror construction. I will start by reviewing the immersed Floer theory introduced by Akaho and Joyce. Then I will discuss how generalized SYZ mirror construction are applied to a single Lagrangian immersion, which should be regarded as the local model. Finally, I will talk about how to glue these local pieces by the so called pseudo-isomorphism. END:VEVENT BEGIN:VEVENT DTSTART:20181206T160000 DTEND:20181206T180000 DTSTAMP:20181205T150000Z UID:1c130282d1c55aee2a26def4f80b1387@cgp.ibs.re.kr SUMMARY:Ring structure of wrapped Floer homology of real Lagrangians in Brieskorn Milnor fibers LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hanwool Bae\n\nEvent: CGP Seminar\n\nAbstract: We compute the ring structure of wrapped Floer homology of a cotangent fiber $L=T^* _e S^n$ in the $A_k$-type plumbing of $T^*S^n$. Such a cotangent fiber can be seen as the fixed locus of some anti-symplectic involution.The main ingredient of the computation is an open string analogue of Seidel representation. We first apply the idea to compute the ring structure of V-shaped wrapped Floer homology $\check{HW}(L)$.The usual wrapped Floer homology and the V-shaped wrapped Floer homology are known to be related by Viterbo transfer map. We determine the ring structure of wrapped Floer homology $HW(L)$ from that of V-shaped wrapped Floer homology using the Viterbo transfer map. END:VEVENT BEGIN:VEVENT DTSTART:20181204T100000 DTEND:20181204T113000 DTSTAMP:20181203T150000Z UID:794322f99fb578263b978ab726b42c0c@cgp.ibs.re.kr SUMMARY:Introduction to Principal Bundles I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sudarshan Gurjar\n\nEvent: Seminar\n\nAbstract: These two talks will introduce the area of Principal Bundles and their moduli in algebraic geometry. After recalling some basic definitions and setting up terminology , I will explain some of the classical theorems in the subject. At the end I will mention my own joint work with Nitin Nitsure. The talks will be basic and accessible to anyone will basic knowledge of algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20181206T100000 DTEND:20181206T113000 DTSTAMP:20181205T150000Z UID:3ab67531251e088e4092e026015b3537@cgp.ibs.re.kr SUMMARY:Introduction to Principal Bundles II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sudarshan Gurjar\n\nEvent: Seminar\n\nAbstract: These two talks will introduce the area of Principal Bundles and their moduli in algebraic geometry. After recalling some basic definitions and setting up terminology , I will explain some of the classical theorems in the subject. At the end I will mention my own joint work with Nitin Nitsure. The talks will be basic and accessible to anyone will basic knowledge of algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20181210T160000 DTEND:20181210T180000 DTSTAMP:20181209T150000Z UID:b7343d1cec821edb372a2cf5fba1334a@cgp.ibs.re.kr SUMMARY:A wrapped Fukaya category of knot complements and hyperbolic knots LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In this talk, I will explain a construction of wrapped Fukaya categoryassociated to the knot complement of a closed 3-manifold and construct a knotinvariant called the Knot Floer Algebra. I will also discuss the proof of a formalityresult entering in the description of the algebra for the case of hyperbolic knots.This is based on a joint work with Youngjin Bae and Seonhwa Kim. END:VEVENT BEGIN:VEVENT DTSTART:20181213T160000 DTEND:20181213T180000 DTSTAMP:20181212T150000Z UID:1a2e73b1ae0b3e4f81d6a4654f944a74@cgp.ibs.re.kr SUMMARY:Little strings and T-duality LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Joonho Kim\n\nEvent: CGP Seminar\n\nAbstract: Six-dimensional little string theory (LST) describes the worldvolume physics of NS5-branes in type IIA or IIB string theory. Its BPS partition function is essentially a generating function for Gopakumar-Vafa invariants of the associated elliptically fibered Calabi-Yau threefolds. I will explain that how the BPS partition function can be obtained from the elliptic genera of supersymmetric strings in little string theory, when all NS5-branes are separated from each other. I will show how the BPS partition function respects T-duality (aka fiber-base duality) which identifies two seemingly different string theories compactified on a circle. END:VEVENT BEGIN:VEVENT DTSTART:20181211T160000 DTEND:20181211T170000 DTSTAMP:20181210T150000Z UID:ca7feb7435b4725d9b2ff86f050d6cb9@cgp.ibs.re.kr SUMMARY:Lax-Milgram theorem revisited and its applications to kinetic equations. LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: Seminar\n\nAbstract: In this talk, we revisit a functional analytic method, the Lax-Milgram theorem, of proving the existence of weak solutions to initial-boundary-value problems for a partial differential equation. We study its applications to the Vlasov-Poisson-Fokker-Planck equation with various types of boundary conditions. END:VEVENT BEGIN:VEVENT DTSTART:20181217T160000 DTEND:20181217T180000 DTSTAMP:20181216T150000Z UID:eb33ff21ebc8711bef2501dc3f59e38f@cgp.ibs.re.kr SUMMARY:Lagrangian Cobordisms and Fukaya categories LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Nadler and I have conjectured that an infinity-category of Lagrangians and their cobordisms can completely recover the Fukaya category for a large class of exact symplectic manifolds. I will explain recent progress in this conjecture, and some applications that have already emerged through the program. END:VEVENT BEGIN:VEVENT DTSTART:20181228T160000 DTEND:20181228T180000 DTSTAMP:20181227T150000Z UID:2d17b687894f6e217f7eea38c743ddfb@cgp.ibs.re.kr SUMMARY:Three block collections in del Pezzo surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yonghwa Cho\n\nEvent: Seminar\n\nAbstract: The derived categories of del Pezzo surfaces admit full exceptional collections consisting of vector bundles. Among these collections, some of them have interesting structures, which are given by so-called three block collections. In this talk, I will briefly review the basic properties of three block collections in del Pezzo surfaces. After that, I will introduce the ongoing attempts to discover how these three block collections can be related to the Q-Gorenstein degenerations of the underlying del Pezzo surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20190104T143000 DTEND:20190104T153000 DTSTAMP:20190103T150000Z UID:43414ff2cdf74a3424386178ea08d1c5@cgp.ibs.re.kr SUMMARY:Elliptic equations with singular drifts on Lipschitz domains LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hyunwoo Kwon\n\nEvent: Seminar\n\nAbstract: We consider the Dirichlet and Neumann problems for second-order linear elliptic equations in a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^n$ ($n\geq 3$) with the first-order term given by a singular vector field b. Under the assumption that $b\in L^n$, we first establish existence and uniqueness of solutions in $L^p_{\alpha}(\Omega)$ for the Dirichlet and Neumann problems. Here $L^p_{\alpha}(\Omega)$ denotes the Sobolev space (or Bessel potential space) with the pair $(\alpha,p)$ satisfying certain conditions. These results extend the classical works of Jerison-Kenig (1995) and Fabes-Mendez-Mitrea (1998) for the Poisson equation. We also prove existence and uniqueness of solutions of the Dirichlet problem with boundary data in $L^2(\partial\Omega)$. This talk is based on joint work with Hyunseok Kim. END:VEVENT BEGIN:VEVENT DTSTART:20190104T160000 DTEND:20190104T180000 DTSTAMP:20190103T150000Z UID:6fdd1c4d9b36a20136117158a2743452@cgp.ibs.re.kr SUMMARY:LaTeX Lectures for Mathematicians LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hyunwoo Kwon\n\nEvent: Seminar\n\nAbstract: The lecture series consists of two parts.
Part I. Some tips on writing mathematics in LaTeX and beamer
I will give several tips on typesetting in math symbols and beamer which are useful.
Part II. How to use TikZ?
TikZ is one of the popular packages when someone draws a picture in LaTeX.
In this lecture, I will give a basic lecture on TikZ by practicing several examples. After introducing several basic notions, we draw some examples from Calculus via TIkZ. Lecture notes will be given at the beginning of the talk via the internet.
Please bring your laptop to practice some examples.
This lecture series is not designed for beginners.
If you do not know how to make a pdf file via LaTeX, this lecture is not for you. END:VEVENT BEGIN:VEVENT DTSTART:20190108T133000 DTEND:20190108T153000 DTSTAMP:20190107T150000Z UID:e63eecb2522a33d090f61ea941098e5b@cgp.ibs.re.kr SUMMARY:Notion of Motives and Grothendieck’s proposal LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: Derived Seminar\n\nAbstract: In the ’60s, one of the key proposals of A. Grothendieck was to find the Q-linear abelian category (Motive) in which all of the Weil cohomology (singular, de Rham, l-adic étale & crystalline cohomology) would factor through. Namely, find universal cohomology in which one could find a universal way to linearize algebraic varieties. His motive for doing so was to prove the Weil conjecture ‘naturally’ by raising the sea level to Interstellar mountain height. This ultimately failed but beginning with Grothendieck, people have tirelessly tried to precisely define this theory for many years which led to Motivic Cohomology and Motivic Homotopy Theory of today that gave the framework for doing homotopy theory in a setting applicable to algebraic geometry and number theory. I will start with a short account of how the Weil cohomology is compatible through the comparisons and trace formulas. END:VEVENT BEGIN:VEVENT DTSTART:20190118T160000 DTEND:20190118T180000 DTSTAMP:20190117T150000Z UID:17b6791cdcdf8fe9c6a07c76be9e6d99@cgp.ibs.re.kr SUMMARY:On Hirschowitz's conjecture on the formal principle LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jun-Muk Hwang\n\nEvent: Seminar\n\nAbstract: A compact complex submanifold of a complex manifold is said tosatisfy the formal principle if its formal neighborhood determines its germ of analyticneighborhoods. In 1981, Hirschowitz conjectured that an unobstructed submanifoldsatisfies the formal principle if its normal bundle is globally generated. I explain an approach to this conjecture by the equivalence method for geometric structures. END:VEVENT BEGIN:VEVENT DTSTART:20190111T140000 DTEND:20190111T160000 DTSTAMP:20190110T150000Z UID:54ad3b58f0d63e98c0f636a5fe0a6b3b@cgp.ibs.re.kr SUMMARY:Lie algebra representations and moduli spaces of sheaves on surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sheldon Katz\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In this talk, I describe a representation of the affine E8 Lie algebra on the cohomology of the moduli space of 1-dimensional stable sheaves on a rational elliptic surface. This gives a precise mathematical explanation of the physicists' "affine E8 global symmetry of the half K3 surface", or "E-string". This construction and proof extends to representations of generalized Kac-Moody Lie algebras on the cohomology of the moduli of stable 1-dimensional sheaves on other surfaces. This is joint with Davesh Maulik. END:VEVENT BEGIN:VEVENT DTSTART:20190128T160000 DTEND:20190128T170000 DTSTAMP:20190127T150000Z UID:82e0c89eea0fb8b8ab33d18a9844764c@cgp.ibs.re.kr SUMMARY:Lectures on SYZ (I) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Mirror symmetry is a duality between complex geometry and symplectic geometry. In 1994, Kontsevich suggested an algebraic way to understand mirror symmetry, which is now known as the homological mirror symmetry. Two years later, Strominger, Yau and Zaslow proposed an entire geometric way to understand mirror symmetry. Roughly speaking, the SYZ conjecture suggests that mirror symmetry can be understood as a duality between two special Lagrangian torus fibrations over an integral affine manifold B with singularities. In this lecture series, I will give an introduction to SYZ mirror symmetry. I will start by reviewing Floer theory and its Morse theoretic approach. Then I will discuss the SYZ construction in details. By coupling with the Witten-Morse theory, I will show that how SYZ approach can be used to understand homological mirror symmetry in the semi-flat case (no singular fibers). The non-semi-flat case will be discussed mainly in dimension 2. We will see the effect of holomorphic disks contribution from the smooth Lagrangian fibers, whose locus on B form a set of geometric objects called walls. I will then discuss the wall crossing and scattering phenomena in the reconstruction problem. END:VEVENT BEGIN:VEVENT DTSTART:20190129T160000 DTEND:20190129T170000 DTSTAMP:20190128T150000Z UID:e1fa6259e0b48c884bf0310ffab96f9e@cgp.ibs.re.kr SUMMARY:Lectures on SYZ (II) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Mirror symmetry is a duality between complex geometry and symplectic geometry. In 1994, Kontsevich suggested an algebraic way to understand mirror symmetry, which is now known as the homological mirror symmetry. Two years later, Strominger, Yau and Zaslow proposed an entire geometric way to understand mirror symmetry. Roughly speaking, the SYZ conjecture suggests that mirror symmetry can be understood as a duality between two special Lagrangian torus fibrations over an integral affine manifold B with singularities. In this lecture series, I will give an introduction to SYZ mirror symmetry. I will start by reviewing Floer theory and its Morse theoretic approach. Then I will discuss the SYZ construction in details. By coupling with the Witten-Morse theory, I will show that how SYZ approach can be used to understand homological mirror symmetry in the semi-flat case (no singular fibers). The non-semi-flat case will be discussed mainly in dimension 2. We will see the effect of holomorphic disks contribution from the smooth Lagrangian fibers, whose locus on B form a set of geometric objects called walls. I will then discuss the wall crossing and scattering phenomena in the reconstruction problem. END:VEVENT BEGIN:VEVENT DTSTART:20190130T160000 DTEND:20190130T170000 DTSTAMP:20190129T150000Z UID:e44465601cf2cf77036aab4847d97de3@cgp.ibs.re.kr SUMMARY:Lectures on SYZ (III) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Mirror symmetry is a duality between complex geometry and symplectic geometry. In 1994, Kontsevich suggested an algebraic way to understand mirror symmetry, which is now known as the homological mirror symmetry. Two years later, Strominger, Yau and Zaslow proposed an entire geometric way to understand mirror symmetry. Roughly speaking, the SYZ conjecture suggests that mirror symmetry can be understood as a duality between two special Lagrangian torus fibrations over an integral affine manifold B with singularities. In this lecture series, I will give an introduction to SYZ mirror symmetry. I will start by reviewing Floer theory and its Morse theoretic approach. Then I will discuss the SYZ construction in details. By coupling with the Witten-Morse theory, I will show that how SYZ approach can be used to understand homological mirror symmetry in the semi-flat case (no singular fibers). The non-semi-flat case will be discussed mainly in dimension 2. We will see the effect of holomorphic disks contribution from the smooth Lagrangian fibers, whose locus on B form a set of geometric objects called walls. I will then discuss the wall crossing and scattering phenomena in the reconstruction problem. END:VEVENT BEGIN:VEVENT DTSTART:20190115T133000 DTEND:20190115T153000 DTSTAMP:20190114T150000Z UID:fd88c7389b2734b979f52667c48a3d24@cgp.ibs.re.kr SUMMARY:Introduction to spectra LOCATION:CGP Main Hall DESCRIPTION:Speaker: Damien Lejay\n\nEvent: Derived Seminar\n\nAbstract: Finding representatives for the cohomology theories defined on the category of varieties is the goal of the theory of motives.A similar story happened in topology where it got a fruitful answer: cohomology theories defined on the category of topological spaces are representable.The objects that represent them are called spectra. END:VEVENT BEGIN:VEVENT DTSTART:20190208T130000 DTEND:20190208T150000 DTSTAMP:20190207T150000Z UID:b6bd427260e0032399620ba741c0240e@cgp.ibs.re.kr SUMMARY:BPS/CFT correspondence: some applications of defects in supersymmetric gauge theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Nikita Nekrasov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: I will explain the formula of Gamayun, Iorgov and Lysovyy relating Painleve VI tau-function to c=1 conformal blocks and some of its generalizations, using the blowup formulas for N_f = 2N_c supersymmetric N=2 d=4 theory. If time permits I will talk about the eigenvalue problem for the elliptic Calogero-Moser system. END:VEVENT BEGIN:VEVENT DTSTART:20190129T133000 DTEND:20190129T153000 DTSTAMP:20190128T150000Z UID:63f6ff5a85864769c57f4ef7de563117@cgp.ibs.re.kr SUMMARY:Reminder on triangulated categories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Derived Seminar\n\nAbstract: In this talk, I will recall the definition of triangulated category. If time permits, I will discuss a few examples. END:VEVENT BEGIN:VEVENT DTSTART:20190213T133000 DTEND:20190213T153000 DTSTAMP:20190212T150000Z UID:913696d3c590324dbd13c0c40a9c6c0b@cgp.ibs.re.kr SUMMARY:Arboreal singularities LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Director's Seminar\n\nAbstract: In this series of seminars, we shall aim at learning about 'arboreal singularities' introduced by the generic structure of skeletons of Weinstein manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20190212T133000 DTEND:20190212T153000 DTSTAMP:20190211T150000Z UID:aa74ee2f6a124879762603ae55a86f59@cgp.ibs.re.kr SUMMARY:t-structures on triangulated categories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Taesu Kim\n\nEvent: Derived Seminar\n\nAbstract: The aim of this talk is to recall the definition of a t-structure on a triangulated category and some related categorical constructions. END:VEVENT BEGIN:VEVENT DTSTART:20190211T160000 DTEND:20190211T180000 DTSTAMP:20190210T150000Z UID:071b45290cfec211bdcaecef4294579b@cgp.ibs.re.kr SUMMARY:A connected sum conjecture and hyperbolic knots LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: There is a well-known trichotomy of knots: hyperbolic, torus or satellite, due to W. Thurston. It has been widely believed that Most of knots are hyperbolic, and precisely stated by C. Adams that the ratio of the number of hyperbolic knots and prime knots up to $n$ crossings goes to 1 as n increases. In other hands, there is another widely believed conjecture by Tait around 120 years ago that the crossing number of a knot is additive under connected sum operation. In 2016. A. Malyutin proved that these two conjectures contradict to each other. In the seminar, I will present his proof and discuss it. END:VEVENT BEGIN:VEVENT DTSTART:20190212T160000 DTEND:20190212T180000 DTSTAMP:20190211T150000Z UID:fdb8f5f2de81364221d54676b52112ea@cgp.ibs.re.kr SUMMARY:delta-invariants of complete intersection log del Pezzo surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: In-kyun Kim\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We estimate delta-invariants of some complete intersection log del Pezzo surfaces of amplitude 1 embedded in weighted projective spaces. As a result, we show that each of these surfaces admit orbifold Kahler–Einstein metrics. This is a joint work with Joonyeong Won. END:VEVENT BEGIN:VEVENT DTSTART:20190219T160000 DTEND:20190219T180000 DTSTAMP:20190218T150000Z UID:dab7adfab31db0b29ac1bb9861087d56@cgp.ibs.re.kr SUMMARY:Geometry and topology of surfaces isogenous to a product and their relatives LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: After the seminal work of Fabrizio Catanese, there have been intensive works studying surfaces isogenous to a product and their relatives. In this talk, I will review these developments and discuss geometry and topology of surfaces isogenous to a product and their relatives. Especially, I will discuss Cox rings and other invariants of some of these surfaces. Part of this talk is based on joint works with JongHae Keum and Davide Frapporti. END:VEVENT BEGIN:VEVENT DTSTART:20190228T160000 DTEND:20190228T180000 DTSTAMP:20190227T150000Z UID:e78749fb7e351fae44b8dab5013d67f8@cgp.ibs.re.kr SUMMARY:Mapping coalgebras LOCATION:CGP Main Hall DESCRIPTION:Speaker: Brice Le Grignou\n\nEvent: CGP Seminar\n\nAbstract: Since Sweedler, we know that the categories of algebras and coalgebras are enriched, tensored over the category of coalgebras. The goal of this talk is to extend this to the case of algebras and coalgebras over an operad. For that purpose, I will use the concepts of Hopf operads and their comodules. I will then show how such enrichements can describe higher structures in homotopical algebra over a field. END:VEVENT BEGIN:VEVENT DTSTART:20190222T130000 DTEND:20190222T140000 DTSTAMP:20190221T150000Z UID:548f773bb813f89fdf875844e754474e@cgp.ibs.re.kr SUMMARY:Algebraic K-theory and motivic cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyun Park\n\nEvent: Seminar\n\nAbstract: During the 3 scheduled talks, I will talk about algebraic K-theory and motivic cohomology of schemes over a field.For the first talk (Thursday) and about half of the second talk (Friday), I will first rapidly introduce the origins of algebraic K-theory and motivic cohomology from the arithmetic, topological and algebro-geometric points of view. Then I will introduce several theorems on motivic cohomology of smooth k-schemes developed from 1980s to 2000s.During the remaining half of the second talk and the third talk (also on Friday), I will talk about my recent approaches on motivic cohomology of k-schemes with singularities, and I will give some flavors of what kinds of interesting applications one can deduce from them. END:VEVENT BEGIN:VEVENT DTSTART:20190221T160000 DTEND:20190221T170000 DTSTAMP:20190220T150000Z UID:4521402784483440e983f4be55525545@cgp.ibs.re.kr SUMMARY:Algebraic K-theory and motivic cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyun Park\n\nEvent: CGP Seminar\n\nAbstract: During the 3 scheduled talks, I will talk about algebraic K-theory and motivic cohomology of schemes over a field.For the first talk (Thursday) and about half of the second talk (Friday), I will first rapidly introduce the origins of algebraic K-theory and motivic cohomology from the arithmetic, topological and algebro-geometric points of view. Then I will introduce several theorems on motivic cohomology of smooth k-schemes developed from 1980s to 2000s.During the remaining half of the second talk and the third talk (also on Friday), I will talk about my recent approaches on motivic cohomology of k-schemes with singularities, and I will give some flavors of what kinds of interesting applications one can deduce from them. END:VEVENT BEGIN:VEVENT DTSTART:20190225T160000 DTEND:20190225T180000 DTSTAMP:20190224T150000Z UID:690559292cb05e476a5a7eb4a62f6e35@cgp.ibs.re.kr SUMMARY:Quasimaps to relative GIT quotients and applications LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jeongseok Oh\n\nEvent: Symplectic Monday Seminar\n\nAbstract: J. Brown proved that the I-function of a toric fibration lies on an overruled Lagrangian cone of its genus zero Gromov-Witten theory which is introduced by A. Givental. In this talk, we will discuss it for partial flag variety fibrations. END:VEVENT BEGIN:VEVENT DTSTART:20190226T160000 DTEND:20190226T180000 DTSTAMP:20190225T150000Z UID:5e44ce77a915504baa8e7224b416265f@cgp.ibs.re.kr SUMMARY:Product formula for volumes. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: For a given algebraic fibre space X -> Y, if X, Y and the general fibre are of general type, then their volumes are related by the Kawamata's product formula. We can prove that his expectation on the characterization of isotriviality using the Okounkov bodies and the weak positivity of the relative canonical divisor. We study a possible further generalization of the product formula in connection with the Iitaka conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20190305T093000 DTEND:20190305T113000 DTSTAMP:20190304T150000Z UID:e7b0b88a14afd383dae8caa46c8148a1@cgp.ibs.re.kr SUMMARY:An Introduction to Algebraic $K$-theory. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bhamidi Sreedhar\n\nEvent: Intensive Lecture Series\n\nAbstract: The goal of these lectures is to give an elementary introduction to algebraic $K$-theory from the very basics. Our primary focus would be to understand these concepts in the context of algebraic geometry. We shall cover the following topics.● Recall the definitions of exact and abelian categories and introduce $K_0$. ● Discuss Waldhausen categories and the definition of higher algebraic $K$-theory. ● Discuss fundamental theorems of algebraic $K$-theory, for example Resolution, Devissage and Localization Theorems.Time permitting we shall discuss further topics related to the $K$-theory of quotient stacks. For references see [1], [2], [3] & [4] REFERENCES 1. D. Quillen, Higher algebraic K-theory:I , Higher K-theories, Springer-Verlag, Berlin Heidelberg, 341, (1973), 85{147.2. V. Srinivas, Algebraic K-theory , Second edition, Progress in Math., Birkhauser, 90, (1995).3. R. W. Thomason, T. Trobaugh, Higher Algebraic K-Theory Of Schemes And Of Derived Categories, The Grothendieck Festschrift III, Progress in Math., Birkhauser, 88, (1990), 247-435.4. C. Weibel, The K-book: An introduction to algebraic K-theory. Vol. 145. Providence, RI: American Mathematical Society, 2013. END:VEVENT BEGIN:VEVENT DTSTART:20190306T093000 DTEND:20190306T113000 DTSTAMP:20190305T150000Z UID:b1fe4a5b97045e85151f33d21dfb50f0@cgp.ibs.re.kr SUMMARY:An Introduction to Algebraic $K$-theory. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bhamidi Sreedhar\n\nEvent: Intensive Lecture Series\n\nAbstract: The goal of these lectures is to give an elementary introduction to algebraic $K$-theory from the very basics. Our primary focus would be to understand these concepts in the context of algebraic geometry. We shall cover the following topics.● Recall the definitions of exact and abelian categories and introduce $K_0$. ● Discuss Waldhausen categories and the definition of higher algebraic $K$-theory. ● Discuss fundamental theorems of algebraic $K$-theory, for example Resolution, Devissage and Localization Theorems.Time permitting we shall discuss further topics related to the $K$-theory of quotient stacks. For references see [1], [2], [3] & [4] REFERENCES 1. D. Quillen, Higher algebraic K-theory:I , Higher K-theories, Springer-Verlag, Berlin Heidelberg, 341, (1973), 85{147.2. V. Srinivas, Algebraic K-theory , Second edition, Progress in Math., Birkhauser, 90, (1995).3. R. W. Thomason, T. Trobaugh, Higher Algebraic K-Theory Of Schemes And Of Derived Categories, The Grothendieck Festschrift III, Progress in Math., Birkhauser, 88, (1990), 247-435.4. C. Weibel, The K-book: An introduction to algebraic K-theory. Vol. 145. Providence, RI: American Mathematical Society, 2013. END:VEVENT BEGIN:VEVENT DTSTART:20190307T093000 DTEND:20190307T113000 DTSTAMP:20190306T150000Z UID:c56d24289ad1f72547ccf0ec030076bf@cgp.ibs.re.kr SUMMARY:An Introduction to Algebraic $K$-theory. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bhamidi Sreedhar\n\nEvent: Intensive Lecture Series\n\nAbstract: The goal of these lectures is to give an elementary introduction to algebraic $K$-theory from the very basics. Our primary focus would be to understand these concepts in the context of algebraic geometry. We shall cover the following topics.● Recall the definitions of exact and abelian categories and introduce $K_0$. ● Discuss Waldhausen categories and the definition of higher algebraic $K$-theory. ● Discuss fundamental theorems of algebraic $K$-theory, for example Resolution, Devissage and Localization Theorems.Time permitting we shall discuss further topics related to the $K$-theory of quotient stacks. For references see [1], [2], [3] & [4] REFERENCES 1. D. Quillen, Higher algebraic K-theory:I , Higher K-theories, Springer-Verlag, Berlin Heidelberg, 341, (1973), 85{147.2. V. Srinivas, Algebraic K-theory , Second edition, Progress in Math., Birkhauser, 90, (1995).3. R. W. Thomason, T. Trobaugh, Higher Algebraic K-Theory Of Schemes And Of Derived Categories, The Grothendieck Festschrift III, Progress in Math., Birkhauser, 88, (1990), 247-435.4. C. Weibel, The K-book: An introduction to algebraic K-theory. Vol. 145. Providence, RI: American Mathematical Society, 2013. END:VEVENT BEGIN:VEVENT DTSTART:20190308T093000 DTEND:20190308T113000 DTSTAMP:20190307T150000Z UID:ca5ce0ea405f99cf592832e044f46a2b@cgp.ibs.re.kr SUMMARY:An Introduction to Algebraic $K$-theory. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bhamidi Sreedhar\n\nEvent: Intensive Lecture Series\n\nAbstract: The goal of these lectures is to give an elementary introduction to algebraic $K$-theory from the very basics. Our primary focus would be to understand these concepts in the context of algebraic geometry. We shall cover the following topics.● Recall the definitions of exact and abelian categories and introduce $K_0$. ● Discuss Waldhausen categories and the definition of higher algebraic $K$-theory. ● Discuss fundamental theorems of algebraic $K$-theory, for example Resolution, Devissage and Localization Theorems.Time permitting we shall discuss further topics related to the $K$-theory of quotient stacks. For references see [1], [2], [3] & [4] REFERENCES 1. D. Quillen, Higher algebraic K-theory:I , Higher K-theories, Springer-Verlag, Berlin Heidelberg, 341, (1973), 85{147.2. V. Srinivas, Algebraic K-theory , Second edition, Progress in Math., Birkhauser, 90, (1995).3. R. W. Thomason, T. Trobaugh, Higher Algebraic K-Theory Of Schemes And Of Derived Categories, The Grothendieck Festschrift III, Progress in Math., Birkhauser, 88, (1990), 247-435.4. C. Weibel, The K-book: An introduction to algebraic K-theory. Vol. 145. Providence, RI: American Mathematical Society, 2013. END:VEVENT BEGIN:VEVENT DTSTART:20190306T133000 DTEND:20190306T153000 DTSTAMP:20190305T150000Z UID:459f1f21fd51f5f6ce992eb7cb54ee89@cgp.ibs.re.kr SUMMARY:Topology of Hessenberg varieties and related topics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mikiya Masuda\n\nEvent: Intensive Lecture Series\n\nAbstract: Schubert varieties are a family of subvarieties of flag varieties and their topology, geometry and combinatorics are well studied (Schubert calculus). Hessenberg varieties are a rather new family of subvarieties of flag varieties including Springer varieties (or fibers), permutohedral varieties and Peterson varieties. In this three talks I will discuss the topology of Hessenberg varieties and its relation to hyperplane arrangements (1st talk), representation theory of symmetric groups and graph theory (2nd talk), and Gelfand-Zetlin polytopes (3rd talk). END:VEVENT BEGIN:VEVENT DTSTART:20190307T160000 DTEND:20190307T180000 DTSTAMP:20190306T150000Z UID:f9eecdf0460c0083f63eb74e55f02036@cgp.ibs.re.kr SUMMARY:Topology of Hessenberg varieties and related topics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mikiya Masuda\n\nEvent: Intensive Lecture Series\n\nAbstract: Schubert varieties are a family of subvarieties of flag varieties and their topology, geometry and combinatorics are well studied (Schubert calculus). Hessenberg varieties are a rather new family of subvarieties of flag varieties including Springer varieties (or fibers), permutohedral varieties and Peterson varieties. In this three talks I will discuss the topology of Hessenberg varieties and its relation to hyperplane arrangements (1st talk), representation theory of symmetric groups and graph theory (2nd talk), and Gelfand-Zetlin polytopes (3rd talk). END:VEVENT BEGIN:VEVENT DTSTART:20190308T130000 DTEND:20190308T150000 DTSTAMP:20190307T150000Z UID:72a93f9d17b4bd44036abbdccf45b56d@cgp.ibs.re.kr SUMMARY:Topology of Hessenberg varieties and related topics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Mikiya Masuda\n\nEvent: Intensive Lecture Series\n\nAbstract: Schubert varieties are a family of subvarieties of flag varieties and their topology, geometry and combinatorics are well studied (Schubert calculus). Hessenberg varieties are a rather new family of subvarieties of flag varieties including Springer varieties (or fibers), permutohedral varieties and Peterson varieties. In this three talks I will discuss the topology of Hessenberg varieties and its relation to hyperplane arrangements (1st talk), representation theory of symmetric groups and graph theory (2nd talk), and Gelfand-Zetlin polytopes (3rd talk). END:VEVENT BEGIN:VEVENT DTSTART:20190312T160000 DTEND:20190312T180000 DTSTAMP:20190311T150000Z UID:2aa45123b4b652a3f96eb331f42d27ba@cgp.ibs.re.kr SUMMARY:Fano deformation rigidity of rational homogeneous spaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Qifeng Li\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk we discuss the question whether rational homogeneous spaces are rigid under Fano deformation. In other words, given any smooth connected family f:X -> Z of Fano manifolds, if one fiber is biholomorphic to a rational homogeneous space S, whether is f an S-fibration? The cases of Picard number one were studied in a series of papers by J.-M. Hwang and N. Mok. For higher Picard number cases, we notice that the Picard number of a rational homogeneous space G/P is less or equal to the rank of G. Recently A. Weber and J. A. Wisniewski proved that rational homogeneous spaces G/P with Picard numbers equal to the rank of G (i.e. complete flag manifolds) are rigid under Fano deformation. We will study the Fano deformation rigidity of G/P whose Picard number equals to rank G-1. END:VEVENT BEGIN:VEVENT DTSTART:20190314T100000 DTEND:20190314T120000 DTSTAMP:20190313T150000Z UID:7c2f0ba38df25370b47b42dcbd38fda1@cgp.ibs.re.kr SUMMARY:Characterizing symplectic Grassmannians by varieties of minimal rational tangents LOCATION:CGP Main Hall DESCRIPTION:Speaker: Qifeng Li\n\nEvent: Seminar\n\nAbstract: During the study of deformation rigidity of rational homogeneous spaces of Picard number one, Hwang and Mok develop the theory of varieties of minimal rational tangents (VMRT). In the theory of VMRT, one of the main problems is to recognize certain varieties from its VMRT, firstly studied by Mok and then by Hwang and Hwang-Hong etc. It turns out that in principle the deformation rigidity could be obtained as a corollary of the characterization by VMRT. In this talk, we will discuss the characterization of Symplectic and odd Symplectic Grassmannians by their VMRT's. This is a joint work with Jun-Muk Hwang. END:VEVENT BEGIN:VEVENT DTSTART:20190327T153000 DTEND:20190327T173000 DTSTAMP:20190326T150000Z UID:c66af1764faf36d39f8231ae97ec672d@cgp.ibs.re.kr SUMMARY:Langlands Duality and Quantum Field Theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Philsang Yoo\n\nEvent: CGP Seminar\n\nAbstract: It is believed that certain physical duality underlies various versions of Langlands duality in its geometric incarnation. By setting upa mathematical model for relevant physical theories, we suggest a program that enriches mathematical subjects such as geometric Langlands theory and symplectic duality. In this talk, I will try to sketch the big picture of the program with the aim of providing ideas while hiding technical aspects. This talk is mainly based on joint works with Chris Elliott and with Justin Hilburn. END:VEVENT BEGIN:VEVENT DTSTART:20190426T130000 DTEND:20190426T150000 DTSTAMP:20190425T150000Z UID:8f02d24356bb1e7be02004e09f035089@cgp.ibs.re.kr SUMMARY:Index theorems for gauge theories, wall crossing and holonomy saddles LOCATION:CGP Main Hall DESCRIPTION:Speaker: Piljin Yi\n\nEvent: Mathematical Physics Seminar\n\nAbstract: This talk will explore topological invariants of susy gauge theories, with some emphasis on index-like quantities and wall-crossing thereof, and introduce the notion of holonomy saddles. We start with an index theorem that compute the twisted partition functions of supersymmetric gauge theories and explain how the wall-crossing occurs generically despite the naive topological robustness. The latter is also related to how the twisted partition functions typically show rational, rather than integral, behavior. We will explain how this oddity is often a blessing in disguise and propose a universal tool for extracting the truely enumerative Witten indices out of rational twisted partition functions. In part, this finally puts to the rest two-decade-old bound state problems which had originated from the M-theory hypothesis.Along the way, we resolve an old and critical conflict between Kac+Smilga and Staudacher/Pestun, circa 1999~2002, whereby the notion of holonomy saddles emerges and plays a crucial role. More importantly,the holonomy saddle prove to be universal features of supersymmetric gauge theories when the spacetime include a small circle. We explore them further ford=4, N=1 theories, with much ramifications on recent claims on Cardy exponents of their partition functions. END:VEVENT BEGIN:VEVENT DTSTART:20190222T140000 DTEND:20190222T150000 DTSTAMP:20190221T150000Z UID:c1a391e585b8376ab0087059b6e68e0b@cgp.ibs.re.kr SUMMARY:Algebraic K-theory and motivic cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jinhyun Park\n\nEvent: Seminar\n\nAbstract: During the 3 scheduled talks, I will talk about algebraic K-theory and motivic cohomology of schemes over a field.For the first talk (Thursday) and about half of the second talk (Friday), I will first rapidly introduce the origins of algebraic K-theory and motivic cohomology from the arithmetic, topological and algebro-geometric points of view. Then I will introduce several theorems on motivic cohomology of smooth k-schemes developed from 1980s to 2000s.During the remaining half of the second talk and the third talk (also on Friday), I will talk about my recent approaches on motivic cohomology of k-schemes with singularities, and I will give some flavors of what kinds of interesting applications one can deduce from them. END:VEVENT BEGIN:VEVENT DTSTART:20190405T130000 DTEND:20190405T150000 DTSTAMP:20190404T150000Z UID:bd58523d29cad79a80d950b205bbf496@cgp.ibs.re.kr SUMMARY:Fundamental Factorization of a GLSM LOCATION:CGP Main Hall DESCRIPTION:Speaker: Bumsig Kim\n\nEvent: Mathematical Physics Seminar\n\nAbstract: A Landau-Ginzburg model is a pair of a smooth stack and a regular function on it. Fora Landau-Ginzburg model one would like to have a Gromov-Witten type theory: a certain cohomological field theory counting curves in the model. There are some developments when the model is a gauged linear sigma model. We discuss the notion of "fundamental factorization" on themoduli space of stable Landau-Ginzburg maps, which plays the role of virtual fundamental classes in derived level. Polishchuck and Vaintrob constructed fundamental matrixfactorizations for pure LG models to define Fan-Jarvis-Ruan-Witten theory algebraically. We generalize their construction to hybrid models.This talk is based on joint work with Ciocan-Fontanine, Favero, Guere, and Shoemaker. END:VEVENT BEGIN:VEVENT DTSTART:20190219T133000 DTEND:20190219T153000 DTSTAMP:20190218T150000Z UID:a01af55a2952456a6f890f22a912fcbd@cgp.ibs.re.kr SUMMARY:T-structrures II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Damien Lejay\n\nEvent: Derived Seminar\n\nAbstract: We shall look at basic lemmas regarding t-structures following Lurie’s book ‘Higher Algebra’. END:VEVENT BEGIN:VEVENT DTSTART:20190226T133000 DTEND:20190226T153000 DTSTAMP:20190225T150000Z UID:5535eaec91e8f6c839f4a732eaa440f3@cgp.ibs.re.kr SUMMARY:Yet another introduction to algebraic $K$-theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Rune Haugseng\n\nEvent: Derived Seminar\n\nAbstract: If $C$ is a category with notions of weak equivalences, direct sums, and short exact sequences, the Grothendieck group $K_{0}(C)$ is the abelian group obtained from the commutative monoid of objects of $C$ under direct sum by (1) identifying weakly equivalent objects, (2) adding negatives for direct sum, (3) splitting short exact sequences. Quillen defined higher K-groups $K_{i}(C)$ as the homotopy groups $\pi_{i}K(C)$ of a space $K(C)$; for various choices of $C$ these turn out to contain interesting information related to algebraic geometry, number theory, and geometric topology. In this talk I will introduce Waldhausen's definition of $K(C)$ via the $S_{\bullet}$-construction, and attempt to convince the audience that this is the homotopical analogue of enforcing conditions (1)--(3). END:VEVENT BEGIN:VEVENT DTSTART:20190225T140000 DTEND:20190225T153000 DTSTAMP:20190224T150000Z UID:47fdbc524f4ad537807dae971d5ed721@cgp.ibs.re.kr SUMMARY:Polynomial invariants of spatial graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngsik Huh\n\nEvent: Seminar\n\nAbstract: Graphs embedded in the Euclidean 3-space are called spatial graphs. As an extension of knot theory, fixing a combinatorial graph, we may challenge to distinguish the equivalence classes of spatial graphs such as ambient isotopic classes. This talk is prepared for a quick introduction to polynomial invariants of spatial graphs.In the 1st talk, we will look over how polynomial invariants are established from skein theory and Temperly-Lieb algebra, and look into a specific example of such invariants, Yamada Polynomial, in the 2nd talk. This talk will be given in Korean. END:VEVENT BEGIN:VEVENT DTSTART:20190305T160000 DTEND:20190305T180000 DTSTAMP:20190304T150000Z UID:335af5a6030c61c25238c559b1f9096b@cgp.ibs.re.kr SUMMARY:On the Motivic Sphere Spectrum and Hilbert Schemes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Elden Elmanto\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will explain the following result: the zero-th space of the motivic sphere spectrum is the group completion of a certain variant of the Hilbert scheme of points on infinite dimensional affine space. This is an algebraic version of (the zeroth-level) of Pontrajgin-Thom's description of the stable homotopy groups of spheres in terms of framed manifolds. No prior knowledge of motivic homotopy theory will be assumed. END:VEVENT BEGIN:VEVENT DTSTART:20190304T160000 DTEND:20190304T180000 DTSTAMP:20190303T150000Z UID:5a910a59f4d1a4fbb46f2e96e4b0be08@cgp.ibs.re.kr SUMMARY:Introduction to defect 2d topological field theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will give an introduction to defected 2d topological field theory and the associated pivotal 2-category. The category of smooth algebraic varieties, symplectic manifolds and Landau-Ginzburg models are typical geometric examples of pivotal 2-categories and they are believed to be the associated pivotal 2-category of some defected 2d TFT. END:VEVENT BEGIN:VEVENT DTSTART:20190311T160000 DTEND:20190311T180000 DTSTAMP:20190310T150000Z UID:0a41b95e256f20ee496cd86d17198e57@cgp.ibs.re.kr SUMMARY:2d TQFTs from Calabi-Yau varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: As a conjectural example of 2d defect TQFT, we will see that Calabi-Yau varieties form a pivotal 2-category and how to extract 2d open/closed TQFTs from it. END:VEVENT BEGIN:VEVENT DTSTART:20190318T133000 DTEND:20190318T153000 DTSTAMP:20190317T150000Z UID:3ea2227fbbdc4d5e2c07768ca3b74b76@cgp.ibs.re.kr SUMMARY:Introduction to Chow motives LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Derived Seminar\n\nAbstract: After proposed by Alexander Grothendieck, the theory of motives has been one of the most attractive and exciting research areas in algebraic geometry. Especially, Chow motives of algebraic varieties are interesting invariants containing lots of information about them. In this talk, we will review basic theory of Chow motives. END:VEVENT BEGIN:VEVENT DTSTART:20190325T133000 DTEND:20190325T153000 DTSTAMP:20190324T150000Z UID:ddf86cc8c9cb0f8dc2314f6b6e22f28e@cgp.ibs.re.kr SUMMARY:Introduction to Voevodsky motives LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Derived Seminar\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20190319T170000 DTEND:20190319T183000 DTSTAMP:20190318T150000Z UID:bfc86557ca3ff37274ff61b70c2e346a@cgp.ibs.re.kr SUMMARY:Brauer groups and rational points on varieties LOCATION:CGP Main Hall DESCRIPTION:Speaker: Taekyung Kim\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Brauer groups are classical invariants of fields with remarkable importance. It orginally came from the classification problem of division algebras or central simple algebras with center being the given field. After Azumaya and Grothendieck, the notion of Brauer groups can also be thought as an invariant of schemes. It has many geometric and arithmetic applications since then. In the seminal talk given by Y.~I.~Manin at ICM in 1970, Manin suggested that the Brauer group of a variety can be used to ``explain'' the (non-)existence (Hasse principle) and/or density of the rational points (weak approximation) on the variety. In this talk, I will quickly recall the classical definition and properties of Brauer groups over fields and algebraic varieties, and will show by example how we can use this notion to explain such arithmetic properties of rational points on algebraic varieties. Current state of this business will be addressed, especially for del Pezzo surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20190326T160000 DTEND:20190326T180000 DTSTAMP:20190325T150000Z UID:706ed19c19cdd48eb4717904d796cc68@cgp.ibs.re.kr SUMMARY:Bundles on prime Fano threefolds of degree 22 LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyeong-Dong Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: According to the classification of Fano threefolds with Picard number one, there exist four classes of such varieties with the vanishing third Betti number. Namely, the projective space $\mathbb P^3$, the quadric $\mathbb Q^3$, the del Pezzo threefold $V_5$ of degree 5, and the Fano threefold $V_{22}$ of genus 12. They have Fano index 4, 3, 2, 1, respectively, and are all deformation-equivalent to the smooth closure of an orbit under the action of $SL(2, \mathbb C)$. Indeed, the Fano threefold $V_{22}$ is the only one with nontrivial infinitesimal deformation among them. Since $V_{22}$ can be defined by nets of alternating 2-form, it is the zero locus of general global section of the vector bundle $(\wedge^2 \mathcal U^*)^{\oplus 3}$ on the Grassmannian $Gr(3, 7)$, where $\mathcal U$ denotes the universal subbundle of rank 3. Using the Koszul complex and Borel-Weil-Bott theorem, we can find some arithmetically Cohen-Macaulay bundles on $V_{22}$ including the restriction of the universal subbundle and universal quotient bundle on $Gr(3, 7)$. As one step in order to study Ulrich bundles on $V_{22}$, I will explain the classification result of irreducible equivariant Ulrich bundles on $Gr(3, 7)$. END:VEVENT BEGIN:VEVENT DTSTART:19700101T133000 DTEND:19700101T153000 DTSTAMP:19700101T000000Z UID:95765768e3497cd47d7758cb0d1e4ebf@cgp.ibs.re.kr SUMMARY:Sheaves and sites LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Derived Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20190401T133000 DTEND:20190401T153000 DTSTAMP:20190331T150000Z UID:f951887c305b046f01f89c1050859173@cgp.ibs.re.kr SUMMARY:Sheaves and sites LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Derived Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20190408T133000 DTEND:20190408T153000 DTSTAMP:20190407T150000Z UID:4a1a3ae35095e1cebb593cf3cccee4f2@cgp.ibs.re.kr SUMMARY:Sheaf cohomology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Derived Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20190419T130000 DTEND:20190419T150000 DTSTAMP:20190418T150000Z UID:4ea5b3198fe23da883f669886a7528c1@cgp.ibs.re.kr SUMMARY:From Walking Backgrounds to the Early Universe LOCATION:CGP Main Hall DESCRIPTION:Speaker: Lilia Anguelova\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Walking gauge theories are a class of theories, whose gauge coupling is approximately constant in a certain intermediate energy range. This nearly-conformal region is of great interest phenomenologically. However, like any strong-coupling regime, it is difficult to address with standard QFT methods. Modern developments in gauge/gravity duality provide powerful tools to address such regimes. In particular, a recently found class of type IIB supergravity solutions is dual to walking gauge theories. Among other topics, this allows non-perturbative description of a class of inflationary models with a composite inflaton. We discuss work in progress on non-standard inflationary or quintessence models, obtained from unstable probe-brane embeddings in such walking backgrounds. END:VEVENT BEGIN:VEVENT DTSTART:20190422T160000 DTEND:20190422T180000 DTSTAMP:20190421T150000Z UID:27e57d1c7438d53782d25b548c80067b@cgp.ibs.re.kr SUMMARY:Introduction to string polytopes and their combinatorics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Seminar\n\nAbstract: Let $G$ be the special linear group $\mathrm{SL}_{n+1}(\mathbb{C})$. For a reduced word $\mathbf{i}$ of the longest element in the Weyl group $\mathfrak{S}_{n+1}$ of $G$ and a dominant weight $\lambda$, one can associate the string polytope $\Delta_{\mathbf i}(\lambda)$ which encodes weights of the $G$-irreducible representation of highest weight $\lambda$. It is known that the combinatorics of string polytopes depend on a choice of $\mathbf i$. In the first talk, we recall the definition of string polytopes for any semisimple simply connected Lie group and study their representation theoretic meaning. Moreover, we review the description of string cones given by Gleizer--Postnikov when $G = \mathrm{SL}_{n+1}(\mathbb{C})$. In the second talk, we study the combinatorics of string polytopes. Indeed, for a regular dominant weight $\lambda$, we present a necessary and sufficient condition on $\mathbf i$ such that the string polytope $\Delta_{\mathbf i}(\lambda)$ is unimodularly equivalent to the Gelfand--Cetlin polytope, which is the most well-known string polytope.The second talk is based on joint work with Yunhyung Cho, Yoosik Kim, and Kyeong-Dong Park. END:VEVENT BEGIN:VEVENT DTSTART:20190424T133000 DTEND:20190424T153000 DTSTAMP:20190423T150000Z UID:e1891edb548b37f09e58ff3a99dccb5d@cgp.ibs.re.kr SUMMARY:Introduction to string polytopes and their combinatorics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Seminar\n\nAbstract: Let $G$ be the special linear group $\mathrm{SL}_{n+1}(\mathbb{C})$. For a reduced word $\mathbf{i}$ of the longest element in the Weyl group $\mathfrak{S}_{n+1}$ of $G$ and a dominant weight $\lambda$, one can associate the string polytope $\Delta_{\mathbf i}(\lambda)$ which encodes weights of the $G$-irreducible representation of highest weight $\lambda$. It is known that the combinatorics of string polytopes depend on a choice of $\mathbf i$. In the first talk, we recall the definition of string polytopes for any semisimple simply connected Lie group and study their representation theoretic meaning. Moreover, we review the description of string cones given by Gleizer--Postnikov when $G = \mathrm{SL}_{n+1}(\mathbb{C})$. In the second talk, we study the combinatorics of string polytopes. Indeed, for a regular dominant weight $\lambda$, we present a necessary and sufficient condition on $\mathbf i$ such that the string polytope $\Delta_{\mathbf i}(\lambda)$ is unimodularly equivalent to the Gelfand--Cetlin polytope, which is the most well-known string polytope.The second talk is based on joint work with Yunhyung Cho, Yoosik Kim, and Kyeong-Dong Park. END:VEVENT BEGIN:VEVENT DTSTART:20190423T160000 DTEND:20190423T180000 DTSTAMP:20190422T150000Z UID:1503fec9772e4e21ae7b1915a3362a51@cgp.ibs.re.kr SUMMARY:Chow and Voevodsky motives of moduli spaces of vector bundles on curves LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, I will discuss recent developments of the theory of Chow and Voevodsky motives of moduli spaces of vector bundles on curves. END:VEVENT BEGIN:VEVENT DTSTART:20190515T133000 DTEND:20190515T153000 DTSTAMP:20190514T150000Z UID:421d172e29e6e9686e29af26337428c3@cgp.ibs.re.kr SUMMARY:Involutive Lie bialgebras: Algebra LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Director's Seminar\n\nAbstract: Lie bialgebras arise in quantum groups and symplectic topology. In this talk I will introduce the definitions of Lie bialgebras and involutive Lie bialgebras, give a few examples, and discuss some aspects of the homotopical versions of Lie bialgebras and involutive Lie bialgebras. END:VEVENT BEGIN:VEVENT DTSTART:20190506T140000 DTEND:20190506T150000 DTSTAMP:20190505T150000Z UID:bc0dbf63fba49f6bf1f4692cf6e7b89e@cgp.ibs.re.kr SUMMARY:Dispersive deformations of Poisson structures of Dubrovin-Novikov type LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Guido Carlet\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: Dispersive Poisson brackets and bi-Hamiltonian structures on formal loop spaces play an important role in the description of integrable hierarchies, especially in the setting of hierarchies of topological type. We will first review the general framework and motivation for the study of such objects, including the triviality theorem for Poisson structures and the notion of central invariants of a bi-Hamiltonian structure. We will then discuss our recent work, which include the proof, using spectral sequences techniques, of the triviality of the bi-Hamiltonian cohomology of semi-simple Poisson brackets of hydrodynamic type. That in turn implies the existence of arbitrary order dispersive deformations, starting from any choice of central invariants. Finally we will briefly describe our recent results on the multivariable setting. Based on joint works with H. Posthuma, S. Shadrin, M. Casati, R. Kramer. END:VEVENT BEGIN:VEVENT DTSTART:20190506T153000 DTEND:20190506T163000 DTSTAMP:20190505T150000Z UID:e3cee3e9ffdd1fe80210987dfc732970@cgp.ibs.re.kr SUMMARY:Polynomial solutions for KdV-type hierarchies LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Johan van de Leur\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: Kac and Peterson showed in 1985 that a level one representation of the affine Lie algebra of type An has p(n+1) different vertex operator realizations. Here p is the partition function. The corresponding Loop group orbit of the highest weight vector, is described by a hierarchy of differential equations. For the case of A1 there are two such realizations, viz. the principal realization, related to the KdV hierarchy, and the homogeneous realization, related to the AKNS hierarchy. In this talk I will describe all polynomial solutions (tau-functions) for the various hierarchies of type An.This is based on joined work with Victor Kac. END:VEVENT BEGIN:VEVENT DTSTART:20190507T094000 DTEND:20190507T104000 DTSTAMP:20190506T150000Z UID:b3f1d94efdd69d99f3b98227ee15adb5@cgp.ibs.re.kr SUMMARY:Gromov-Witten invariants of P1 coupled to the BGW KdV tau function LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Paul Norbury\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: We consider the pull-back of a natural sequence of cohomology classes on the moduli space of stable curves to the moduli space of stable maps. These classes are related to the Brezin-Gross-Witten tau function of the KdV hierarchy. Insertions of the pull-backs of the classes into the integrals defining Gromov-Witten invariants define new invariants which we show in the case of target P1 are given by a random matrix integral and satisfy the Toda equation. END:VEVENT BEGIN:VEVENT DTSTART:20190507T110000 DTEND:20190507T120000 DTSTAMP:20190506T150000Z UID:3d6517299b7438c527daccdd6bb99f73@cgp.ibs.re.kr SUMMARY:Tau functions, Fredholm determinants and combinatorics LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Oleg Lisovyi\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: I will explain how to associate a tau function to the Riemann-Hilbert problem set on a union of non-intersecting smooth closed curves with generic jump matrix. The main focus will be on the one-circle case, relevant to the analysis of Painlevé VI equation and its degenerations to Painlevé V and III. The tau functions in question will be defined as block Fredholm determinants of integral operators with integrable kernels. They can be alternatively represented as combinatorial sums over tuples of Young diagrams which coincide with the dual Nekrasov-Okounkov instanton partition functions for Riemann-Hilbert problems of isomonodromic origin. END:VEVENT BEGIN:VEVENT DTSTART:20190507T140000 DTEND:20190507T150000 DTSTAMP:20190506T150000Z UID:9a4f7b0f628f6408ba2fcec31950ac24@cgp.ibs.re.kr SUMMARY:Integrable structures of cubic Hodge integrals LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kanehisa Takasaki\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: Around 2003, C.-C. Mellissa Liu, Kefeng Liu and Jian Zhou presented a combinatorial description of two-partition cubic Hodge integrals that generalizes the Marino-Vafa formula for one-partition cubic Hodge integrals. Moreover, Zhou pointed out that generating functions of those combinatorial expressions become tau functions of the (one-and two-component) KP and 2D Toda hierarchies. I reconsider these tau functions in the case where a parameter of the cubic Hodge integrals is specialized to a set of particular discrete values. The tau functions therein turn out to be related to the generalized KdV hierarchies or the hungry Lotka-Volterra (aka Bogoyavlensky-Itoh) hierarchies depending on the value of the parameter. This talk is based on collaboration with Toshio Nakatsu. END:VEVENT BEGIN:VEVENT DTSTART:20190508T094000 DTEND:20190508T104000 DTSTAMP:20190507T150000Z UID:2324703953dada858ebbe26417cd0960@cgp.ibs.re.kr SUMMARY:Interacting integrable tops and long-range spin chains LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Andrei Zotov\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: We discuss a family of classical integrable systems describing dynamics of M interacting gl(N) integrable tops. Our construction is based on the GL(N) R-matrix satisfying the associative Yang-Baxter equation. The obtained systems can be considered as extensions of the spin type Calogero-Moser models with (the classical analogues of) anisotropic spin exchange operators given in terms of the R-matrix data. The models can be described as Hitchin type systems on SL(NM) bundles with non-trivial characteristic classes. Possible applications to the quantum spin chains of the Inozemtsev-Haldane-Shastry type are explained. END:VEVENT BEGIN:VEVENT DTSTART:20190508T110000 DTEND:20190508T120000 DTSTAMP:20190507T150000Z UID:29d503e76a40b99a582071de46d9a066@cgp.ibs.re.kr SUMMARY:Gromov--Witten invariants of Fano orbifold lines of type D and integrable hierarchies. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Todor Milanov\n\nEvent: 2nd IBS-CGP Workshop on integrable systems and applications\n\nAbstract: This is a joint work with Jipeng Cheng. We prove that the Gromov--Witten invariants of a Fano orbifold line of type D, are governed by an integrable hierarchy which can be identified with an extension of a certain Kac--Wakimoto hierarchy of type D. The hierarchy can be described in terms of Hirota Bilinear Equations and Lax equations. My plan is to explain both formulations and the application to Gromov--Witten theory. END:VEVENT BEGIN:VEVENT DTSTART:20190523T100000 DTEND:20190523T110000 DTSTAMP:20190522T150000Z UID:1002a54661370253927106f7f9908e0e@cgp.ibs.re.kr SUMMARY:Deformation problems from Koszul duality. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joost Nuiten\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Over a field of characteristic zero, work of Lurie and Pridham expresses the Koszul duality between the Lie operad and the commutative operad in terms of deformation theory: they establish an equivalence between differential graded Lie algebras and formal moduli problems indexed by Artin commutative algebras. I will discuss how this result can be extended to more general Koszul dual pairs of operads over a field of characteristic zero. For example, the pre-Lie algebra structure on the deformation complex of an algebra corresponds to a concrete deformation problem indexed by Perm-algebras. One can also apply this to the coloured operad for nonunital operads, which is, in a relative sense, Koszul self-dual. This provides an equivalence between nonunital operads and certain kinds of formal moduli problems, which extends to the level of algebras. Joint work with D. Calaque and R. Campos. END:VEVENT BEGIN:VEVENT DTSTART:20190522T100000 DTEND:20190522T110000 DTSTAMP:20190521T150000Z UID:dbdc0c8eb483f6b22f06e4aa8694d67d@cgp.ibs.re.kr SUMMARY:Tangent ∞-categories and Goodwillie calculus LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Michael Ching\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Cockett and Cruttwell (following Rosický) have developed an abstract categorical framework which includes tangent bundles on smooth manifolds, tangent structures in algebraic geometry, synthetic differential geometry and other situations arising in logic and theoretical computer science. This talk is on joint work with Kristine Bauer and Matthew Burke that puts tangent bundles on ∞-categories into the same picture. We introduce a notion of tangent structure on an (∞,2)-category, and show that the (∞,2)-category of presentable ∞-categories admits such a structure. This result lays the foundation for importing concepts from differential geometry, such as jet bundles and connections, into homotopy theory in a formal way. For example, we show that n-jets in the tangent structure correspond precisely to the n-excisive functors of Goodwillie calculus. END:VEVENT BEGIN:VEVENT DTSTART:20190521T100000 DTEND:20190521T110000 DTSTAMP:20190520T150000Z UID:d2bc16b8208bdb713289e8c1b59fa822@cgp.ibs.re.kr SUMMARY:Model structures for correspondences and bifibrations. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Daniel Stevenson\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: In ordinary category theory, profunctors from a category A to a category B have several equivalent descriptions, for example as correspondences or as two sided fibrations. In this talk we will discuss these concepts in the context of ∞-categories. If A and B are ∞-categories we will describe a model structure on the category of correspondences from A to B. We will also describe a model structure on the category of simplicial sets over A x B whose fibrant objects are the bifibrations from A to B in the sense of Lurie. Finally we will discuss several Quillen equivalences which relate these model structures and the model structure for left fibrations over $A^{op}$ x B. END:VEVENT BEGIN:VEVENT DTSTART:20190521T113000 DTEND:20190521T123000 DTSTAMP:20190520T150000Z UID:ab18f11139cf9c84819c7779710a6cbe@cgp.ibs.re.kr SUMMARY:The theory of real cyclotomic spectra. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jay Shah\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: The topological Hochschild homology groups $THH_n(R)$ give powerful and well-studied invariants of associative rings. They refine to the structure of a cyclotomic spectrum. When one is given an associative ring with an anti-involution, or more generally an $E_\sigma$-algebra in $C_2$-equivariant spectra, one has the more sophisticated invariant of real topological Hochschild homology $THR$, which admits the structure of a real cyclotomic spectrum. In joint work with J.D. Quigley, we reformulate the theory of real cyclotomic spectra along the lines of Thomas Nikolaus and Peter Scholze's beautiful reimagining of the theory of cyclotomic spectra. The key idea is to make use of the $C_2$-parametrized Tate construction. END:VEVENT BEGIN:VEVENT DTSTART:20190524T113000 DTEND:20190524T123000 DTSTAMP:20190523T150000Z UID:cac5b175a205434e5aac30a0a32baa03@cgp.ibs.re.kr SUMMARY:Operadic categories and 2-Segal spaces. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joachim Kock\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Batanin and Markl introduced the notion of operadic category as a machinery used to prove the duoidal Deligne conjecture. I will explain a new approach to operadic categories based on the decalage comonad, and explain how discrete 2-Segal spaces are a special case of operadiccategories. This is joint work with Richard Garner and Mark Weber. END:VEVENT BEGIN:VEVENT DTSTART:20190520T100000 DTEND:20190520T110000 DTSTAMP:20190519T150000Z UID:0d726817e4656f217cfa890f9785d559@cgp.ibs.re.kr SUMMARY:Broken techniques for disappearing things. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hiro Lee Tanaka\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: I'll talk about some applications of moduli stacks of "broken" objects to help encode higher algebraic structures. One application, from joint work with Jacob Lurie, is to use broken gradient trajectories on a point to encode associative algebra structures, and to ultimately construct spectrum-level lifts of Floer-theoretic invariants. A new application is to encode the s-dot construction for Fukaya categories, and in particular, the paracyclic structure of the s-dot construction. This involves the use of broken "paracyclic lines," which we'll also define and explain. END:VEVENT BEGIN:VEVENT DTSTART:20190524T100000 DTEND:20190524T110000 DTSTAMP:20190523T150000Z UID:c33687aea1460d6d4b695db2e4059d46@cgp.ibs.re.kr SUMMARY:Decomposition spaces and objective models of symmetric functions. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Imma Gálvez Carrillo\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Joint work with Joachim Kock (UAB) and Andy Tonks (Leicester).I will outline the theory of decomposition (a.k.a. 2-Segal) spaces and present a particularly rich family of examples that provide an abstract (combinatorial) framework for symmetric functions and their generalisations, and their associated Hopf algebras. END:VEVENT BEGIN:VEVENT DTSTART:20190521T143000 DTEND:20190521T153000 DTSTAMP:20190520T150000Z UID:7433cb619910da78a2b338c510894560@cgp.ibs.re.kr SUMMARY:Cellular diagonal approximation for the associahedra. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Andrew Tonks\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Stasheff's associahedron is a central object (at least on the conference poster!) in homotopical algebra, in particular because the cellular chain complexes of the associahedra define the d.g. A-infinity operad . They also appear in areas such as representation theory and theoretical physics. In this talk we use the theory of fibre polytopes to give a topological operad structure on a certain realization of the associahedra as topological spaces, and provide a compatible topological diagonal approximation. This talk is based on [arxiv.org/abs/1902.08059] with Naruki Masuda, Hugh Thomas and Bruno Vallette. END:VEVENT BEGIN:VEVENT DTSTART:20190520T143000 DTEND:20190520T153000 DTSTAMP:20190519T150000Z UID:67ff8df4a04990637c106787e1ba0c7a@cgp.ibs.re.kr SUMMARY:Symmetries of enriched category theory. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Andrew Macpherson\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: I will present a calculation of the automorphism group of the category of V-enriched categories in terms of the monoidal automorphism group of V and the symmetry properties of the monoidal structure, generalising work of Barwick and Schommer-Pries in the case of n-categories. It has implications for the uniqueness of additional structures on the category VCat, such as the formation of opposites when V is symmetric monoidal. END:VEVENT BEGIN:VEVENT DTSTART:20190520T113000 DTEND:20190520T123000 DTSTAMP:20190519T150000Z UID:062ca50589425b7186488b54c0d7a8a6@cgp.ibs.re.kr SUMMARY:Linear cogebras up to homotopy LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Damien Lejay\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: The homotopy theory of algebras over an operad can be understood using cocomplete (i.e locally conilpotent) cogebras.For this, one uses the Bar adjunction and shows that it induces an equivalence of model categories.For example: one can endow the category of cocomplete coassociative cogebra with a model structure such thatit becomes equivalent to the model category of A_∞-algebras.Dualising all the constructions, I will show how the homotopy theory of cogebras over an operadcan be understood using a Cobar adjunction with the category of complete algebras.for example: one can endow the category of complete associative algebras with a model structure such thatit becomes equivalent to the model category of A_∞-cogebras. This is Joint work with Brice Le Grignou. END:VEVENT BEGIN:VEVENT DTSTART:20190523T113000 DTEND:20190523T123000 DTSTAMP:20190522T150000Z UID:23912a82c7e598f592d761b415bc2f7c@cgp.ibs.re.kr SUMMARY:Twisted Calabi-Yau algebras and duality. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Inbar Klang\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: Calabi-Yau algebras satisfy a certain dualizability condition, which implies that they give rise to noncompact 2-dimensional topological field theories. I will discuss joint work with Ralph Cohen, in which we defined and studied a spectrum-level generalization of the Calabi-Yau condition, and talk about factorization homology and how it ties in with this topic. END:VEVENT BEGIN:VEVENT DTSTART:20190522T113000 DTEND:20190522T123000 DTSTAMP:20190521T150000Z UID:cd05963ce99af3b11ba1441d18c2fe66@cgp.ibs.re.kr SUMMARY:Tate coalgebras and spaces. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Gijs Heuts\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: The suspension spectrum of a space is a homotopy-coherent commutative coalgebra spectrum. This assignment is far from fully faithful, though; the homotopy teory of such coalgebras is not a good model for the homotopy theory of spaces. I will discuss what refinement is needed to get a homotopy theory which is equivalent to that of simply-connected spaces, inspired by Goodwillie calculus. This refinement involves the Tate diagonal (and higher analogs of it) in the category of spectra. END:VEVENT BEGIN:VEVENT DTSTART:20190514T160000 DTEND:20190514T180000 DTSTAMP:20190513T150000Z UID:834ddac8762f3a72ed196bbe54bf4e84@cgp.ibs.re.kr SUMMARY:$3$-folds of general type and canonically of fiber type with high genus LOCATION:CGP Main Hall DESCRIPTION:Speaker: YongJoo Shin\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Let $S$ be a minimal surface of general type with $p_g(S)=0$. Bogomolov-Miyaoka-Yau inequality gives $K_S^2=1,2,\dots, 8$ or $9$. In this talk, we deal with the case $K_S^2=7$ in detail, and also consider how to construct smooth minimal $3$-folds of general type whose smooth birational model $F$ of the generic irreducible component in the generic fiber of the canonical map has $p_g(F)>19$ when $F$ is a surface, and $g(F)>13$ when $F$ is a curve. They would give an answer for a question of Chen and Cui to find such $3$-folds of general type canonically fibred by surfaces with high geometric genus or by curves of high genus. END:VEVENT BEGIN:VEVENT DTSTART:20190524T133000 DTEND:20190524T153000 DTSTAMP:20190523T150000Z UID:b885bc8212b8789d73f6144021156838@cgp.ibs.re.kr SUMMARY:Quantum toroidal algebras and instantons in supersymmetric gauge theories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jean-Emile Bourgine\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Quantum toroidal algebras are obtained from standard Liealgebra by two affinizations (toroidal) and one quantization. Thus,they correspond to affine quantum groups and, like the latter, can beused to build quantum integrable systems. These algebras also describethe symmetries of instanton moduli spaces for five dimensional (N=1)supersymmetric gauge theories, thereby providing proofs of thecorrespondence with q-deformed conformal blocks (the 5D version of theAGT-correspondence). In this talk, I will give an elementaryintroduction to quantum toroidal algebras. Then, considering the stringtheory realization of the gauge theory, I will introduce acorrespondence between branes and representations of the algebra. Usingthe idenfication of the topological strings vertex with an intertwinerof the algebra, the algebraic construction of gauge theory observables(partition function and qq-characters) will be derived. Finally, I willconclude with a brief overview of recent results, including theinterpretation of strings' S-duality, the emergence of new algebras,the degenerate limit reducing 5D (N=1) to 4D (N=2) gauge theories, andcomment on the AGT-correspondence. END:VEVENT BEGIN:VEVENT DTSTART:20190523T143000 DTEND:20190523T153000 DTSTAMP:20190522T150000Z UID:d0a1a41fd45c60862b05729f8c8a6a24@cgp.ibs.re.kr SUMMARY:The Universal Property of Derived Manifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: David Carchedi\n\nEvent: Current Directions in Homotopical Algebra\n\nAbstract: The role of transversality in differential topology has a rich history. It is well known that non-transverse pullbacks need not exist in the category of manifolds, and when they do, they do not have the good cohomological properties one would expect of a good intersection. Derived manifolds generalize the concept of smooth manifolds to allow arbitrary (iterative) intersections to exist as smooth objects, regardless of transversality. In this talk we will explain a recent result of ours together with Pelle Steffens concerning the universal property of the infinity-category of derived manifolds, and its connection with the concept of a $C^\infty$-ring. END:VEVENT BEGIN:VEVENT DTSTART:20190708T130000 DTEND:20190708T143000 DTSTAMP:20190707T150000Z UID:d6a498fe6f24f577474b785a65a83b51@cgp.ibs.re.kr SUMMARY:Introduction to Mathematical Theory for Many Particle System 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donghyun Lee\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: Interacting particle system (such as gas, fluid, plasma, etc) is very important physical system.Under hypothesis of continuum mechanics, it can be analyzed mathematically by various partialdifferential equation models. There are two big branches depending on our view points : mesoscopic description (PDE for probability density function) and macroscopic one (PDE for velocity).In this short lecture series, we study basic mathematical theory for two fundamental equationsthat describe fluid and gas : Navier-Stokes equation and Boltzmann equation, respectively. More-over, using basic energy method and functional analysis, we study asymptotic behaviors for somesimple cases.
* Class 1 : Many particle system : Introduction to Navier-Stokes and Boltzmann equations
* Class 2 : Basic mathematical tools : $L^p$, Sobolev spaces, and functional inequalities
* Class 3 : Energy estimate and asymptotic behavior analysis of many particle system.
END:VEVENT BEGIN:VEVENT DTSTART:20190709T110000 DTEND:20190709T120000 DTSTAMP:20190708T150000Z UID:12f62cc0ced43d0cc8178c8bcc397a3a@cgp.ibs.re.kr SUMMARY:Introduction to Mathematical Theory for Many Particle System 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donghyun Lee\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: Interacting particle system (such as gas, fluid, plasma, etc) is very important physical system.Under hypothesis of continuum mechanics, it can be analyzed mathematically by various partialdifferential equation models. There are two big branches depending on our view points : mesoscopic description (PDE for probability density function) and macroscopic one (PDE for velocity).In this short lecture series, we study basic mathematical theory for two fundamental equationsthat describe fluid and gas : Navier-Stokes equation and Boltzmann equation, respectively. More-over, using basic energy method and functional analysis, we study asymptotic behaviors for somesimple cases.
* Class 1 : Many particle system : Introduction to Navier-Stokes and Boltzmann equations
* Class 2 : Basic mathematical tools : $L^p$, Sobolev spaces, and functional inequalities
* Class 3 : Energy estimate and asymptotic behavior analysis of many particle system.
END:VEVENT BEGIN:VEVENT DTSTART:20190710T170000 DTEND:20190710T183000 DTSTAMP:20190709T150000Z UID:95622a62502b1f9668a2a626fdb1d1ac@cgp.ibs.re.kr SUMMARY:Introduction to Mathematical Theory for Many Particle System 3 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donghyun Lee\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: Interacting particle system (such as gas, fluid, plasma, etc) is very important physical system.Under hypothesis of continuum mechanics, it can be analyzed mathematically by various partialdifferential equation models. There are two big branches depending on our view points : mesoscopic description (PDE for probability density function) and macroscopic one (PDE for velocity).In this short lecture series, we study basic mathematical theory for two fundamental equationsthat describe fluid and gas : Navier-Stokes equation and Boltzmann equation, respectively. More-over, using basic energy method and functional analysis, we study asymptotic behaviors for somesimple cases.
* Class 1 : Many particle system : Introduction to Navier-Stokes and Boltzmann equations
* Class 2 : Basic mathematical tools : $L^p$, Sobolev spaces, and functional inequalities
* Class 3 : Energy estimate and asymptotic behavior analysis of many particle system.
END:VEVENT BEGIN:VEVENT DTSTART:20190708T150000 DTEND:20190708T163000 DTSTAMP:20190707T150000Z UID:e7d16c5beeb3a8a51c4972b7f89eaa20@cgp.ibs.re.kr SUMMARY:Low-dimensional Topology and Geometric Group Theory 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyungryul Baik\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: We will provide a basic introduction to hyperbolic geometry (mostly in dimension 2). Here the hyperbolic space means a Riemannian metric with constant negativecurvature -1. After that, we will introduce the notion of large-scale geometry (or coarsegeometry). Two metric spaces are said to be coarsely equivalent (or quasi-isometric) ifthey look about the same when we see them from a very very far away. This flexiblenotion of "geometry" will allow us to generalize the notion of hyperbolicity so that we donot have to worry too much about the classical notion of the curvature. END:VEVENT BEGIN:VEVENT DTSTART:20190710T100000 DTEND:20190710T113000 DTSTAMP:20190709T150000Z UID:463b0379b5ff4ef1541765832db2d11a@cgp.ibs.re.kr SUMMARY:Low-dimensional Topology and Geometric Group Theory 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyungryul Baik\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: We will introduce the notion of mapping class groups and some metric spaceson which mapping class groups act. Here a mapping class group is the group of homeo-morphisms from a space to itself up to homotopy (i.e., a continuous deformation). Theelements of mapping class groups for surfaces have been classi ed by Thurston in thegeometric topology perspective which was reproved by Bers in more analytic terms. END:VEVENT BEGIN:VEVENT DTSTART:20190711T093000 DTEND:20190711T103000 DTSTAMP:20190710T150000Z UID:1d6951c62702c814d1640c586817710a@cgp.ibs.re.kr SUMMARY:Low-dimensional Topology and Geometric Group Theory 3 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyungryul Baik\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: We will discuss various recent researches using the notions introduced in twoprevious lectures. END:VEVENT BEGIN:VEVENT DTSTART:20190708T100000 DTEND:20190708T113000 DTSTAMP:20190707T150000Z UID:c46ce9a5637ce7991a955777bc72131e@cgp.ibs.re.kr SUMMARY:첫번째 강의: 페르마의 마지막 정리와 와일즈의 결과 소개 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: 이번 강의에서는 다음 정리의 역사와 증명에 대해 간단하게 공부할 것이다.Theorem 1 (Fermat’s Last theorem, Wiles). 임의의 자연수 n $\ge$ 3에 대하여 다음의 방정식$x^n + y^n = z^n$ and $ xyz \neq 0$은 정수해를 갖지 않는다.이 문제를 해결하기 위해 도입된 여러가지 현대수학들과 와일즈의 증명에 대해서 각종 유명한정리들을 소개하고, 그들의 의미에 대해서 알아본다. END:VEVENT BEGIN:VEVENT DTSTART:20190709T093000 DTEND:20190709T103000 DTSTAMP:20190708T150000Z UID:a9cbd47c3e6ecae7e58204a6bb09d3f1@cgp.ibs.re.kr SUMMARY:두번째 강의: 타원곡선과 리만곡면론 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: 타원곡선과 리만곡면에 대해 소개하고, 복소함수론의 여러결과들을 이용하여 타원곡선과 리만곡면에 대한 여러 정리들을 소개한다. 좀더 자세히 말해서 j-invariant, Weierstrass의 결과와 Riemann-Hurwitz의 정리를 소개한다. 리만곡면 위에 정의된 meromorphic 함수와 differential forms에 대한내용을 공부한다. END:VEVENT BEGIN:VEVENT DTSTART:20190710T150000 DTEND:20190710T163000 DTSTAMP:20190709T150000Z UID:9b26b914704b850dd2ff87d33ab183bd@cgp.ibs.re.kr SUMMARY:세번째 강의: 보형곡선과 보형형식 소개 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: 두 번째 강의에서 했던 내용을 바탕으로 보형곡선과 보형형식을 소개한다. 특히 다음의 군$ \Gamma(N) :={ \bigl(\begin{smallmatrix}a&b \\ c&d\end{smallmatrix} \bigr) \in SL_2(\mathbb{Z} : c \equiv 0 (mod N )} $에 대하여 보형곡선 $X_0(N)$을 정의하고 cusps에 대하여 소개한다. 특정한 $N$에 대하여 $X_0(N)$의 cusps을 분류하고 $X_0(N)$의 종수를 계산하는 공식을 도출해본다. END:VEVENT BEGIN:VEVENT DTSTART:20190708T170000 DTEND:20190708T183000 DTSTAMP:20190707T150000Z UID:4d715bed204a67dd82fbfbf8b8958859@cgp.ibs.re.kr SUMMARY:Introduction to Invariant Theory 1 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jin hyung Park\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: The group action of the general linear group $GL(n,\mathbb{C})$, which is a group of $n \times n$ invertiblematrices under matrix multiplication, on the polynomial ring $S = \mathbb{C}[x_1,..., x_n]$ is given as follows.We may regard $(x_1,..., x_n)$ as an $n \times 1$ matrix, so $A \cdot (x_1,..., x_n)$ is an $n \times 1$ matrix for all$A \in GL(n,\mathbb{C})$. Then the action is given by $A \cdot f(x_1,..., x_n) = f(A \cdot (x_1,..., x_n)).$ This groupaction induces a group action of a subgroup $G \leq GL(n,\mathbb{C})$ on $S$.The purpose of the invariant theory is to study the ring of invariance $S^G$, which consists ofpolynomials $ f(x_1,..., x_n) $ in $S$ such that $A \cdot f(x_1,..., x_n) = f(x_1,..., x_n)$ for all $A \in G.$ One of themost fundamental problems in the invariant theory is Hilbert's 14th problem, which asks whether$S^G$ is always finitely generated. Hilbert proved that the answer is yes when $G$ is a reductive group(this result is known as the Hilbert finiteness theorem). Note that every finite group is reductive.In this lecture, we will show that $S^G$ is finitely generated when $G$ is a finite group. We closelyfollow Hilbert's original approach; we first prove the Hilbert basis theorem, and then, deduce theHilbert finiteness theorem for finite groups. In fact, the proof for the reductive group case is similarto the finite group case. Even though we can prove that $S^G$ is finitely generated, the proof doesnot tell us how to find finite generators of $S^G$. To obtain the finite generators, we consider theHilbert series of $S^G$, which help us find finite generators of $S^G$. In the second lecture, I introducea powerful technique to compute the Hilbert series of $S^G$. Finally, note that a counterexample ofHilbert's 14th problem was constructed by Nagata in 1959. In the final lecture, I briefly explainNagata's counterexample. His example is coming from algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20190710T130000 DTEND:20190710T143000 DTSTAMP:20190709T150000Z UID:9a7866554b0f6e049f53d5b893143d8d@cgp.ibs.re.kr SUMMARY:Introduction to Invariant Theory 2 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jin hyung Park\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: The group action of the general linear group $GL(n,\mathbb{C})$, which is a group of $n \times n$ invertiblematrices under matrix multiplication, on the polynomial ring $S = \mathbb{C}[x_1,..., x_n]$ is given as follows.We may regard $(x_1,..., x_n)$ as an $n \times 1$ matrix, so $A \cdot (x_1,..., x_n)$ is an $n \times 1$ matrix for all$A \in GL(n,\mathbb{C})$. Then the action is given by $A \cdot f(x_1,..., x_n) = f(A \cdot (x_1,..., x_n)).$ This groupaction induces a group action of a subgroup $G \leq GL(n,\mathbb{C})$ on $S$.The purpose of the invariant theory is to study the ring of invariance $S^G$, which consists ofpolynomials $ f(x_1,..., x_n) $ in $S$ such that $A \cdot f(x_1,..., x_n) = f(x_1,..., x_n)$ for all $A \in G.$ One of themost fundamental problems in the invariant theory is Hilbert's 14th problem, which asks whether$S^G$ is always finitely generated. Hilbert proved that the answer is yes when $G$ is a reductive group(this result is known as the Hilbert finiteness theorem). Note that every finite group is reductive.In this lecture, we will show that $S^G$ is finitely generated when $G$ is a finite group. We closelyfollow Hilbert's original approach; we first prove the Hilbert basis theorem, and then, deduce theHilbert finiteness theorem for finite groups. In fact, the proof for the reductive group case is similarto the finite group case. Even though we can prove that $S^G$ is finitely generated, the proof doesnot tell us how to find finite generators of $S^G$. To obtain the finite generators, we consider theHilbert series of $S^G$, which help us find finite generators of $S^G$. In the second lecture, I introducea powerful technique to compute the Hilbert series of $S^G$. Finally, note that a counterexample ofHilbert's 14th problem was constructed by Nagata in 1959. In the final lecture, I briefly explainNagata's counterexample. His example is coming from algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20190711T110000 DTEND:20190711T120000 DTSTAMP:20190710T150000Z UID:58ecb8d2f2f097e77707eb801d29c0fc@cgp.ibs.re.kr SUMMARY:Introduction to Invariant Theory 3 LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jin hyung Park\n\nEvent: 2019 IBS-CGP Mathematics Festival\n\nAbstract: The group action of the general linear group $GL(n,\mathbb{C})$, which is a group of $n \times n$ invertiblematrices under matrix multiplication, on the polynomial ring $S = \mathbb{C}[x_1,..., x_n]$ is given as follows.We may regard $(x_1,..., x_n)$ as an $n \times 1$ matrix, so $A \cdot (x_1,..., x_n)$ is an $n \times 1$ matrix for all$A \in GL(n,\mathbb{C})$. Then the action is given by $A \cdot f(x_1,..., x_n) = f(A \cdot (x_1,..., x_n)).$ This groupaction induces a group action of a subgroup $G \leq GL(n,\mathbb{C})$ on $S$.The purpose of the invariant theory is to study the ring of invariance $S^G$, which consists ofpolynomials $ f(x_1,..., x_n) $ in $S$ such that $A \cdot f(x_1,..., x_n) = f(x_1,..., x_n)$ for all $A \in G.$ One of themost fundamental problems in the invariant theory is Hilbert's 14th problem, which asks whether$S^G$ is always finitely generated. Hilbert proved that the answer is yes when $G$ is a reductive group(this result is known as the Hilbert finiteness theorem). Note that every finite group is reductive.In this lecture, we will show that $S^G$ is finitely generated when $G$ is a finite group. We closelyfollow Hilbert's original approach; we first prove the Hilbert basis theorem, and then, deduce theHilbert finiteness theorem for finite groups. In fact, the proof for the reductive group case is similarto the finite group case. Even though we can prove that $S^G$ is finitely generated, the proof doesnot tell us how to find finite generators of $S^G$. To obtain the finite generators, we consider theHilbert series of $S^G$, which help us find finite generators of $S^G$. In the second lecture, I introducea powerful technique to compute the Hilbert series of $S^G$. Finally, note that a counterexample ofHilbert's 14th problem was constructed by Nagata in 1959. In the final lecture, I briefly explainNagata's counterexample. His example is coming from algebraic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20190527T160000 DTEND:20190527T180000 DTSTAMP:20190526T150000Z UID:787995f85a8f44d986dfb747ebe4312d@cgp.ibs.re.kr SUMMARY:Variation of Kahler-Einstein metrics on noncompact fibrations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In this talk, we will study the positivity of fiberwise Kahler-Einstein metrics on a holomorphic family of noncompact Kahler manifolds. If time permits, we will discuss the extension of the variation across singular fibers. END:VEVENT BEGIN:VEVENT DTSTART:20190530T160000 DTEND:20190530T180000 DTSTAMP:20190529T150000Z UID:f78af4deaa7e74f4e2752f477398a53e@cgp.ibs.re.kr SUMMARY:Localizing quantum Chern classes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yasha Savelyev\n\nEvent: CGP Seminar\n\nAbstract: We describe an analogue of classical Chern classes constructed via Gromov-Witten theory and quantum homology. We may call these $q$-Chern classes. Like Chern classes $q$-Chern classes can be defined for any complex vector bundle, but are also defined for more general smooth fibrations called Hamiltonian fibrations. Moreover $q$-Chern classes can recover classical Chern classes in the complex vector bundle case, in the "semi-classical limit". The latter uses the celebrated Bott periodicity theorem. In particular, like Chern classes $q$-Chern classes give rise to a basic invariant of a smooth manifold: $q$-Pontryagin classes of the tangent bundle. Little is knows about these invariants; one interesting question is whether Novikov's fundamental theorem on topological invariance of Pontryagin classes holds in the $q$-world. Either possibility could be interesting. To get started on this question we develop a local to global approach to $q$-Chern classes, called the global Fukaya category and this is based on the theory of Fukaya categories, ∞-categories and related constructions like (co)-cartesian fibrations, developed by Joyal and Lurie. We overview a part of this story. END:VEVENT BEGIN:VEVENT DTSTART:20190605T133000 DTEND:20190605T153000 DTSTAMP:20190604T150000Z UID:dc79aeb34e8fdcf7bfddae040f100fe2@cgp.ibs.re.kr SUMMARY:Involutive Lie bialgebras: Algebra II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Gabriel C. Drummond-Cole\n\nEvent: Director's Seminar\n\nAbstract: In this talk I will review L-infinity algebras, introduce IBL-infinity algebras (homotopy involutive Lie bialgebras), and discuss some aspects of their homotopy theory. END:VEVENT BEGIN:VEVENT DTSTART:20190617T160000 DTEND:20190617T180000 DTSTAMP:20190616T150000Z UID:7880d670c7dc152add8d818b1f3a7595@cgp.ibs.re.kr SUMMARY:Entropy of symplectomorphisms via Lagrangian cobordisms LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will introduce a notion of entropy of multifunctors of a multicategory (= colored operad) and explain that it can be considered as a generalization of the categorical entropy of exact functors of a triangulated category introduced by Dimitrov-Haiden-Katzarkov-Kontsevich. Applying this to an extended version of Biran-Cornea’s multicategory of Lagrangian cobordisms, I will define an entropy of symplectomorphisms. Finally, I will discuss its basic properties relating it with various other notions of growth rate of symplectomorphisms. END:VEVENT BEGIN:VEVENT DTSTART:20190822T160000 DTEND:20190822T180000 DTSTAMP:20190821T150000Z UID:c9d4f322d296147236e6164dfc4f69ea@cgp.ibs.re.kr SUMMARY:On a GIT characterization of cofree representations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Matthew Satriano\n\nEvent: CGP Seminar\n\nAbstract: A representation $V$ of an algebraic group $G$ over a field $k$ is said to be cofree if $k[V]$ is free as a module over its invariant ring $k[V]^G$. When $G$ is a finite group, the Chevalley-Shephard-Todd Theorem gives a beautiful characterization for when a $G$-representation is cofree. In his 1986 ICM address, V. L. Popov asked whether this criterion could be extended to Lie groups. We give a conjectural answer to Popov's question for irreducible representations of semi-simple Lie groups and prove our conjecture for $SL_n$. This is joint work with Dan Edidin. END:VEVENT BEGIN:VEVENT DTSTART:20190624T101500 DTEND:20190624T110000 DTSTAMP:20190623T150000Z UID:083205559704372632f5d728ffd177f6@cgp.ibs.re.kr SUMMARY:A glance at entropy and complexity in dynamical systems LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kyewon Koh Park\n\nEvent: Women in Geometry and Topology\n\nAbstract: We will investigate the notions of metric entropy and topological entropy. They measure the exponential divergence rate of orbits over time. Metric entropy is the information of the present knowing the past. We will explore examples and different levels of complexity of entropy zero systems. They arise more naturally in the study of general group actions. We are still at the beginning stage of understanding subexponential growth rates of entropy zero systems. END:VEVENT BEGIN:VEVENT DTSTART:20190624T111500 DTEND:20190624T120000 DTSTAMP:20190623T150000Z UID:4182efb6d4e4c0c810ad12970f399b74@cgp.ibs.re.kr SUMMARY:On some relatively hyperbolic groups LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Donghi Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: The notion of relatively hyperbolic groups is an important generalization of hyperbolic groups in geometric group theory. Motivating examples for this generalization include the fundamental groups of non-compact hyperbolic manifolds of finite volume. In particular, every $2$-bridge link complement except for a torus link is a hyperbolic manifold with cusps, so its fundamental group, that is, the $2$-bridge link group, is hyperbolic relative to its peripheral subgroups. In this talk, we discuss the non-residual finiteness of relatively hyperbolic groups obtained by modifying $2$-bridge link groups. END:VEVENT BEGIN:VEVENT DTSTART:20190624T140000 DTEND:20190624T144500 DTSTAMP:20190623T150000Z UID:57a10123e00f1d9e159842e7e82c6d8c@cgp.ibs.re.kr SUMMARY:Grid diagram for singular links LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hwa Jeong Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: In this talk, we define the set of singular grid diagrams which provides a unified description for singular links, singular Legendrian links, singular transverse links, and singular braids. We also classify the complete set of all equivalence relations on the singular grid diagrams which induce the bijection onto each singular object. This is a joint work with Byung Hee An. END:VEVENT BEGIN:VEVENT DTSTART:20190624T150000 DTEND:20190624T153000 DTSTAMP:20190623T150000Z UID:cec83ddef8ef78e093dc5ca8e2a5c5c4@cgp.ibs.re.kr SUMMARY:A study on the relation between 2nd cohomolgy group of a quandle and the inner automorphism group LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Byeorhi Kim\n\nEvent: Women in Geometry and Topology\n\nAbstract: A quandle is an algebraic structure closely related to knot theory. It was introduced in 1980s, by Joyce and Matveev, independently. Joyce also proposed that every quandle can be represented by using its automorphism group, so we can study a quandle by using this group representations of quandles. Quandle homology theory was developed by modifying the group homology theory and Carter, Kamada and Saito showed that there exists a one-to-one correspondence between quandle second cohomology group $H^{2}_{q}(Q;A)$ and the set of abelian extensions of $Q$ by $A$ up to equivalence. In this talk, we observe the quandle second cohomology group and abelian extensions with Joyce's representation of a quandle. We begin studying the mod-2 quandle extension of the 4-elements tetrahedral quandle that is defined by a quandle cocycle in terms of the inner automorphism groups of each. We also observe the relationship between the second quandle cohomology group and the second group cohomology group in the example. This is a joint work with Y. Bae and J. S. Carter. END:VEVENT BEGIN:VEVENT DTSTART:20190624T170000 DTEND:20190624T174500 DTSTAMP:20190623T150000Z UID:80d6005fecb8be5e8e8762393248f402@cgp.ibs.re.kr SUMMARY:On Conway algebras of links and surface-links LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seonmi Choi\n\nEvent: Women in Geometry and Topology\n\nAbstract: In 1987, the HOMFLY-PT polynomial is a 2-variable polynomial invariant discovered by Hoste, Ocneanu, Millett, Freyd, Lickorish, Yetter, Przytycki and Traczyk. Przytycki and Traczyk introduced a new algebraic structure, called $\textit{the Conway algebra}$, and constructed invariants of oriented links valued in Conway algebras. The HOMFLY polynomial can be obtained from the invariant. In 2018, Kim constructed a generalized Conway algebra, which is an algebraic structure with two skein relations related to a self crossing and a mixed crossing. A generalized Conway algebra can be used to construct polynomial invariants.In this talk, we deal with surface-links in a 4-dimensional space represented by marked graph diagrams. In 2017, Joung, Kamada, Kawauchi and Lee constructed a polynomial invariant of oriented surface-links by using marked graph diagrams. We will define a generalization of a Conway algebra, which is called $\textit{a marked Conway algebra}$, and construct invariants for oriented surface-links valued in marked Conway algebras. The polynomial invariant constructed by Joung, Kamada, Kawauchi and Lee is obtained from the invariant valued in the marked Conway algebra satisfying additional conditions. In the end of this talk, we will also introduce a generalized marked Conway algebra and construct invariants. END:VEVENT BEGIN:VEVENT DTSTART:20190625T111500 DTEND:20190625T120000 DTSTAMP:20190624T150000Z UID:15fbabef04ee79a7a64a911822bf8322@cgp.ibs.re.kr SUMMARY:Tropical geometry and Newton-Okounkov theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jihyeon Jessie Yang\n\nEvent: Women in Geometry and Topology\n\nAbstract: In this talk, I will present a broad landscape of my research that is founded on algebraic geometry, representation theory and combinatorics. In particular, I will introduce two developments in (polyhedral) combinatorics in the approach to solve problems in algebraic geometry and representation theory. They are Tropical geometry and Newton-Okounkov theory. I will talk about the following three questions: 1.What are they? : Find an explicit description of each combinatorial object.2.How to use them? : Find applications3.How are they related? : Find relations between these two theories. END:VEVENT BEGIN:VEVENT DTSTART:20190625T150000 DTEND:20190625T154500 DTSTAMP:20190624T150000Z UID:f38d3998616a4c4cb4c76a31959f6ceb@cgp.ibs.re.kr SUMMARY:Minimal surfaces in Euclidean space: helicoid and beyond LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Eunjoo Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: A minimal surface, which is a mathematical model for soap film, is a very classical subject in differential geometry. After briefly reviewing its properties and examples, we move our focus on helicoids. First, we characterize a compact piece of the helicoid in a cylinder as an area-minimizing or a unique surface in a certain geometrical setting. Furthermore, we investigate uniqueness properties of the associate family of helicoids. END:VEVENT BEGIN:VEVENT DTSTART:20190626T093000 DTEND:20190626T101500 DTSTAMP:20190625T150000Z UID:2be685add390add10f1e10da1cf6b842@cgp.ibs.re.kr SUMMARY:Homogeneous dynamics and inhomogeneous Diophantine approximation LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seonhee Lim\n\nEvent: Women in Geometry and Topology\n\nAbstract: We will explain how to use the diagonal flow on homogeneous spaces to solve some family of questions in Diophantine approximation. We will start with the idea of Einsiedler and Lindenstrauss on the exceptional set of Littlewood conjecture and the extension of the idea to inhomogeneous problems. The latter part is joint work with Uri Shapira and Nicolas de Saxce and joint work with Wooyeon Kim. END:VEVENT BEGIN:VEVENT DTSTART:20190626T111500 DTEND:20190626T120000 DTSTAMP:20190625T150000Z UID:f470e84ae5efbb38f645cb0f7abb12fb@cgp.ibs.re.kr SUMMARY:Homogeneous dynamics and the equidistribution problem of $S$-integral vectors LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jiyoung Han\n\nEvent: Women in Geometry and Topology\n\nAbstract: By examining the dynamical properties of orbits of $\mathrm{SO}(p,q)$ in the homogeneous space $\mathrm{SL}_n(\mathbb R)/\mathrm{SL}_n(\mathbb Z)$, Margulis completely proved Oppenheim conjecture in 1987. Since then, the importance of the homogeneous dynamics has been raised. In this talk, we first explain two sample examples $\mathrm{SL}_2(\mathbb R)$ and $\mathrm{SL}_2(\mathbb Q_p)$ ($p$ : odd prime), which act on the hyperbolic plane $\mathbb H^2=\{ z=x+it\in \mathbb C : t>0\}$ and the $(p+1)$-regular tree $\mathcal T_p$, respectively. And then we introduce the Oppenheim conjecture-type problems,the way in which the homogeneous dynamics is involved to solve the problems, and their generalization to the $S$-arithmetic case. END:VEVENT BEGIN:VEVENT DTSTART:20190627T111500 DTEND:20190627T120000 DTSTAMP:20190626T150000Z UID:a41d2f78445b43a8dd3f9a484ab41bf0@cgp.ibs.re.kr SUMMARY:A Kobayashi pseudo-distance for holomorphic bracket generating distributions LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Aeryeong Seo\n\nEvent: Women in Geometry and Topology\n\nAbstract: In this talk, a generalization of Kobayashi pseudo-distance on complex manifolds with holomorphic bracket generating distributions will be presented. For a semisimple Lie group G, a G-homogeneous complex manifold M with an invariant holomorphic bracket generating distribution is Kobayashi hyperbolic if and only if the universal covering of M is a canonical flag domain with the superhorizontal distribution. END:VEVENT BEGIN:VEVENT DTSTART:20190627T140000 DTEND:20190627T144500 DTSTAMP:20190626T150000Z UID:e5172cc79a68952ca048ef4c38113324@cgp.ibs.re.kr SUMMARY:Several types of cubic hypersurfaces with degenerate Gauss map LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yewon Jeong\n\nEvent: Women in Geometry and Topology\n\nAbstract: Given a hypersurface $X = V ( f )$ in a complex projective space, the Gauss map of $X$ can be regarded as the restriction of the gradient map of $f$ on $X$. We say, the hypersurface $X$ has degenerate Gauss map if general fibers of the Gauss map have positive dimension. Especially for cubic hypersurfaces with degenerate Gauss map, there is an interesting classification of them. We will study several types of cubic hypersurfaces and the relation between them. END:VEVENT BEGIN:VEVENT DTSTART:20190627T150000 DTEND:20190627T153000 DTSTAMP:20190626T150000Z UID:8c604473b31dcb89b76f7d3277edbb03@cgp.ibs.re.kr SUMMARY:Real Lagrangian submanifolds in symplectic toric manifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jiyeon Moon\n\nEvent: Women in Geometry and Topology\n\nAbstract: A real Lagrangian in a symplectic manifold is a Lagrangian given by the fixed point set of an anti-symplectic involution. On symplectic toric manifolds, it is natural to consider real Lagrangians which are compatible with the torus actions. We shall study the topology of the real Lagrangians in symplectic toric manifolds. In particular, we explain the Delzant construction for the real Lagrangians. This is an ongoing work with Joe Brendel and Joontae Kim. END:VEVENT BEGIN:VEVENT DTSTART:20190627T170000 DTEND:20190627T174500 DTSTAMP:20190626T150000Z UID:2dd7443f16a83060acdc562e93cb9cb9@cgp.ibs.re.kr SUMMARY:Signature of surface bundles over surfaces and Double Kodaira fibrations LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ju A Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: The fundamental problem in 4 dimensional topology is about topologicalconstraints on a smooth closed oriented 4 manifold with a certain preassignedadditional structure such as a symplectic, a complex, or a fibration structure. In particular, we focus on the studies on the determination of possible signature andthe Euler characteristic of smooth 4 manifolds (or complex surfaces) admittinga surface bundle over a surface with nonzero signature. In the first part of the talk, I’d like to explain how we can construct smoothsurface bundles with signature 4 and small Euler characteristic using Lefschetzfibrations. However, if we require the total space to be complex, all the knownexamples (often called Kodaira fibrations) have signature 16 and more, and thegenus of the fiber or the base large. So in the second part, I’d like to introducetheorems about the construction of Kodaira fibrations using the ramified covering,and then about the minimal signature and minimal base genus of suchconstruction by studying the monodromy action. Finally, if time permits, I’dlike to talk about the recent progress on the torus surgery on smooth 4 manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20190628T093000 DTEND:20190628T101500 DTSTAMP:20190627T150000Z UID:1762fe54ed41f7517743ac7dbe7cf752@cgp.ibs.re.kr SUMMARY:Quasiconformal conjugacy classes of parabolic isometries acting on complex hyperbolic space LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Youngju Kim\n\nEvent: Women in Geometry and Topology\n\nAbstract: In this talk, we study noncompact complex 2-dimensional hyperbolic manifolds obtained by quotienting the complex hyperbolic 2-spaceby cyclic groups of parabolic isometries. In particular, we consider the quasiconformal conjugacy classes of such manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20190628T103000 DTEND:20190628T110000 DTSTAMP:20190627T150000Z UID:3f082b9937f882373ac9e48fca3bdf51@cgp.ibs.re.kr SUMMARY:Polygon spaces in Euclidean plane and connectedness LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: The polygon space is the collection of polygons in Euclidean spaces. In particular, the polygon space is related to a moduli space in algebraic geometry andtoric degenerations in theory of mirror symmetry. The foundations of geometryand topology of the polygon spaces were established by Kapovich and Millson.By applying the theory of rectified simplex, we introduce a new approach togeometry and topology of polygon spaces. In this talk, from new point of viewwe discuss the connectedness of the polygon space of fixed side-length. This isa joint work with Jae-Hyouk Lee. END:VEVENT BEGIN:VEVENT DTSTART:20190628T111500 DTEND:20190628T120000 DTSTAMP:20190627T150000Z UID:1482015e4a2d8d3385d104c09b7b3b0b@cgp.ibs.re.kr SUMMARY:Explicit equations of a complex 2-ball quotient LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: JongHae Keum\n\nEvent: Women in Geometry and Topology\n\nAbstract: A compact complex manifold of dimension 1 (Riemann surface) can always be uniformized and its universal cover is the complex projective line(Riemann sphere) or the complex line or the complex 1-ball (the real hyperbolic plane). In higher dimensions, not all complex manifolds can be uniformized. A compact complex surface with the same Betti numbers as the complex projective plane is called a fake projective plane if it is not isomorphic to the complex projective plane. By Aubin and Yau, a fake projective plane can be uiformized and its universal cover is the complex 2-ball.The existence of a fake projective plane was first proved by Mumford in1979 based on the theory of 2-adic uniformization.It has long been of great interest since Mumford to find explicit equations of a FPP. With Lev Borisov we find explicit equations of a conjugate pair of fake projective planes. END:VEVENT BEGIN:VEVENT DTSTART:20190625T101500 DTEND:20190625T110000 DTSTAMP:20190624T150000Z UID:5da25e8597ffef9b6b1cf75b9dd8d174@cgp.ibs.re.kr SUMMARY:Brill-Noether loci in the moduli space of curves of genus $g$ LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Seonja Kim\n\nEvent: Women in Geometry and Topology\n\nAbstract: It is a classical and fundamental problem to describe all the ways in which a given algebraic curve is mapped into a projective space. Alexander von Brill and Max Noether established in 1874 the Brill-Noether theorem which estimates the dimension of the space of maps from a curve to an $r$-dimensional projective space with given degree $d$. Since then Brill-Noether theory has been developed and played a key role in the theory of algebraic curves. In this respect, it is interesting to study the sublocus $M(r,d)$ of the moduli space $M_g$ of smooth genus $g$ curves whose general point corresponds to a curve possessing a map to an $r$-dimensional projective space with degree $d$. The locus $M(r,d)$ is called a Brill-Noether locus of $M_g$. In this talk, we consider some relations among Brill-Noether loci in the moduli space $ M_g$. END:VEVENT BEGIN:VEVENT DTSTART:20190624T160000 DTEND:20190624T164500 DTSTAMP:20190623T150000Z UID:7ff875f6b24101a1b1ebd2c8955647a8@cgp.ibs.re.kr SUMMARY:On a bi-gauss diagram of surface-links LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jieon Kim\n\nEvent: Women in Geometry and Topology\n\nAbstract: M. Polyak and O. Viro introduced a gauss diagram of classical links. A marked graph diagram is a diagram of a finite spatial regular graph with 4-valent rigid vertices such that each vertex has a marker. For a given marked graph diagram $D$, let $L_-(D)$ and $L_+(D)$ be classical link diagrams obtained from $D$ by replacing each marked vertex
with $)($and $\asymp$ respectively. We call $L_-(D)$ and $L_+(D)$ the $ \textit{negative resolution}$ and the $ \textit{positive resolution}$ of D, respectively. Every surface-link can be represented by marked graph diagrams. In this paper, by using the gauss diagrams of two resolutions of a marked graph diagram of a surface-link, we introduce a new method of describing surface-links, called a bi-gauss diagram. This is a joint work with S. Bost, B. Garbuz and S. Nelson.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190625T134500
DTEND:20190625T141500
DTSTAMP:20190624T150000Z
UID:62895aaeb896fbfc684fc492c89b131a@cgp.ibs.re.kr
SUMMARY:Complex surfaces of general type with $K^2=3,4$ and $p_g=q=0$
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Yoonjeong Yang\n\nEvent: Women in Geometry and Topology\n\nAbstract: We construct complex minimal surfaces of general type with $p_g=q=0$ and $K^2=3,4$ as double covers of Enriques surfaces (called Keum-Naie surfaces) with a different way to the original constructions of Keum and Naie. As a result, we show that there is a $(-4)$-curve on our example with $K^2=3$, which might imply a special relation between Keum-Naie surfaces with $K^2=3$ and $K^2=4$.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190626T101500
DTEND:20190626T110000
DTSTAMP:20190625T150000Z
UID:9e85429ee1c53c5062694f7048eb3828@cgp.ibs.re.kr
SUMMARY:Odd-odd continued fraction
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Seul Bee Lee\n\nEvent: Women in Geometry and Topology\n\nAbstract: It is known that regular continued fraction gives the best approximation of an irrational number with rationals.We investigate a continued fraction, say odd-odd continued fraction, which gives the best approximation of an irrational with rationals whose numerator and denominator are odd.To show our results, we see that our continued fraction is related to Farey graph and Ford circles.This is joint work with Dong Han Kim and Lingmin Liao.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190627T160000
DTEND:20190627T164500
DTSTAMP:20190626T150000Z
UID:4d9b38455a7576b115b41e48dec36ad0@cgp.ibs.re.kr
SUMMARY:Smooth toric Richardson varieties
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Seonjeong Park\n\nEvent: Women in Geometry and Topology\n\nAbstract: The flag variety $\mathcal{F}\ell_n$ is a smooth projective variety consisting of chains $(\{0\}\subset V_1\subset\cdots\subset V_n=\mathbb{C}^n)$ of subspaces of $\mathbb{C}^n$ with $\dim_{\mathbb{C}} V_i=i$. Then the standard action of $\mathbb{T}=(\mathbb{C}^\ast)^n$ on $\mathbb{C}^n$ induces a natural action of $\mathbb{T}$ on $\mathcal{F}\ell_n$. For $v$ and $w$ in the symmetric group $\mathfrak{S}_n$ with $v\leq w$ in Bruhat order, the Richardson variety $X^v_w$ is defined to be the intersection of the Schubert variety $X_w$ and the opposite Schubert variety $w_0X_{w_0v}$, and it is an irreducible $\mathbb{T}$-invariant subvariety of $\mathcal{F}\ell_n$. In this talk, we give some combinatorial interpretation of geometric properties of Richardson varieties, and show that every smooth toric Richardson variety is a Bott tower. This talk is based on joint work with Eunjeong Lee and Mikiya Masuda.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190627T101500
DTEND:20190627T110000
DTSTAMP:20190626T150000Z
UID:606ad2417bd2af8c2b53e56423730dd2@cgp.ibs.re.kr
SUMMARY:CR maps between closed $SU(l,m)$-orbits
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Sung Yeon Kim\n\nEvent: Women in Geometry and Topology\n\nAbstract: In this talk, we study germs of smooth CR mappings sending a closed orbit of $SU(l,m)$into another closed orbit of $SU({l}',{m}')$ in Grassmannian manifolds. We show that if the signaturedifference of the Levi forms of two orbits is not too large, then the mapping can be factored into asimple form and one of the factors extends to a totally geodesic embedding of the ambient Grassmannian with respect to the standard metric. As an application, we give a sufficient condition for aproper holomorphic mapping between type I bounded symmetric domains to be the product of trivialembedding and a holomorphic mapping into a subdomain.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190709T160000
DTEND:20190709T180000
DTSTAMP:20190708T150000Z
UID:acd201bfa6a3cd18e81cb60ad97d4e4f@cgp.ibs.re.kr
SUMMARY:On span of generalized Dold manifolds
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Soumen Sarkar\n\nEvent: Seminar\n\nAbstract: In this talk, I will extend the category of Dold manifolds. Then I will discuss few interesting topological properties of generalized Dold manifolds. This is a joint work with S. Poddar and P. Zvengrowski.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190702T160000
DTEND:20190702T180000
DTSTAMP:20190701T150000Z
UID:a09fb6d1fae110a125cba512b89ac11b@cgp.ibs.re.kr
SUMMARY:Chow cohomology rings of complete flag varieties and Gelfand-Zetlin toric varieties
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Kyeong-Dong Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The complete flag variety parametrizing complete flags of subspaces in a complex vector space can be identified with a homogeneous space $GL(n, \mathbb C)/B$, where $B$ is the Borel subgroup of upper triangular matrices. Since the complete flag variety has a paving by Schubert cells, its Chow ring and cohomology ring are naturally isomorphic. By the Borel's description, this ring is isomorphic to the corresponding polynomial algebra quotient by the ideal generated by non-constant symmetric polynomials. Motivated from the Khovanskii-Pukhlikov description on the cohomology ring of a smooth projective toric variety in terms of Newton polytopes, Kaveh obtained a description on the cohomology ring of a complete flag variety in terms of Gelfand-Zetlin polytopes. Caldero and Alexeev-Brion gave a flat degeneration of the flag variety to the toric variety associated with Gelfand-Zetlin polytopes, more generally string polytopes. Note that the cohomology ring is not preserved under a flat degeneration. Recently, Kaveh and Villella showed that the cohomology ring of a complete flag variety is the Gorenstein quotient of the Lefschetz subalgebra generated by degree one elements of Chow cohomology ring of the Gelfand-Zetlin toric variety. Because the Gelfand-Zetlin toric variety is not smooth, for the Chow cohomology ring of a singular complete toric variety I will explain the ring of Minkowski weights on the corresponding fan due to Fulton and Sturmfels. For a concrete example, I will compute the Chow cohomology ring of the 3-dimensional Gelfand-Zetlin toric variety using the Minkowski weights.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190716T160000
DTEND:20190716T180000
DTSTAMP:20190715T150000Z
UID:76e935f8d492a2409414a981d65fd25e@cgp.ibs.re.kr
SUMMARY:Del Pezzo surfaces: toric systems, degenerations, and minimal model program
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Yonghwa Cho\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk we consider two different subjects related to the del Pezzo surfaces. The first one is toric systems originated from full exceptional collections. The other one is Q-Gorenstein toric degenerations. We apply relative MMP to the total spaces of such degenerations, and see how relative MMP can be read off from toric systems. Afterwards, we introduce our recent approach to understand the relation between toric systems and Q-Gorenstein toric degenerations using relative MMP.
END:VEVENT
BEGIN:VEVENT
DTSTART:20190708T160000
DTEND:20190708T164000
DTSTAMP:20190707T150000Z
UID:46ffd14cd3a900b3713ded932b995847@cgp.ibs.re.kr
SUMMARY:Talk1. Degenerations in Algebra, Geometry, and Combinatorics from the tropical viewpoint
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Jihyeon Jessie Yang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will introduce two developments in (polyhedral) combinatorics in the approach to solve problems in algebraic geometry and representation theory. They are Tropical geometry and Newton-Okounkov theory. I will talk about the following three questions: 1.What are they? : Find an explicit description of each combinatorial object.
2.How to use them? : Find applications.
3.How are they related? : Find relations between these two theories.
Particularly, for the question 3, I will consider the case of Grassmannian of 2-planes. We construct a family of compactifications of the affine cone of the Grassmannian of 2-planes. We show that both the Tropical and Newton-Okoukov results can be recovered from these compactifications. END:VEVENT BEGIN:VEVENT DTSTART:20190708T164000 DTEND:20190708T172000 DTSTAMP:20190707T150000Z UID:f11f863c6e0aebff5c2409779ccb2bb0@cgp.ibs.re.kr SUMMARY:Talk 2. Introduction to Newton-Okounkov theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jihyeon Jessie Yang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will introduce two developments in (polyhedral) combinatorics in the approach to solve problems in algebraic geometry and representation theory. They are Tropical geometry and Newton-Okounkov theory. I will talk about the following three questions:
1.What are they? : Find an explicit description of each combinatorial object.
2.How to use them? : Find applications.
3.How are they related? : Find relations between these two theories.
Particularly, for the question 3, I will consider the case of Grassmannian of 2-planes. We construct a family of compactifications of the affine cone of the Grassmannian of 2-planes. We show that both the Tropical and Newton-Okoukov results can be recovered from these compactifications. END:VEVENT BEGIN:VEVENT DTSTART:20190708T172000 DTEND:20190708T180000 DTSTAMP:20190707T150000Z UID:6770072a87164c5d1c684e74295e8a23@cgp.ibs.re.kr SUMMARY:Talk 3: Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jihyeon Jessie Yang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will introduce two developments in (polyhedral) combinatorics in the approach to solve problems in algebraic geometry and representation theory. They are Tropical geometry and Newton-Okounkov theory. I will talk about the following three questions:
1.What are they? : Find an explicit description of each combinatorial object.
2.How to use them? : Find applications.
3.How are they related? : Find relations between these two theories.
Particularly, for the question 3, I will consider the case of Grassmannian of 2-planes. We construct a family of compactifications of the affine cone of the Grassmannian of 2-planes. We show that both the Tropical and Newton-Okoukov results can be recovered from these compactifications. END:VEVENT BEGIN:VEVENT DTSTART:20190715T160000 DTEND:20190715T180000 DTSTAMP:20190714T150000Z UID:f1c3ac048ad63ce8aa29e41d4ba3be38@cgp.ibs.re.kr SUMMARY:Motivic integrations LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Derived Seminar\n\nAbstract: In this talk, I will discuss the theory of motivic integrations and its recent developments. END:VEVENT BEGIN:VEVENT DTSTART:20190723T160000 DTEND:20190723T180000 DTSTAMP:20190722T150000Z UID:5f6f331393e3b5944ccd40ba9ec47fc9@cgp.ibs.re.kr SUMMARY:Cox rings and combinatorics LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Cox ring is one of the fundamental tools in modern algebraic geometry. In this talk, I will briefly review basic results about Cox rings. Then I will discuss how to extract geometric properties of algebraic varieties from certain combinatorial data related to Cox rings. END:VEVENT BEGIN:VEVENT DTSTART:20191019T090000 DTEND:20191019T090000 DTSTAMP:20191018T150000Z UID:544c01d63a8fdf95234261fb4ac61a17@cgp.ibs.re.kr SUMMARY:공간의 수학 LOCATION:포항 시청 대잠홀 DESCRIPTION:Speaker: Jae Choon Cha\n\nEvent: 제4회 IBS 기하학 수리물리 연구단 수학 문화 강연\n\nAbstract: 공간의 구조와 연결성의 본질을 탐구하는 것은 현대 수학의 주요 주제 중 하나입니다. 잘 알려진 예로, 도넛과 커피잔이 동등한 형태라는 사실이 있는데, 이와 같은 공간의 변형은 직관적으로 이해할 수 있지만 수치로 표현하거나 계산으로 다루기가 난감하다는 독특한 면이 있습니다. 실제 공간의 수학은 그 추상적 어려움으로 인해 20세기에 와서야 본격적으로 연구되었는데, 이 강연에서는 과거로부터 현대에 이르기까지 공간을 탐구하고 있는 수학자들의 이야기, 그리고 첨단 연구의 도전과 함께 여러 차원의 신비스러운 난제들에 대해 이해하기 쉽게 소개하고자 합니다. END:VEVENT BEGIN:VEVENT DTSTART:20191019T090000 DTEND:20191019T090000 DTSTAMP:20191018T150000Z UID:6246d6459df3a9f330b77a0daa9971e5@cgp.ibs.re.kr SUMMARY:잘 다니기 --- 어떻게 최적인 방법을 찾을까. LOCATION:포항 시청 대잠홀 DESCRIPTION:Speaker: Sang-il Oum\n\nEvent: 제4회 IBS 기하학 수리물리 연구단 수학 문화 강연\n\nAbstract: 오일러가 해결했던 쾨니히스베르크의 다리 문제부터 여러 도시를 한 번씩 들리는 가장 짧은 경로를 찾는 외판원 문제까지, 그래프이론 및 조합적 최적화 이론에서 다루는 흥미로운 문제들을 소개합니다. END:VEVENT BEGIN:VEVENT DTSTART:20190805T140000 DTEND:20190805T160000 DTSTAMP:20190804T150000Z UID:a81376551bdf0eb784ad6d8b7af9e99c@cgp.ibs.re.kr SUMMARY:Towards homological mirror symmetry for cluster quivers LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kyungyong Lee\n\nEvent: Seminar\n\nAbstract: For a given quiver without oriented 2-cycles Q, the associated cluster algebra is defined by using seed mutations. These seed mutations are expected to give some homological data for modules over the Ginzburg algebra of Q. We would also like to develop a symplecto-geometric interpretation for the mutations in the sense of homological mirror symmetry. We explain our initial approach. This is a joint work with Kyu-Hwan Lee. END:VEVENT BEGIN:VEVENT DTSTART:20190826T160000 DTEND:20190826T180000 DTSTAMP:20190825T150000Z UID:5fd704da95edf1398d977802b774aa18@cgp.ibs.re.kr SUMMARY:Cluster algebras and Newton-Okounkov bodies I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Intensive Lecture Series\n\nAbstract: The theory of Newton-Okounkov bodies 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 compactified cluster varieties, a different approach to toric degenerations was given by Gross-Hacking-Keel-Kontsevich, using the theory of cluster algebras with principal coefficients. In this series of talks, we discuss relations between these two constructions of toric degenerations.In the 1st talk, we review some basic facts about cluster algebras, including the finite type classification. In the 2nd talk, we overview the theory of cluster ensembles and related topics. In particular, Gross-Hacking-Keel-Kontsevich's construction of toric degenerations is explained. The 3rd talk is devoted to studying Newton-Okounkov bodies of projective varieties from their cluster structures. In the case of flag varieties, we discuss how these bodies are related to string polytopes arising from representation theory. This series of talks is partly based on a joint work with Hironori Oya. END:VEVENT BEGIN:VEVENT DTSTART:20190827T160000 DTEND:20190827T180000 DTSTAMP:20190826T150000Z UID:845bebf23ba51514d443bfb8e7c0c05a@cgp.ibs.re.kr SUMMARY:Cluster algebras and Newton-Okounkov bodies II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Intensive Lecture Series\n\nAbstract: The theory of Newton-Okounkov bodies 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 compactified cluster varieties, a different approach to toric degenerations was given by Gross-Hacking-Keel-Kontsevich, using the theory of cluster algebras with principal coefficients. In this series of talks, we discuss relations between these two constructions of toric degenerations.In the 1st talk, we review some basic facts about cluster algebras, including the finite type classification. In the 2nd talk, we overview the theory of cluster ensembles and related topics. In particular, Gross-Hacking-Keel-Kontsevich's construction of toric degenerations is explained. The 3rd talk is devoted to studying Newton-Okounkov bodies of projective varieties from their cluster structures. In the case of flag varieties, we discuss how these bodies are related to string polytopes arising from representation theory. This series of talks is partly based on a joint work with Hironori Oya. END:VEVENT BEGIN:VEVENT DTSTART:20190828T133000 DTEND:20190828T153000 DTSTAMP:20190827T150000Z UID:8871a5ce5fb0b6ac734b34085d392848@cgp.ibs.re.kr SUMMARY:Cluster algebras and Newton-Okounkov bodies III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Intensive Lecture Series\n\nAbstract: The theory of Newton-Okounkov bodies 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 compactified cluster varieties, a different approach to toric degenerations was given by Gross-Hacking-Keel-Kontsevich, using the theory of cluster algebras with principal coefficients. In this series of talks, we discuss relations between these two constructions of toric degenerations.In the 1st talk, we review some basic facts about cluster algebras, including the finite type classification. In the 2nd talk, we overview the theory of cluster ensembles and related topics. In particular, Gross-Hacking-Keel-Kontsevich's construction of toric degenerations is explained. The 3rd talk is devoted to studying Newton-Okounkov bodies of projective varieties from their cluster structures. In the case of flag varieties, we discuss how these bodies are related to string polytopes arising from representation theory. This series of talks is partly based on a joint work with Hironori Oya. END:VEVENT BEGIN:VEVENT DTSTART:20190801T160000 DTEND:20190801T180000 DTSTAMP:20190731T150000Z UID:b3d18d885d27cdd2a01211ae60b29391@cgp.ibs.re.kr SUMMARY:Double Poisson algebras up to homotopy LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Johan Leray\n\nEvent: CGP Seminar\n\nAbstract: The double Poisson algebras are noncommutative analogous of Poisson algebras which appear in many areas, like noncommutative geometry, string topology or symplectic topology. A natural question is the following what is a double Poisson algebra up to homotopy? In order to determine what is such structure, it is useful to work on the level of algebraic objects which encode algebraic structures and which are called properads. After recalling the definitions of double Poisson algebra and properad, I will present the strategy to understand what is a double Poisson algebra up to homotopy. END:VEVENT BEGIN:VEVENT DTSTART:20190802T160000 DTEND:20190802T180000 DTSTAMP:20190801T150000Z UID:79809fa7659247ee618d71f5778acaec@cgp.ibs.re.kr SUMMARY:Exact Lagrangian fillings of Legendrian torus knots. LOCATION:CGP Main Hall DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: Seminar\n\nAbstract: I will discuss how many exact Lagrangian fillings ofLegendrian torus knots are possible up to Hamiltonian isotopies. Themain tools are augmentations of Legendrian DGA and Lagrangian saddlecobordisms. I will also talk about how the cluster structure andDynkin diagrams are related to this subject.This is a joint work in progress with Byunghee An. END:VEVENT BEGIN:VEVENT DTSTART:20190808T160000 DTEND:20190808T180000 DTSTAMP:20190807T150000Z UID:22d810fe011fa54f9e011179f2f26171@cgp.ibs.re.kr SUMMARY:BPS invariants for Seifert manifolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hee-Joong Chung\n\nEvent: CGP Seminar\n\nAbstract: It was conjectured in physics literature that the Chern-Simons partition function or the Witten-Reshtikhin-Turaev invariant for closed 3-manifolds can be expressed in a particular form in terms of q-series with integer powers and integer coefficients. These q-series are new topological invariants, which are called the homological blocks. In physics, such q-series can be interpreted as BPS invariants of 3d N=2 supersymmetric theories via the 3d-3d correspondence. In this talk, I will discuss the homological blocks for Seifert manifolds with gauge group G=SU(N) and the ones in the case of the rational Chern-Simons levels when G=SU(2). END:VEVENT BEGIN:VEVENT DTSTART:20190731T133000 DTEND:20190731T153000 DTSTAMP:20190730T150000Z UID:00f1a277082b29d3b3f0cbf332c7a3a2@cgp.ibs.re.kr SUMMARY:Augmentations and sheaves for Legendrian graphs LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tao Su\n\nEvent: Director's Seminar\n\nAbstract: Legendrian graphs are singular generalizations of Legendrian knots in the contact three-space, which arise naturally as the micro-support at contact infinity of constructible sheaves on the front plane. In this talk, I will discuss Legendrian isotopy invariants of Legendrian graphs similar to the story of Legendrian knots: Legendrian contact homology differential graded algebras, counting of their augmentations by ruling polynomials, time permitting, also the Fukaya-like category of augmentations (augmentation category), and its relation to a sheave category on the front planedefined via the same Legendrian graph. Joint work in progress with Byunghee An, andYoungjin Bae. END:VEVENT BEGIN:VEVENT DTSTART:20190814T133000 DTEND:20190814T153000 DTSTAMP:20190813T150000Z UID:0ec9ff674de48a7aede7e654dc94de75@cgp.ibs.re.kr SUMMARY:Wall crossing formula and Floer homology I LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formulaof Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witteninvariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of thislecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOOpotential function under the mutation of Lagrangian submanifolds in 4-dimensional symplecticmanifolds. Their proof in turn uses Seidel's comparison betweenthe Floer homologies of a (monotone) Lagrangian torus in the closed ambient spaceand in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20190819T160000 DTEND:20190819T180000 DTSTAMP:20190818T150000Z UID:7e489010078e49f09a63eafdce455293@cgp.ibs.re.kr SUMMARY:A higher-dimensional generalization of pseudo-Anosov surface automorphisms LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In 80's, Thurston classified the mapping class group of orientable surfaces. A generic element of the mapping class group is of the pseudo-Anosov type. In 2014, from pseudo-Anosov surface automorphisms, Dimitrov, Haiden, Katzarkov and Kontsevich constructed Bridgeland stability conditions on the Fukaya category of the surface. They also gave a question asking the existence of higher-dimensional generalization of pseudo-Anosov automorphisms on symplectic manifolds.To answer their question, we found a construction of symplectomorphisms which preserve a stable Lagrangian lamination. In this talk, we will discuss the construction and some following questions. END:VEVENT BEGIN:VEVENT DTSTART:20190813T160000 DTEND:20190813T180000 DTSTAMP:20190812T150000Z UID:910a4b7b99b86b30f4dc3d4835b6afca@cgp.ibs.re.kr SUMMARY:Quotient singularities of algebraic surfaces with small Betti numbers LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, I will discuss various aspects of normal surface singularities. Then I will discuss several attempts to understand quotient singularities of algebraic surfaces with small Betti numbers. Last part of this talk is based on a joint work in progress with JongHae Keum. END:VEVENT BEGIN:VEVENT DTSTART:20190821T133000 DTEND:20190821T153000 DTSTAMP:20190820T150000Z UID:ddfccaeb78b53b6aba7b51dba4e733a6@cgp.ibs.re.kr SUMMARY:Wall crossing formula and Floer homology II LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formula of Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witten invariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of this lecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOO potential function under the mutation of Lagrangian submanifolds in 4-dimensional symplectic manifolds. Their proof in turn uses Seidel's comparison between the Floer homologies of a (monotone) Lagrangian torus in the closed ambient space and in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20190904T133000 DTEND:20190904T153000 DTSTAMP:20190903T150000Z UID:bc959badb0fbb2f6e362219109133887@cgp.ibs.re.kr SUMMARY:On SYZ fibrations LOCATION:CGP Delta DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Director's Seminar\n\nAbstract: In this lecture, I will talk about SYZ fibrations and the walling crossing phenomena appear in the reconstruction problem in mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20190924T100000 DTEND:20190924T110000 DTSTAMP:20190923T150000Z UID:bf6742a84729242e5743bec2b29f1c75@cgp.ibs.re.kr SUMMARY:Weighted Hurwitz numbers and topological recursion LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: In my talk I will discuss some elements of the proof of thetopological recursion for the weighted Hurwitz numbers. The mainingredient is the tau-function - the all genera generating function,which is a solution of the integrable KP or Toda hierarchy. The associatedclassical and quantum spectral spectral curves are derived. The paircorrelators are given a finite Christoffel-Darboux representation anddeterminantal expressions are obtained for the multipair correlators.A fermionic representation is given for all the quantities entering inthe generating function approach to weighted Hurwitz numbers andtopological recursion. The genus expansion of the multicurrentcorrelators is shown to provide the generating series for weighted Hurwitznumbers of fixed ramification profile lengths. The WKB series for theBaker function is derived and used to deduce the loop equations andthe topological recursion relations. My talk isbased on a series of joint papers with G. Chapuy, B. Eynard, and J.Harnad. END:VEVENT BEGIN:VEVENT DTSTART:20190924T112000 DTEND:20190924T122000 DTSTAMP:20190923T150000Z UID:9493aa4fee2bbeaa875709072b45157a@cgp.ibs.re.kr SUMMARY:Generalization of the Givental theory for the open WDVV equations. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Alexandr Buryak\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: The WDVV equations, also called the associativity equations, is a system of non-linear partial differential equations for one function that describes the localstructure of a Frobenius manifold. In enumerative geometry the WDVV equations control the Gromov-Witten invariants in genus zero. In his fundamental works, A. Givental interpreted solutions of the WDVV equations as cones in a certain infinite-dimensional vector space. This allowed him to introduce a group action on solutions of the WDVV equations which proved to be a powerful tool in Gromov-Witten theory. I will talk about a generalization of the Givental theory for the open WDVV equations that appeared in a work of A. Horev and J. Solomon in the context of open Gromov-Witten theory. END:VEVENT BEGIN:VEVENT DTSTART:20190924T143000 DTEND:20190924T153000 DTSTAMP:20190923T150000Z UID:c8ca407c11b01b681fc328960f053219@cgp.ibs.re.kr SUMMARY:Central charge functions in Landau-Ginzburg orbifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Emanuel Scheidegger\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: We consider Landau-Ginzburg orbifolds and their associated gauged linear sigma models. We discuss the relation between the hemisphere partition function in the LG phase of the gauged linear sigma model and the central charge function in the LG orbifold. The latter is given in terms of Chern characters of equivariant matrix factorizations of the LG potential and generating functions of FJRW invariants. END:VEVENT BEGIN:VEVENT DTSTART:20190924T160000 DTEND:20190924T170000 DTSTAMP:20190923T150000Z UID:59e7b1d5fe8c2fec42515b58a950610e@cgp.ibs.re.kr SUMMARY:Higher-genus correspondence between local and relative Gromov-Witten theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Longting Wu\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: In this talk, we will establish an explicit formula relating virtual fundamental cycles associated to local and relative Gromov-Witten theory. This generalizes a result of Garrel, Graber and Ruddat in genus zero. Then we make a conjecture that similar results (explicit formulae in low genus, finite generation, holomorphic anomaly equation) for local P^2 also hold for Gromov-Witten theory of P^2 relative to a smooth cubic, and give some evidence.This is a work in progress with Pierrick Bousseau and Honglu Fan. END:VEVENT BEGIN:VEVENT DTSTART:20190925T112000 DTEND:20190925T122000 DTSTAMP:20190924T150000Z UID:2d1f0cd29b7d106b9ddd0922d52a5c32@cgp.ibs.re.kr SUMMARY:Global mirror symmetry for the quintic threefold in higher genus LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Shuai Guo\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: During the last two decades, it has been a central problem to compute the Gromov-Witten (GW) invariants of Calabi-Yau threefolds, in both geometry and physics. In this talk, we will discuss the recent mathematical approaches to the all genera Gromov-Witten potential functions of the quintic threefolds. END:VEVENT BEGIN:VEVENT DTSTART:20190925T143000 DTEND:20190925T153000 DTSTAMP:20190924T150000Z UID:e8307b96daf02223229e470060cf35f4@cgp.ibs.re.kr SUMMARY:Uniruledness of symplectic orbifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jianxun Hu\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: For symplectic manifolds, one can define the notion of uniruledness by testing the vanishing of certain type of Gromov-Witten invariants, and it is well-known that uniruled property of symplectic manifolds is invariant under blow-ups and blow-downs. In this talk, we will explain that such results may be generalized to the orbifold case. We show that the similar vanishing property is preserved by any weighted blow-ups and blow-downs. This is based on the joint work with Bohui Chen and Cheng-Yong Du . END:VEVENT BEGIN:VEVENT DTSTART:20190925T160000 DTEND:20190925T170000 DTSTAMP:20190924T150000Z UID:8409c7c7bee28b0afef46d413f38fcdb@cgp.ibs.re.kr SUMMARY:Cohomological field theory and its applications in Gromov-Witten theory. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Hyenho Lho\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: I will explain the finitely generatedness properties in Cohomological field theory and its applications in Gromov-Witten theory. First application is the holomorphic anomaly equation and crepant resolution correspondece in Calabi-Yau geometries. Second application is to find tautological relations in the moduli space of stable maps. First part of the talk is based on the joint work with Rahul Pandharipande, and second is based on the joint work in progress with Younghan Bae. END:VEVENT BEGIN:VEVENT DTSTART:20190925T100000 DTEND:20190925T110000 DTSTAMP:20190924T150000Z UID:607d49f3cab9128528e48021acf6e5c7@cgp.ibs.re.kr SUMMARY:Adiabatic limit of gauged Witten equation LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Guangbo Xu\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: Tian and I constructed correlation functions associated to a gauged linear sigma model space in the geometric phase. These correlators are expected to agree with Gromov--Witten invariants up to a “coordinate change.” I will explain how to prove this correspondence using the adiabatic limit of the gauged Witten equation (joint work with Tian). END:VEVENT BEGIN:VEVENT DTSTART:20190926T100000 DTEND:20190926T110000 DTSTAMP:20190925T150000Z UID:20d5328788cf335bd7f1b1d29beb0656@cgp.ibs.re.kr SUMMARY:Fukaya Category of Landau-Ginzburg Model LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Huijun Fan\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: Recently we gives the mathematical foundation of the open string Floer theory of Landau-Ginzburg model via Witten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler manifold, and define the notion of Landau-Ginzburg branes, as the objects of the Fukaya category. The study on Witten equation in our context provides the construction of the Fukaya category of Landau-Ginzburg model which was conjectured to be existed in Gaiotto-Moore-Witten’s paper and Kapranov-Kontsevich-Soibelman’s paper on the infrared algebraic structure. The key point in the construction is a C0-C1 joint compactness estimate. This is the joint work with Wenfeng Jiang and Dingyu Yang. END:VEVENT BEGIN:VEVENT DTSTART:20190926T112000 DTEND:20190926T122000 DTSTAMP:20190925T150000Z UID:c02fbcd412e443014535c20711500f9c@cgp.ibs.re.kr SUMMARY:Real/complex stratification and forgetful maps in Gromov-Witten-Floer theory LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: The 3rd IBS-CGP & BICMR Joint Symplectic Geometry Workshop\n\nAbstract: The proof of many of the interesting properties of Gromov-Witten invariant and of symplectic Floer theory uses a map between moduli spaces which forgets marked points. There are several heavy technical and/or conceptional problems to define and study such maps in symplectic setting.I will explain certain aspects about it. END:VEVENT BEGIN:VEVENT DTSTART:20190918T133000 DTEND:20190918T153000 DTSTAMP:20190917T150000Z UID:7432acf31ba0056b19ff024946ea6c4a@cgp.ibs.re.kr SUMMARY:Wall-crossing formula and Floer theory III LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formulaof Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witteninvariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of thislecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOOpotential function under the mutation of Lagrangian submanifolds in 4-dimensional symplecticmanifolds. Their proof in turn uses Seidel's comparison betweenthe Floer homologies of a (monotone) Lagrangian torus in the closed ambient spaceand in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20191010T160000 DTEND:20191010T180000 DTSTAMP:20191009T150000Z UID:1a80e4ada350d693313abef841152bf6@cgp.ibs.re.kr SUMMARY:Towards A+B theory in conifold transitions for Calabi-Yau threefolds LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuan-Pin Lee\n\nEvent: CGP Seminar\n\nAbstract: For projective conifold transitions between Calabi-Yau threefolds X and Y, with X close to Y in the moduli, we show that the combined information provided by the A model (Gromov--Witten theory in all genera) and B model (variation of Hodge structures) on X, linked along the vanishing cycles, determines the corresponding combined information on Y. Similar result holds in the reverse direction when linked with the exceptional curves. This is based on a joint project with Hui-Wen Lin, Chin-Lung Wang. END:VEVENT BEGIN:VEVENT DTSTART:20191001T160000 DTEND:20191001T180000 DTSTAMP:20190930T150000Z UID:62265aa9f27c725a7c8ac29fc03f1565@cgp.ibs.re.kr SUMMARY:Tropical geometry and Hodge theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yuto Yamamoto\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, we will briefly review basic results of tropical geometry, and discuss relations with Hodge theory. The goal will be to see the relation between tropical geometry and asymptotic behaviors of period maps in the case of Calabi—Yau hypersurfaces. END:VEVENT BEGIN:VEVENT DTSTART:20191014T160000 DTEND:20191014T170000 DTSTAMP:20191013T150000Z UID:814952ba96438a4d72f526a42fc2f477@cgp.ibs.re.kr SUMMARY:Configuration spaces of $\mathbb{S}^1$ and $\mathbb{R}^n$ by way of higher categories I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Anna Cepek\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We approach manifold topology by examining configurations of finite subsets of manifolds. The homotopy-types of such configurations organize as an $\infty$-category, the construction of which makes use of $stratified spaces$ and $exit-path $$\infty$$-categories$ thereof. The goal of this lecture series is to supply the constructions of these $\infty$-categories and to identify these $\infty$-categories in the case of$\mathbb{S}^1$ and$\mathbb{R}^n$in terms of the combinatorially defined $parasimplex category$ and Joyal's category ${\Theta}_n$, respectively. END:VEVENT BEGIN:VEVENT DTSTART:20191015T160000 DTEND:20191015T170000 DTSTAMP:20191014T150000Z UID:dc02fc5f7af48834eb6e88f9b73104da@cgp.ibs.re.kr SUMMARY:Configuration spaces of $\mathbb{S}^1$ and $\mathbb{R}^n$ by way of higher categories II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Anna Cepek\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We approach manifold topology by examining configurations of finite subsets of manifolds. The homotopy-types of such configurations organize as an $\infty$-category, the construction of which makes use of $stratified spaces$ and $exit-path $$\infty$$-categories$ thereof. The goal of this lecture series is to supply the constructions of these $\infty$-categories and to identify these $\infty$-categories in the case of $\mathbb{S}^1$ and $\mathbb{R}^n$in terms of the combinatorially defined $parasimplex category$ and Joyal's category ${\Theta}_n$, respectively. END:VEVENT BEGIN:VEVENT DTSTART:20191017T160000 DTEND:20191017T170000 DTSTAMP:20191016T150000Z UID:dd6b07da22309d3f722b3048e24c80a4@cgp.ibs.re.kr SUMMARY:Configuration spaces of $\mathbb{S}^1$ and $\mathbb{R}^n$ by way of higher categories III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Anna Cepek\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: We approach manifold topology by examining configurations of finite subsets of manifolds. The homotopy-types of such configurations organize as an $\infty$-category, the construction of which makes use of $stratified spaces$ and $exit-path $$\infty$$-categories$ thereof. The goal of this lecture series is to supply the constructions of these $\infty$-categories and to identify these $\infty$-categories in the case of $\mathbb{S}^1$ and $\mathbb{R}^n$in terms of the combinatorially defined $parasimplex category$ and Joyal's category ${\Theta}_n$, respectively. END:VEVENT BEGIN:VEVENT DTSTART:20191031T160000 DTEND:20191031T180000 DTSTAMP:20191030T150000Z UID:9dff1d1abfdd78586170e33e9a54d741@cgp.ibs.re.kr SUMMARY:Categorical systolic inequality for the Fukaya category of 4-dimensional Milnor fiber of ADE singularity LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: CGP Seminar\n\nAbstract: In 2018, Yu-Wei Fan introduced the notion of the categorical systole using Bridgeland stability condition and proved that analogues of classical systolic inequalities hold for the derived categories of elliptic curves and K3 surfaces of Picard rank 1. In this talk, I will talk about the categorical systolic inequality for the Fukaya category of 4-dimensional Milnor fiber of ADE singularity. END:VEVENT BEGIN:VEVENT DTSTART:20191023T133000 DTEND:20191023T153000 DTSTAMP:20191022T150000Z UID:b599b6966f6ec32fe3a0b5baab172214@cgp.ibs.re.kr SUMMARY:Wall-crossing formula and Floer theory IV LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formulaof Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witteninvariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of thislecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOOpotential function under the mutation of Lagrangian submanifolds in 4-dimensional symplecticmanifolds. Their proof in turn uses Seidel's comparison betweenthe Floer homologies of a (monotone) Lagrangian torus in the closed ambient spaceand in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20191106T133000 DTEND:20191106T153000 DTSTAMP:20191105T150000Z UID:7c4f1c6ee92353513c988a31f072b6b7@cgp.ibs.re.kr SUMMARY:Wall-crossing formula and Floer theory V LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formula of Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witten invariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of this lecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOO potential function under the mutation of Lagrangian submanifolds in 4-dimensional symplectic manifolds. Their proof in turn uses Seidel's comparison between the Floer homologies of a (monotone) Lagrangian torus in the closed ambient space and in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20191114T160000 DTEND:20191114T180000 DTSTAMP:20191113T150000Z UID:0ad4886345df27a0cc4c3cccf31497be@cgp.ibs.re.kr SUMMARY:Characteristic numbers of elliptic fourfolds LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Monica Jinwoo Kang\n\nEvent: CGP Seminar\n\nAbstract: I will consider crepant resolutions of Weierstrass models corresponding to elliptically fibered fourfolds with simple Lie algebras. Furthermore, I will discuss the fibrations with multisections or nontrivial Mordell-Weil groups. In contrast to the case of fivefolds, Chern and Pontryagin numbers of fourfolds are invariant under crepant birational maps. It follows that Chern and Pontryagin numbers are independent of a choice of a crepant resolution. I will explain how to compute Chern and Pontryagin numbers and other characteristic numbers such as the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory. END:VEVENT BEGIN:VEVENT DTSTART:20191118T100000 DTEND:20191118T110000 DTSTAMP:20191117T150000Z UID:e9ab40f0e386ce58bbc37377b8a751ed@cgp.ibs.re.kr SUMMARY:On the degree of irrationality of quartic 3-folds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: The degree of irrationality of an n-dimensional algebraic variety X is the minimal degree of a rational map from X to the projective n-space. We expect that the degree of irrationality is 3 for any nonsingular quartic 3-fold, which has been verified in most cases. I will explain that, for the remaining cases, this study is reduced to the irrationality of suitable del Pezzo fibrations ofdegree 2 and also explain their birational geometry. This is a joint work in progress with Igor Krylov, and my talk is connected to Igor's. END:VEVENT BEGIN:VEVENT DTSTART:20191118T113000 DTEND:20191118T123000 DTSTAMP:20191117T150000Z UID:198128d8aac436915bf4c71d96a4d6e3@cgp.ibs.re.kr SUMMARY:Toric G-Solid Fano Threefolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: In this talk, I will explain which finite quasi-simple non-abelian groups can faithfully act on rationally connected threefolds. This is a joint work with Jeremy Blanc, Alexander Duncan and Yuri Prokhorov. END:VEVENT BEGIN:VEVENT DTSTART:20191118T140000 DTEND:20191118T150000 DTSTAMP:20191117T150000Z UID:ea8581687407e8780f4791c73219a59c@cgp.ibs.re.kr SUMMARY:On log deformations of degenerate Calabi-Yau varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Taro Sano\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Kawamata-Namikawa developed log deformation theory of normal crossing varieties. By using this, we can construct Calabi-Yau manifolds as smoothings of normal crossing varieties. I’ll explain construction of non-Kähler Calabi-Yau 3-folds by this method. If time permits, I’ll also mention construction of more examples by recent results. This is based on joint work with Kenji Hashimoto. END:VEVENT BEGIN:VEVENT DTSTART:20191118T153000 DTEND:20191118T163000 DTSTAMP:20191117T150000Z UID:5c6d1c5fdb406d80483d31328a9ad1f5@cgp.ibs.re.kr SUMMARY:Calabi-Yau metrics on some symmetric spaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Thibaut Delcroix\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: In this talk, I will present how, in a joint work with O. Biquard, we constructed Ricci flat Kähler metrics on some rank two complex symmetric spaces. On compact complex manifolds, the existence of such metrics is fully understood by the famous solution by Yau of the Calabi conjecture. For non-compact manifolds as in our case, results of existence mostly rely on determining an asymptotic model. We determined geometrically meaningful asymptotic models in our situation by using the wonderful compactifications of symmetric spaces.The paper is available at \url{https://jep.centre-mersenne.org/item/JEP_2019__6__163_0/} END:VEVENT BEGIN:VEVENT DTSTART:20191118T170000 DTEND:20191118T180000 DTSTAMP:20191117T150000Z UID:d6d001ee5758961587c260b32ee9f2c8@cgp.ibs.re.kr SUMMARY:Local numerical equivalences and Okounkov bodies LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: In this talk, we study the relation between local numerical properties of divisors and behaviors of Okounkov bodies. More precisely, we show that the set of Okounkov bodies of a pseudoeffective divisor with respect to admissible flags centered at a fixed point determines the local numerical equivalence class of divisors which is defined in terms of refined divisorial Zariski decompositions. This result extends Roe’s work on surfaces to higher dimensional varieties. This is joint work with Sung Rak Choi and Joonyeong Won. END:VEVENT BEGIN:VEVENT DTSTART:20191119T100000 DTEND:20191119T110000 DTSTAMP:20191118T150000Z UID:f3a9313eec4c813fa4e762c5e69c2e98@cgp.ibs.re.kr SUMMARY:Finite groups of bimeromorphic selfmaps of uniruled Kähler threefolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: I am going to speak about finite groups of bimeromorphic selfmaps of uniruled compact Kähler threefolds. In particular, I classify those threefolds whose groups of bimeromorphic selfmaps do not have Jordan property. The talk is based on the joint work with C. Shramov. END:VEVENT BEGIN:VEVENT DTSTART:20191119T113000 DTEND:20191119T123000 DTSTAMP:20191118T150000Z UID:efd93734cd93fc92c625e9add55c6a67@cgp.ibs.re.kr SUMMARY:Equivariant K-stability and Valuative Criteria LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Ziwen Zhu\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: It is conjectured that in order to test K-polystability of a Fano variety, it is enough to consider only equivariant test configurations with respect to a reductive group action. This has been proved for Fano manifolds and in singular cases, only for torus actions. In this talk, I will talk about a valuative criterion of equivariant K-stability with respect to an arbitrary group action. This generalizesparallel results for usual K-stability. END:VEVENT BEGIN:VEVENT DTSTART:20191119T140000 DTEND:20191119T150000 DTSTAMP:20191118T150000Z UID:c7042fa270e9f475f27f22c6369691d4@cgp.ibs.re.kr SUMMARY:Sasaki-Einstein metrics on simply connected rational homology 5-spheres. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Boyer, Galicki and Kollar found many examples of Sasaki-Einstein Smale manifolds, simply connected 5-manifold. They verified existence of orbifold Kähler-Einstein metrics on various log delPezzo surfaces via links. By the recent development of method, delta invariant method via Newton polygon, to show the existence of orbifold Kähler-Einstein metrics, we complete the classification of simply connected rational homology 5-spheres that admits Sasaki-Einstein metrics. This is a joint work with Jihun Park. END:VEVENT BEGIN:VEVENT DTSTART:20191119T153000 DTEND:20191119T163000 DTSTAMP:20191118T150000Z UID:4c10472d6a6e57bfd4249a007cafb1f6@cgp.ibs.re.kr SUMMARY:Delta-invariants for Fano varieties with infinite automorphism groups. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Alexei Golota\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: The delta-invariant of a Fano variety X is a numerical invariant detecting uniform K-stability of X. Therefore, in case when the group of automorphisms of X is finite, this invariant also gives a criterion for existence of Kähler-Einstein metrics on X. In my talk I will discuss the ways to adapt delta-invariants and uniform K-stability to G-equivariant setting, G being a connected reductive group acting on a Fano variety X by automorphisms. I will also consider some classes of examples, including spherical Fano varieties and Fano varieties with group actions of complexity one. END:VEVENT BEGIN:VEVENT DTSTART:20191119T170000 DTEND:20191119T180000 DTSTAMP:20191118T150000Z UID:c79e86cca77556c8efb9aa9a2d6b00fd@cgp.ibs.re.kr SUMMARY:Kähler-Einstein Metrics on Symmetric General Arrangement Varieties LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jacob Cable\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20191120T100000 DTEND:20191120T110000 DTSTAMP:20191119T150000Z UID:d31f0fc6861a41af8b400616079cccf5@cgp.ibs.re.kr SUMMARY:Positivity in the asymptotic regime LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Yanir Rubinstein\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: A general theme in geometry is the classification of algebraic/differential geometric structures which satisfy a positivity property. I will describe an "asymptotic" version of this theme based on joint work over the years with Cheltsov, Martinez-Garcia, and Zhang. This leads to unexpected relations with convex optimization as well as deep relations to differential geometry. On the algebraic side, we introduce the class of asymptotically log Fano varieties and state a classification theorem in dimension 2, generalizing the classical efforts of the 19th century Italian school. The novelty here is the use of a convex optimization theorem that reduce the asymptotic positivity to determining intersection properties of high-dimensional convex bodies. On the differential side I will describe relations to Kähler-Einstein edge metrics. END:VEVENT BEGIN:VEVENT DTSTART:20191120T113000 DTEND:20191120T123000 DTSTAMP:20191119T150000Z UID:053095ccad69b05689ae0472671a2d96@cgp.ibs.re.kr SUMMARY:Partial $C^0$ estimates on polarized Kähler manifolds LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Kewei Zhang\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Partial $C^0$ estimate was first introduced by Tian in 1990, which is a crucial step in the solution of the Yau-Tian-Donaldson conjecture. In this talk I will discuss several aspects of the partial $C^0$ estimate and present some recent progress. END:VEVENT BEGIN:VEVENT DTSTART:20191121T100000 DTEND:20191121T110000 DTSTAMP:20191120T150000Z UID:3eba0674ee180a281b3b78bf3423f8e6@cgp.ibs.re.kr SUMMARY:Birational geometry of vector fields on a threefold. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Paolo Cascini\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: I will survey some old and new results towards the study of the birational geometry of vectors fields on a complex threefold. Joint work with C. Spicer. END:VEVENT BEGIN:VEVENT DTSTART:20191121T113000 DTEND:20191121T123000 DTSTAMP:20191120T150000Z UID:ba1c06b0a910ca653cecaab02f515a8b@cgp.ibs.re.kr SUMMARY:On embeddings of Klein simple group into the Cremona group. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Igor Krylov\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: The Cremona group is the group of the birational transformations of the projective space. It is known that for any finite subgroup $G$ in the Cremona group there is a rational variety $X$ on each $G$ acts biregularly. By running $G-MMP$ on $X$ we get a rational GQ-Mori fiber space. The study of embeddings of $G$ into the Cremona group is equivalent to study of rational GQ-Mori fiber spaces. I will talk about $PSL_2(7)Q$-del Pezzo fibrations, their rationality, and the relation to quotients of certain quartic threefolds. This a joint work with Takuzo Okada. This talk is related to his talk at this conference. END:VEVENT BEGIN:VEVENT DTSTART:20191121T140000 DTEND:20191121T150000 DTSTAMP:20191120T150000Z UID:cec54a7768b1f1073ab51713aff65255@cgp.ibs.re.kr SUMMARY:Kähler degenerations and Okounkov bodies LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: David Witt Nystrom\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Okounkov bodies were introduced by Okounkov in the 90's as a way of generalizing the correspondence between line bundles and polytopes in toric geometry to the setting of ample line bundles on projective manifolds. I will discuss a new way of thinking of Okounkov bodies as arising from certain degenerations of the manifold together with its Kähler structure. This is work in progress together Ya Deng. END:VEVENT BEGIN:VEVENT DTSTART:20191121T153000 DTEND:20191121T163000 DTSTAMP:20191120T150000Z UID:40473f90000f25340e6e0cebe5f4b65a@cgp.ibs.re.kr SUMMARY:Hodge minimality of weighted complete intersections LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Victor Przyjalkowski\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: We discuss Fano varieties whose Hodge diamonds are close to minimal ones. We discuss several conjectures related to them, and classify those of them who can be represented as smooth Fano weighted complete intersections. It turns out that the minimality has derived categories origin. END:VEVENT BEGIN:VEVENT DTSTART:20191121T170000 DTEND:20191121T180000 DTSTAMP:20191120T150000Z UID:9ed92b4f733182098c0c4f26a50e7257@cgp.ibs.re.kr SUMMARY:Quotients of del Pezzo surfaces LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Andrey Trepalin\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Let $X$ be a del Pezzo surface over arbitrary field $k$ of characteristic 0, and $G$ be a finite subgroup in $Aut(X)$. Assume that there is a smooth $k$-point on the quotient $X / G$. We want to find possibilities of $X$ and $G$ such that the quotient $X / G$ is not rational over $k$. In the talk I will give a complete list of such possibilities, show that for the other pairs $X$ and $G$ the quotient $X / G$ is rational over $k$, and discuss some related questions. END:VEVENT BEGIN:VEVENT DTSTART:20191122T100000 DTEND:20191122T110000 DTSTAMP:20191121T150000Z UID:66ad2eea7f995ac11526f685257ebc58@cgp.ibs.re.kr SUMMARY:Higher-rank Khovanskii-Teissier Inequalities LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Julius Ross\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: The Hard-Lefschetz theorem and the Hodge-Riemann bilinear relations touch many parts of algebraic geometry, including birational geometry and K-stability. Classically this involves the choice of some positive cohomology class, such as (a power of) the first Chern class of an ample line bundle. I shall discuss a generalization of this package of ideas to Schur classes of ample vector bundles. From this we obtain various applications, including various new log-concavity type inequalities of characteristic classes that can be thought of as higher rank version of the Khovanskii-Tessier inequalities. All of this is joint work with Matei Toma. END:VEVENT BEGIN:VEVENT DTSTART:20191122T113000 DTEND:20191122T123000 DTSTAMP:20191121T150000Z UID:6aedaa34fc2c5b2bbe3c1bfa476530fc@cgp.ibs.re.kr SUMMARY:Abundant divisors, Iitaka fibrations and Okounkov bodies LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Being abundant for a divisor is a very strong condition and it is worthwhiie to give nice characterizations of abundant divisors. We will study some equivalent conditions to being abundant through the properties of Iitaka fibrations. We will also point out some subtle issues raised recently by Lesieutre. We then study the Okounkov bodies of abundant divisors. This is a joint work by J. Park and J. Won. END:VEVENT BEGIN:VEVENT DTSTART:20191122T140000 DTEND:20191122T150000 DTSTAMP:20191121T150000Z UID:9767c52618fc2e87e0c0453d7e5db3c0@cgp.ibs.re.kr SUMMARY:Boundedness of K-semistable $\mathbb{Q}$-Fano varieties with degrees bounded from below. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Jiang Chen\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: Applying recent development in birational geometry by Birkar, we show that $\mathbb{Q}$ Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family. This is an important step towards the moduli problem of K-(semi)stable Fano varieties. If time permits, I will also introduce another nice approach to this result by Yuchen Liu. END:VEVENT BEGIN:VEVENT DTSTART:20191122T153000 DTEND:20191122T163000 DTSTAMP:20191121T150000Z UID:ed938b2733a8895a0880dc98bb05b5a5@cgp.ibs.re.kr SUMMARY:Automorphisms of elliptic surfaces. LOCATION:Math. Bldg. #404 DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Birational Geometry, Kaehler-Einstein Metrics and Degenerations: Moscow-Shanghai-Pohang\n\nAbstract: I will discuss automorphism groups acting on compact complex surfaces that have a structure ofan elliptic fibration, and stabilizers of points therein. In particular, we will see that the image of an automorphism group of a surface of Kodaira dimension 1 in the automorphism group of the base of its pluricanonical fibration is finite. I will also speculate on possible higher dimensional generalizations. END:VEVENT BEGIN:VEVENT DTSTART:20191113T133000 DTEND:20191113T153000 DTSTAMP:20191112T150000Z UID:3f140cd45464f9dade778c9a2dbd8c30@cgp.ibs.re.kr SUMMARY:Wall-crossing formula and Floer theory VI LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: In this series of lectures, I will survey the general wall crossing formula of Kontsevich-Soibelman and its implication in the study of open genus 0 Geomov-Witten invariants and its generating function, the Fukaya-Oh-Ohta-Ono(FOOO) potential function. The goal of this lecture series is to explain Pascaleff-Tongnog's proof of the wall crossing formula for the FOOO potential function under the mutation of Lagrangian submanifolds in 4-dimensional symplectic manifolds. Their proof in turn uses Seidel's comparison between the Floer homologies of a (monotone) Lagrangian torus in the closed ambient space and in the complement of its canonical divisor. END:VEVENT BEGIN:VEVENT DTSTART:20191128T160000 DTEND:20191128T180000 DTSTAMP:20191127T150000Z UID:e1b2b8846e3de66e4e98f8d4b1b68d63@cgp.ibs.re.kr SUMMARY:Doubling stops and spherical swaps LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Zachary Sylvan\n\nEvent: CGP Seminar\n\nAbstract: I'll discuss the partially wrapped Fukaya category associated to a stop (e.g. a Legendrian) in the boundary of a Liouville domain and the Orlov-type functor associated to it. When the stop admits a particular type of self-isotopy, the corresponsing Orlov functor is spherical in the sense of Anno--Logvinenko. I'll explain how this happens and state some basic consequences of it. END:VEVENT BEGIN:VEVENT DTSTART:20191125T160000 DTEND:20191125T180000 DTSTAMP:20191124T150000Z UID:c1f8aea675cbdfd48cde1afa63ce63bc@cgp.ibs.re.kr SUMMARY:A Survey for LG/LG Mirror Symmetry LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yifan Li\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Originated by an old physical construction, the mirror phenomenon between Landau-Ginzburg models (Berglund-Hübsch-Krawitz mirror) is an important topic in both Physics and in Mathematics. As a conjectured equivalence between two different types of singularity theories, surprisingly, it was rarely investigated by Mathematicians. This is mainly duo to the late appearance of a rigorous construction for Landau-Ginzburg A-models and lack of a generalization of K. Saito's theory of primitive forms for Landau-Ginzburg B-models. In this talk, I will give a brief introduction for the present progress of LG/LG mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20191212T160000 DTEND:20191212T180000 DTSTAMP:20191211T150000Z UID:d39c579c52e5a251d6dfcac34ff0b385@cgp.ibs.re.kr SUMMARY:Artin's primitive root conjecture for function fields without Riemann Hypothesis LOCATION:CGP Main Hall DESCRIPTION:Speaker: Seoyoung Kim\n\nEvent: CGP Seminar\n\nAbstract: Artin's primitive root conjecture for function fields is known by Bilharz in his thesis in 1937, which was conditional on the proof of the Riemann hypothesis for global function fields, which was proved by Weil in 1948. In this talk, we suggest a simple proof of Artin's primitive root conjecture for function fields by using the technique from the proof of the prime number theorem by Hadamard and de la Vall/'ee Poussin. This is joint work with M. Ram Murty. END:VEVENT BEGIN:VEVENT DTSTART:20191202T101500 DTEND:20191202T111500 DTSTAMP:20191201T150000Z UID:5907c7af3bdad054a5db4fda6b5c76f7@cgp.ibs.re.kr SUMMARY:Sectorial Viterbo functor LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Zachary Sylvan\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191202T113000 DTEND:20191202T123000 DTSTAMP:20191201T150000Z UID:76be8f584dc36801caff87701fc9f305@cgp.ibs.re.kr SUMMARY:Non-displaceable Lagrangian links in four-manifolds LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Cheuk Yu Mak\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191202T140000 DTEND:20191202T150000 DTSTAMP:20191201T150000Z UID:ef9b867f8cd78fe272654df59a0ebec6@cgp.ibs.re.kr SUMMARY:Symplectic Banach-Mazur distance and Riemannian metrics LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jun Zhang\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191202T151500 DTEND:20191202T160000 DTSTAMP:20191201T150000Z UID:9bd07fafc77b54af30fec1161cf3e0ce@cgp.ibs.re.kr SUMMARY:Categorical systolic inequality for the Fukaya category of Milnor fiber of ADE singularity LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191202T161500 DTEND:20191202T170000 DTSTAMP:20191201T150000Z UID:a552fcf3b9d1baac03035ae037cfc78a@cgp.ibs.re.kr SUMMARY:On Sebastian-Thom type theorem for Fukaya-Seidel categories LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Masahiro Futaki\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191203T101500 DTEND:20191203T111500 DTSTAMP:20191202T150000Z UID:dc9b370748bf492a0b92a9dcc8446f7e@cgp.ibs.re.kr SUMMARY:Knotted symplectic embeddings LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jean Gutt\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191203T113000 DTEND:20191203T123000 DTSTAMP:20191202T150000Z UID:a4826623afa461b6f8ba998efe327a7d@cgp.ibs.re.kr SUMMARY:Viterbo transfer as localization LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Zachary Sylvan\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191203T140000 DTEND:20191203T150000 DTSTAMP:20191202T150000Z UID:585096e8dea22dd54596da8ec1a54692@cgp.ibs.re.kr SUMMARY:Fukaya-Seidel categories of nilpotent slices and category O LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Cheuk Yu Mak\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191203T151500 DTEND:20191203T160000 DTSTAMP:20191202T150000Z UID:e700935cf443323022b57c174fee96c7@cgp.ibs.re.kr SUMMARY:A higher-dimensional generalization of pseudo-Anosov surface automorphisms LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191203T161500 DTEND:20191203T170000 DTSTAMP:20191202T150000Z UID:4515289c4ff79a8f04eee03703245114@cgp.ibs.re.kr SUMMARY:Liouville manifolds of Weinstein type LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Toru Yoshiyasu\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191204T101500 DTEND:20191204T111500 DTSTAMP:20191203T150000Z UID:aacdc8998df18caf6771a8044eeebb9a@cgp.ibs.re.kr SUMMARY:Shape invariant and coarse Banach-Mazur distance LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jun Zhang\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191204T113000 DTEND:20191204T123000 DTSTAMP:20191203T150000Z UID:1bf3c9f14db9563063b5b095b7721920@cgp.ibs.re.kr SUMMARY:Symplectic homology is a Morse theory LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jean Gutt\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191204T140000 DTEND:20191204T143000 DTSTAMP:20191203T150000Z UID:d1e07262c67b573ba8d7be98289bf466@cgp.ibs.re.kr SUMMARY:Wrapped Fukaya category of Riemann surface of infinite type LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Jae-Young Choi\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191204T144500 DTEND:20191204T151500 DTSTAMP:20191203T150000Z UID:8bea08a47ccc96bdb40836db56592a49@cgp.ibs.re.kr SUMMARY:Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a,b,c}$ in ${ \mathbb \ CP}^2$ LOCATION:RIMS, Room 110, Kyoto University DESCRIPTION:Speaker: Weonmo Lee\n\nEvent: RIMS&IBS-CGP Joint Symplectic Geometry Workshop\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191206T100000 DTEND:20191206T104000 DTSTAMP:20191205T150000Z UID:618e49a64d6f08663fe3919a661db4a7@cgp.ibs.re.kr SUMMARY:Legendrian Pretzel knots, Lagrangian fillings, and cluster structures LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: The space of exact orientable Lagrangian fillings of a Legendrian knot is of special interest. Even though the topology of the filling is determined by the slice genus of the knot, there are many distinct Lagrangian fillings up to exact Lagrangian isotopy. Moreover, it forms a cluster structure, which is also related to the wall-crossing phenomenon in symplectic geometry. In this talk, I will discuss Legendrian Pretzel knots and give an estimate for the number of fillings of them. This is a joint work in progress with Byung Hee An. END:VEVENT BEGIN:VEVENT DTSTART:20191127T133000 DTEND:20191127T153000 DTSTAMP:20191126T150000Z UID:9a987317c04928fb9f61a00117b64367@cgp.ibs.re.kr SUMMARY:'Organizational meeting' for `Cluster algebra and related topics' LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20191207T140000 DTEND:20191207T144000 DTSTAMP:20191206T150000Z UID:430f238a0e94161a28eaa5ebeb5e4c20@cgp.ibs.re.kr SUMMARY:From complex to p-adic theta functions LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Clifford Blakestad\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: Complex theta functions have played a major role in geometry and number theory for the last 150 years. We will introduce the complex theta function of Riemann and the associated complex torus. Such complex tori must admit the structure of an abelian variety. We will switch to discuss the p-adic perspective, where we will describe the structure of p-adic abelian varieties along with the landscape for p-adic analogs of theta functions and how they work in some special cases. END:VEVENT BEGIN:VEVENT DTSTART:20191206T111000 DTEND:20191206T115000 DTSTAMP:20191205T150000Z UID:73250e0eb623fb342a43eb008f2f2948@cgp.ibs.re.kr SUMMARY:Singularities of class T and orthogonal collections LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Yonghwa Cho\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: In a smooth projective variety, exceptional vector bundles can be viewed as a simplest building block of the derived category. For instance, in the projective plane, it is known that the derived category can be decomposed into three exceptional vector bundles having certain relations. The classification of such triples were done by Gorodentsev-Rudakov. Surprisingly, the classification looks very similar to the classification of the toric degenerations done by Manetti and Hacking-Prokhorov. In this talk, we briefly introduce the Hacking's work which explains the reason why those similarities occur. Then, we discuss our recent attempts to answer the next question: what can we say if we consider a del Pezzo surface instead of a projective plane? To answer this question, we need consider the singularities of class T and their Q-Gorenstein smoothing. END:VEVENT BEGIN:VEVENT DTSTART:20191206T140000 DTEND:20191206T144000 DTSTAMP:20191205T150000Z UID:3207885385d3042d7f871f4cb33b70b8@cgp.ibs.re.kr SUMMARY:On the deformation rigidity of smooth projective symmetric varieties with Picard number one LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Shinyoung Kim\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: I will talk about the deformation rigidity of smooth projective symmetric varieties with Picard number one, and background about this problem. This is joint work with K.-D.Park END:VEVENT BEGIN:VEVENT DTSTART:20191207T100000 DTEND:20191207T104000 DTSTAMP:20191206T150000Z UID:d2686070e4847a481421c3b496aea570@cgp.ibs.re.kr SUMMARY:String polytopes and their small resolutions LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: For a given smooth projective variety X and a flat toric degeneration with the central fiber Y, one can construct a Lagrangian torus fibration on X over the polytope P associated to Y. It is known that one can compute the disc potential of each Lagrangian fiber in terms of the combinatorics of P whenever Y admits a small resolution. In this talk, we consider a full flag variety X and a toric degeneration associated to so-called a string polytope and show the existence of a small resolution of Y in a low dimensional case. This is joint work with Yoosik Kim, Eunjeong Lee, and Kyeong-Dong Park. END:VEVENT BEGIN:VEVENT DTSTART:20191125T133000 DTEND:20191125T153000 DTSTAMP:20191124T150000Z UID:1f66b991cf50e9fe1de17e313fd305a8@cgp.ibs.re.kr SUMMARY:Introduction to configuration spaces I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Anna Cepek\n\nEvent: Derived Seminar\n\nAbstract: The Derived Seminar is an informal seminar where CGP members gather to discover a new topic of interest. Each talk shall be made by, and for, the participants. It is subject to constant and unpredictable evolution. END:VEVENT BEGIN:VEVENT DTSTART:20191202T133000 DTEND:20191202T153000 DTSTAMP:20191201T150000Z UID:c50ceb0ff54525516731a56c2b36b1fb@cgp.ibs.re.kr SUMMARY:Introduction to configuration spaces II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Derived Seminar\n\nAbstract: The Derived Seminar is an informal seminar where CGP members gather to discover a new topic of interest. Each talk shall be made by, and for, the participants. It is subject to constant and unpredictable evolution. END:VEVENT BEGIN:VEVENT DTSTART:20191207T111000 DTEND:20191207T115000 DTSTAMP:20191206T150000Z UID:0bdad4993dc852fe4d25b360c66e244e@cgp.ibs.re.kr SUMMARY:Local Tamagawa volume and smooth integral scheme LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Sungmun Cho\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: Local Tamagawa volume is a core ingredient in many branches of number theory, such as Siegel mass formula, Kudla's program, Fundamental Lemma, and so on. Although there are several approaches for computing/figuring out local Tamagawa volume, it seems "the" best way is Weil's observation, through the number of the special fiber of a certain smooth integral scheme. In this talk, I will explain a method to construct smooth integral schemes and explain its contribution to the topics listed above. END:VEVENT BEGIN:VEVENT DTSTART:20191207T145000 DTEND:20191207T153000 DTSTAMP:20191206T150000Z UID:3b0a71a54ff3f52d69581370c62ba578@cgp.ibs.re.kr SUMMARY:Geometric manifolds and character varieties LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Hongtaek Jung\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: The theory of geometric manifolds is one of the essential tools to study the geometry of character varieties and representations. I will introduce the notion of geometric structures on manifolds and their deformation spaces. A particular emphasis will be given to hyperbolic and projective manifolds. Then I will explain how the deformation spaces of geometric structures and character varieties are related. Through this bridge many interesting properties on representations and character varieties have been obtained and I will discuss some of those results. END:VEVENT BEGIN:VEVENT DTSTART:20191207T160000 DTEND:20191207T164000 DTSTAMP:20191206T150000Z UID:a976ef6cf094993169ee31aaaad0e570@cgp.ibs.re.kr SUMMARY:Relative Kähler-Ricci flow on a family of strongly pseudoconvex domains LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: In 2012, Schumacher proved that the variation of Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive definite on the total space. In his paper, he showed that the geodesic curvature, which measures the positivity of the horizontal direction, satisfies a certain elliptic PDE. Applying the maximum principle to this PDE, he obtained the positivity. In 2013, Berman proved the parabolic version of the Schumahcer's result. More precisely, he proved that the geodesic curvature of a family of canonically polarized compact Kähler manifolds satisfies a parabolic equation. A parabolic maximum principle implies that the positivity of the geodesic curvature is preserved along the Kähler-Ricci flow. In this talk, we will briefly introduce the results of Schumacher and Berman and show how to apply Berman's method to a family of strongly pseudoconvex domains. This is joint work with Young-Jun Choi. END:VEVENT BEGIN:VEVENT DTSTART:20191208T091000 DTEND:20191208T095000 DTSTAMP:20191207T150000Z UID:d55481fa9cf2b9f6f115600243596795@cgp.ibs.re.kr SUMMARY:Isotopies of surfaces in 4-manifolds LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Seungwon Kim\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: In this talk, we consider surfaces embedded in 4-manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary 4-manifold. This extends work of Swenton and Kearton-Kurlin in 4-sphere. We consider applications of this result to bridge trisections of surfaces in 4-manifolds and Gluck twist in 4-sphere.This project is joint with Mark Hughes and Maggie Miller. END:VEVENT BEGIN:VEVENT DTSTART:20191208T100000 DTEND:20191208T104000 DTSTAMP:20191207T150000Z UID:8995f283a8a2f6bab61ab1bac5a14f2a@cgp.ibs.re.kr SUMMARY:Effect of noise on stochastic heat equations LOCATION:Maison Glad Jeju DESCRIPTION:Speaker: Kunwoo Kim\n\nEvent: 2019 Pohang Mathematics Workshop\n\nAbstract: Stochastic heat equations usually refer to heat equations perturbed by noise. We first consider what “noise” means mathematically, and then consider stochastic heat equations perturbed by space-time white noise. Those stochastic heat equations have similar properties as heat equations (such as positivity) and some other properties which cannot be seen from heat equations (such as intermittency). We characterize various properties of stochastic heat equations in this talk. END:VEVENT BEGIN:VEVENT DTSTART:20191217T160000 DTEND:20191217T180000 DTSTAMP:20191216T150000Z UID:fd730a6683b5bd916b1e3c2dde0a1807@cgp.ibs.re.kr SUMMARY:On the way to a proof of the dlt extension of the abundance conjecture LOCATION:CGP Main Hall DESCRIPTION:Speaker: Tsz On Mario Chan\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, I'm going to give an brief overview of the conjecture of the "dlt extension" in relation to the abundance conjecture, and a review of the proof of the plt extension following the line in the work of Demailly-Hacon-Paun. I'm also going to introduce the "lc-measure", a potential candidate of the replacement of the Ohsawa measure in the estimate of the Ohsawa-Takegoshi $L^2$ extension theorem, which will hopefully lead to a proof to the dlt extension. END:VEVENT BEGIN:VEVENT DTSTART:20191210T170000 DTEND:20191210T180000 DTSTAMP:20191209T150000Z UID:6d39b687f3a686818710a086704b26b6@cgp.ibs.re.kr SUMMARY:Compactifications of rational curve spaces in del Pezzo $3$-fold LOCATION:CGP Main Hall DESCRIPTION:Speaker: Kiryong Chung\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Let $V_5$ be the del Pezzo $3$-fold defined by the $6$-dimensional linear section of the Grassmannian variety $\mathrm{Gr}(2,5)$ under the Plücker embedding. In this talk, we present an explicit birational relation of compactifications of degree two rational curves (i.e., conics) in $V_5$. By a product, we obtain the virtual Poincaré polynomial of compactified moduli spaces. This is joint work with Sang-Bum Yoo (UNIST). If time permits, we also discuss the twisted cubic case. END:VEVENT BEGIN:VEVENT DTSTART:20191219T160000 DTEND:20191219T180000 DTSTAMP:20191218T150000Z UID:bd5a2cf9ae1c77942c517c55d9e2c021@cgp.ibs.re.kr SUMMARY:Link homology theories, ribbon concordances, and their generalizations LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sungkyung Kang\n\nEvent: CGP Seminar\n\nAbstract: It was recently proven by Zemke, by his "doubling trick", that knot Floer homology induces injective maps under ribbon concordances, and this result was quickly generalized to other link homology theories, under weaker conditions than being ribbon. I will present the proof that the doubling trick can be used to prove that almost all link TQFTs known up to now induce injective maps under ribbon concordances, and discuss what happens in the strongly homotopy-ribbon case. END:VEVENT BEGIN:VEVENT DTSTART:20191211T133000 DTEND:20191211T153000 DTSTAMP:20191210T150000Z UID:cf37afa811cacf54cebebedd2be4e831@cgp.ibs.re.kr SUMMARY:Introduction to cluster structures I LOCATION:CGP Delta DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Director's Seminar\n\nAbstract: Let $M$ be an $n \times n$ matrix with real entries. We call $M$ is totally positive if its all minors are positive numbers. Studying totally positivity was one of the main motivations for the development of cluster algebras. In these two talks, we will study totally positive matrices, and basic notion on cluster structures, e.g., quivers, mutations, seeds, and so on. END:VEVENT BEGIN:VEVENT DTSTART:20191218T160000 DTEND:20191218T180000 DTSTAMP:20191217T150000Z UID:ea2e863fef9c88b6a4d6b6eae14097f1@cgp.ibs.re.kr SUMMARY:Introduction to cluster structures II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Director's Seminar\n\nAbstract: Let $M$ be an $n \times n$ matrix with real entries. We call $M$ is totally positive if its all minors are positive numbers. Studying totally positivity was one of the main motivations for the development of cluster algebras. In these two talks, we will study totally positive matrices, and basic notion on cluster structures, e.g., quivers, mutations, seeds, and so on. END:VEVENT BEGIN:VEVENT DTSTART:20200120T160000 DTEND:20200120T180000 DTSTAMP:20200119T150000Z UID:646615237f2589a6bca783d4710c1e0b@cgp.ibs.re.kr SUMMARY:Weakly 1-completeness of fiber bundles over compact Kahler manifolds I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Aeryeong Seo\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In 1985 Diederich and Ohsawa proved that every disc bundle over a compact Kahler manifold is weakly 1-complete. In this talk I will talk about a generalization of this result to the case of fiber bundles over compact Kahler manifolds whose fibers are irreducible bounded symmetric domains under certain conditions. Moreover if the bundle is obtained by the diagonal action on the product of irreducible bounded symmetric domains, it is hyperconvex. END:VEVENT BEGIN:VEVENT DTSTART:20200121T160000 DTEND:20200121T180000 DTSTAMP:20200120T150000Z UID:814e5574887c4c2ed03848851fda9a79@cgp.ibs.re.kr SUMMARY:Weakly 1-completeness of fiber bundles over compact Kahler manifolds II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Aeryeong Seo\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In 1985 Diederich and Ohsawa proved that every disc bundle over a compact Kahler manifold is weakly 1-complete. In this talk I will talk about a generalization of this result to the case of fiber bundles over compact Kahler manifolds whose fibers are irreducible bounded symmetric domains under certain conditions. Moreover if the bundle is obtained by the diagonal action on the product of irreducible bounded symmetric domains, it is hyperconvex. END:VEVENT BEGIN:VEVENT DTSTART:20200116T160000 DTEND:20200116T180000 DTSTAMP:20200115T150000Z UID:935c7306c3fd05544640e7ea397bfa65@cgp.ibs.re.kr SUMMARY:Virtual Intersection Theories LOCATION:CGP Main Hall DESCRIPTION:Speaker: Hyeonjun Park\n\nEvent: CGP Seminar\n\nAbstract: In this talk, I will give an introduction to virtual fundamental classes, which played a crucial role in modern enumerative geometry. We will begin with the construction of virtual classes and explaining the three most influential properties: virtual pullback, torus localization, and cosection localization, in the setting of Chow theory. Then we will discuss joint work with Young-Hoon Kiem (arXiv:1908.03340) on how to generalize this theory of virtual classes to other types of intersection theories, including algebraic K-theory and algebraic cobordism. END:VEVENT BEGIN:VEVENT DTSTART:20200102T160000 DTEND:20200102T180000 DTSTAMP:20200101T150000Z UID:d7b670ff7dad1d02bc9fcbee1edd343b@cgp.ibs.re.kr SUMMARY:Birational geometry of moduli spaces of curves and K3 surfaces LOCATION:CGP Main Hall DESCRIPTION:Speaker: Changho Han\n\nEvent: CGP Seminar\n\nAbstract: Observe that any construction of "meaningful" compactification of moduli spaces of objects involves enlarging the class of objects in consideration. For example, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g. First, I will briefly introduce the two general strategies (both geometric and Hodge-theoretic) for obtaining a reasonably nice compactification. Then, I will introduce different realizations of smooth curves of genus 4, which gives a birational map between the moduli of alpha-stable curves, moduli of 'almost K3' stable log surfaces (where the underlying surfaces are rational), and the moduli of degree 6 K3 surfaces with nonsymplectic Z/3Z group action. The main goal of this talk is to describe the (known and unknown) birational relations between these different realizations. This is a joint work in progress with Valery Alexeev, Anand Deopurkar, and Philip Engel. END:VEVENT BEGIN:VEVENT DTSTART:20200130T160000 DTEND:20200130T180000 DTSTAMP:20200129T150000Z UID:a8a2cf87c30ccd8c2cd297f1a55d46ee@cgp.ibs.re.kr SUMMARY:Fiberwise Kähler-Einstein metric and Kähler-Ricci flow on a family of strongly pseudoconvex domains LOCATION:CGP Main Hall DESCRIPTION:Speaker: Young-Jun Choi\n\nEvent: CGP Seminar\n\nAbstract: In 2012, Schumacher proved that the variation of Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive definite on the total space. In his paper, he showed that the geodesic curvature, which measures the positivity of the horizontal direction, satisfies a certain elliptic PDE. Applying the maximum principle to this PDE, he obtained the positivity.In 2013, Berman proved the parabolic version of the Schumahcer's result.More precisely, he proved that the geodesic curvature of a family of canonically polarized compact Kähler manifolds satisfies a parabolic equation. A parabolic maximum principle implies that the positivity of the geodesic curvature is preserved along the Kähler-Ricci flow. In this talk, we will briefly introduce the above results and discuss how to apply their methods to a family of strongly pseudoconvex domains. END:VEVENT BEGIN:VEVENT DTSTART:20200122T133000 DTEND:20200122T153000 DTSTAMP:20200121T150000Z UID:1c835f71f79a77841824e09601e8395d@cgp.ibs.re.kr SUMMARY:Cluster algebras, quiver representations and Caldero-Chapoton formula LOCATION:CGP Delta DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: Director's Seminar\n\nAbstract: There is a one-to-one correspondence between non-initial cluster variables and positive roots for ADE Dynkin case (Fomin-Zelevinsky, 2003). On the other hand, for ADE Dynkin case, positive roots are in one-to-one correspondence with indecomposable representations (Gabriel, 1972). In this talk, I will start by reviewing Auslander-Reiten theory and then explain how to obtain cluster variables directly from indecomposable representations as weighted Euler characteristics of some quiver Grassmannians (Caldero-Chapoton, 2006). END:VEVENT BEGIN:VEVENT DTSTART:20200113T133000 DTEND:20200113T153000 DTSTAMP:20200112T150000Z UID:b5cb9fa043ad6036123883f4f728e954@cgp.ibs.re.kr SUMMARY:Mapping spaces I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Anna Cepek\n\nEvent: Derived Seminar\n\nAbstract: The Derived Seminar is an informal seminar where CGP members gather to discover a new topic of interest. Each talk shall be made by, and for, the participants. It is subject to constant and unpredictable evolution. END:VEVENT BEGIN:VEVENT DTSTART:20200121T130000 DTEND:20200121T150000 DTSTAMP:20200120T150000Z UID:0342b991e9902a26f4d739ccfaaa4271@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200128T130000 DTEND:20200128T150000 DTSTAMP:20200127T150000Z UID:2f8d75b0a690d52f4b10c323fe0c2023@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200204T130000 DTEND:20200204T150000 DTSTAMP:20200203T150000Z UID:88d5c4157ef2f8125645882cd44c4d8a@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200211T130000 DTEND:20200211T150000 DTSTAMP:20200210T150000Z UID:0accd8a5f9ccb1e667d7484076d3ba5b@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200218T130000 DTEND:20200218T150000 DTSTAMP:20200217T150000Z UID:631673913508a75c7915c455b07ea070@cgp.ibs.re.kr SUMMARY:Symplectic cohomology of Liouville sectors II LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dogancan Karabas\n\nEvent: Seminar\n\nAbstract: In this talk, we will define symplectic cohomology of Liouville sectors following Ganatra-Pardon-Shende. We will recall some facts about infinity categories and homotopy colimits. We will mainly discuss the admissible Hamiltonians and almost complex structures which we need to use in the definition of symplectic cohomology, in particular, near the boundary of the Liouville sectors. END:VEVENT BEGIN:VEVENT DTSTART:20200207T130000 DTEND:20200207T150000 DTSTAMP:20200206T150000Z UID:4974cd27ea3dcfaaa88cec4b57f4f1ad@cgp.ibs.re.kr SUMMARY:M. Kontsevich’s graph complexes and universal structures on graded symplectic manifolds LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Kevin Morand\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a universal version of the deformation theory for the Schouten algebra of polyvector fields on affine manifolds. This construction is generalised to graded symplectic manifolds of arbitrary degree n ≥ 1. The corresponding graph model is given by the full Kontsevich graph complex fGCd where d=n+1 stands for the dimension of the associated AKSZ type σ-model. This generalisation is instrumental to classify universal structures on graded symplectic manifolds. We conclude by discussing the possible rôle played by this new deformation theory regarding the quantization problem for Courant algebroids and higher symplectic Lie-n algebroids. END:VEVENT BEGIN:VEVENT DTSTART:20200205T133000 DTEND:20200205T153000 DTSTAMP:20200204T150000Z UID:3135b517b3a372634a9e713cddb2662e@cgp.ibs.re.kr SUMMARY:Cluster structure for Vianna’s Lagrangian tori LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: I will discuss the cluster structure of the Laurent polynomials associated to Vianna’s family of Lagrangian tori following Galkin and Usnich. END:VEVENT BEGIN:VEVENT DTSTART:20200303T130000 DTEND:20200303T150000 DTSTAMP:20200302T150000Z UID:2b550ef09657b5adc7873d7bbe208b30@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200310T130000 DTEND:20200310T150000 DTSTAMP:20200309T150000Z UID:707b0f36fe45cae6e35878e2ef975d92@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:Nowhere DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: \n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200317T130000 DTEND:20200317T150000 DTSTAMP:20200316T150000Z UID:357aa98028c57ecb1bc83b7b10800fce@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:Nowhere DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: \n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200507T133000 DTEND:20200507T153000 DTSTAMP:20200506T150000Z UID:13f68d4df54f9e6485aae465177e7907@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200512T133000 DTEND:20200512T153000 DTSTAMP:20200511T150000Z UID:312ce18fc1cc256738d5ea97fbdc82d2@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200519T133000 DTEND:20200519T153000 DTSTAMP:20200518T150000Z UID:60c339883425f899f0f890077ee8b2b5@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200526T133000 DTEND:20200526T153000 DTSTAMP:20200525T150000Z UID:f47ccb3fb389c77c9f3ca80d20a60c8f@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200506T133000 DTEND:20200506T153000 DTSTAMP:20200505T150000Z UID:f5ff0e2921138ae90b96e1b70fdebede@cgp.ibs.re.kr SUMMARY:Quantum cohomology ring of birational Calabi-Yau manifolds LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: Mark McLean recently showed that any two birational Calabi-Yau manifoldshave isomorphic (small) quantum cohomology algebras after a change of Novikov rings, using the tool of symplectic cohomogy of the complements ofsome birational loci of the two birational Calabi-Yau manifolds. We will read throughhis paper "Birational Calabi-Yau manifolds have the same small quantum products. Ann. of Math. (2) 191 (2020), no. 2, 439–579". END:VEVENT BEGIN:VEVENT DTSTART:20200514T133000 DTEND:20200514T153000 DTSTAMP:20200513T150000Z UID:d3291b10aab92f73557c372859bdbc4c@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200521T133000 DTEND:20200521T153000 DTSTAMP:20200520T150000Z UID:756fef1a6213a5c3b54f38418a1e8b08@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200528T133000 DTEND:20200528T153000 DTSTAMP:20200527T150000Z UID:d048a4425c09a3e9fe83c6dd74c1f0c3@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200513T130000 DTEND:20200513T150000 DTSTAMP:20200512T150000Z UID:78fba3e621189038311938aedbe4adf2@cgp.ibs.re.kr SUMMARY:Birational Calabi–Yau n-folds have the same Zeta functions. LOCATION:CGP Delta DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: Director's Seminar\n\nAbstract: Victor V. Batyrev showed in 1999 through the p-adic integration that any two birational Calabi-Yau n-folds have the same Betti numbers as a consequence of them having the same Weil Zeta functions. His paper articulates the special class of geometric objects where one could effectively use the motivic principle as evidenced by the later work of Kontsevich in showing the equality of Hodge numbers through the motivic integration. We will read through his paper "Birational Calabi–Yau n-folds have equal Betti numbers. New Trends in Algebraic Geometry (London Mathematical Society Lecture Note Series, pp. 1-12). Cambridge University Press.” END:VEVENT BEGIN:VEVENT DTSTART:20200519T160000 DTEND:20200519T180000 DTSTAMP:20200518T150000Z UID:f64ccc1e2f9472d1aae6cbb59b4db8fd@cgp.ibs.re.kr SUMMARY:Bott manifolds and Grossberg--Karshon twisted cubes LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: A Bott manifold is a smooth projective toric variety which is an iterated $\mathbb{C} P^1$-bundle starting with a point. Bott manifolds provide an interesting connection between representation theory and combinatorics. Let $G$ be a complex semisimple algebraic group of rank $r$. For a word $\mathbf i \in [r]^n$ and an integer vector $\mathbf \ell \in \mathbb{Z}^n$, one can associate a Bott manifold $B(\mathbf i)$ with a line bundle and a representation, called a generalized Demazure module. The character of this module can be captured by counting lattice points with sign in a certain combinatorial object, called a $\textit{Grossberg--Karshon twisted cube}$. A twisted cube is a virtual polytope, i.e., which can be neither closed nor convex. In this talk, we review Bott manifolds and Grossberg--Karshon twisted cubes, and study a necessary and sufficient condition on $\mathbf i$ and $\ell$ such that the associated Grossberg--Karshon twisted cube is a polytope, i.e., it is closed and convex, so that the Grossberg--Karshon character formula is a purely combinatorial positive formula. This talk is based on my preprint "Grossberg–Karshon twisted cubes and hesitant jumping walk avoidance (arXiv:2001.04399)". END:VEVENT BEGIN:VEVENT DTSTART:20200526T160000 DTEND:20200526T180000 DTSTAMP:20200525T150000Z UID:36e370256b3ac52925087554e940ede8@cgp.ibs.re.kr SUMMARY:Cohomological rigidity problems for toric varieties (especially for Bott manifolds) LOCATION:CGP Main Hall DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In the early beginning of the 2000s, the $\textit{cohomological rigidity}$ problem for toric varieties was raised which asks whether two smooth projective toric varieties having isomorphic cohomology rings (as graded rings) are diffeomorphic or not. There are many partial affirmative answers to the problem. For instance, it has been known that the above property holds when the Picard number is smaller than or equal to $2$. In this talk, I will present an overview of this problem, especially for Bott manifolds. Moreover, we will prove the following statement: for two Fano Bott manifolds, if there exists a $c_1$-preserving graded ring isomorphism between their cohomology rings with $\mathbb{Z}$-coefficient, then they are isomorphic (as toric varieties). This talk is based on joint work with Yunhyung Cho, Mikiya Masuda, and Seonjeong Park "Unique toric structure on a Fano Bott manifold (arXiv:2005.02740)".
* This talk also provides via the real-time online seminar, if you want to attend the online seminar please contact Speaker or admin(ibscgpmeeting@gmail.com) END:VEVENT BEGIN:VEVENT DTSTART:20200520T133000 DTEND:20200520T153000 DTSTAMP:20200519T150000Z UID:46f45d16dcab1cfc7ea9c24d6cddfb23@cgp.ibs.re.kr SUMMARY:Birational Calabi-Yau manifolds have the same small quantum product LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yifan Li\n\nEvent: Director's Seminar\n\nAbstract: I will continue with the discussion on Mark Mclean's paper “Birational Calabi-Yau manifolds have the same small quantum product”. In this paper, he translates this hard problem into a tractable one via his version of symplectic cohomology. I will talk about his direct-inverse limit construction for symplectic cohomology and his main idea to prove that birational CY's share the same symplectic cohomology. END:VEVENT BEGIN:VEVENT DTSTART:20200602T130000 DTEND:20200602T150000 DTSTAMP:20200601T150000Z UID:c1e2d202aab61c61a78499e545199850@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200609T130000 DTEND:20200609T150000 DTSTAMP:20200608T150000Z UID:1ba04e48e06dc56fcbbc22776abe4739@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200616T130000 DTEND:20200616T150000 DTSTAMP:20200615T150000Z UID:faaf95081a141ce44bd5788686904bde@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200623T130000 DTEND:20200623T150000 DTSTAMP:20200622T150000Z UID:2770069e7d6f09ec00b792f17fc4ee33@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200630T130000 DTEND:20200630T150000 DTSTAMP:20200629T150000Z UID:50dc00e7d98cce6a97fe078acde742ef@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS(Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200604T133000 DTEND:20200604T153000 DTSTAMP:20200603T150000Z UID:a093d6f193b7a75ca48120a8f5b4cd51@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200618T133000 DTEND:20200618T153000 DTSTAMP:20200617T150000Z UID:40aea320b3950aa2047e9bd5eeec8cc8@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200625T133000 DTEND:20200625T153000 DTSTAMP:20200624T150000Z UID:be0136107960df54f55da230cc6355d8@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: Seminar\n\nAbstract: We will read the paper "SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family (Yang Li)". END:VEVENT BEGIN:VEVENT DTSTART:20200608T160000 DTEND:20200608T180000 DTSTAMP:20200607T150000Z UID:ed84f308833f75ab55ba7c495990777c@cgp.ibs.re.kr SUMMARY:Overview of Springer theory LOCATION:Online Streaming DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: Intensive Lecture Series\n\nAbstract: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs. END:VEVENT BEGIN:VEVENT DTSTART:20200609T100000 DTEND:20200609T120000 DTSTAMP:20200608T150000Z UID:bb8bd22ab472c191f49c7e1a2878d542@cgp.ibs.re.kr SUMMARY:Overview of Springer theory LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: Intensive Lecture Series\n\nAbstract: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs. END:VEVENT BEGIN:VEVENT DTSTART:20200610T100000 DTEND:20200610T120000 DTSTAMP:20200609T150000Z UID:3f9003600a342578805a8d76c7f2810c@cgp.ibs.re.kr SUMMARY:Overview of Springer theory LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: Intensive Lecture Series\n\nAbstract: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs. END:VEVENT BEGIN:VEVENT DTSTART:20200611T100000 DTEND:20200611T120000 DTSTAMP:20200610T150000Z UID:53f9ab6608c8cf75441a736af5c728d6@cgp.ibs.re.kr SUMMARY:Overview of Springer theory LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: Intensive Lecture Series\n\nAbstract: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs. END:VEVENT BEGIN:VEVENT DTSTART:20200612T100000 DTEND:20200612T120000 DTSTAMP:20200611T150000Z UID:ebc5d0b0c92e3a3a9c792ad2f0ee5826@cgp.ibs.re.kr SUMMARY:Overview of Springer theory LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: Intensive Lecture Series\n\nAbstract: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs. END:VEVENT BEGIN:VEVENT DTSTART:20200611T160000 DTEND:20200611T180000 DTSTAMP:20200610T150000Z UID:a118bada254abb1efa0f70e8738427b8@cgp.ibs.re.kr SUMMARY:Two-row W-graphs in affine type A LOCATION:Online Streaming DESCRIPTION:Speaker: Dongkwan Kim\n\nEvent: CGP Seminar\n\nAbstract: For a Coxeter group W, a W-graph is a graph which produces a nice basis of the corresponding representation of W and also describes the action of W on the basis elements. Even when W is finite and its irreducible characters are known, W-graphs are still useful for understanding representations of W. In this talk, I will talk about W-graphs when W is an (extended) affine symmetric group, especially when these graphs are associated with "two-row partitions". Also I will discuss the connection between them and Lusztig's periodic W-graph. This work is joint with Pavlo Pylyavskyy. END:VEVENT BEGIN:VEVENT DTSTART:20200709T130000 DTEND:20200709T150000 DTSTAMP:20200708T150000Z UID:91a87a36c459009e393cdea06ee6c156@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS (Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200714T130000 DTEND:20200714T150000 DTSTAMP:20200713T150000Z UID:ce9fb8b85ab7eb90599276d8d9572f58@cgp.ibs.re.kr SUMMARY:Reading Seminar LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: We will read GPS (Ganatra, Pardon, Shende) papers together to understand "local to global principle". END:VEVENT BEGIN:VEVENT DTSTART:20200714T160000 DTEND:20200714T180000 DTSTAMP:20200713T150000Z UID:182bbb9613e38b6dbed9a63f6a1261ef@cgp.ibs.re.kr SUMMARY:Connectivity and the Nef cone of the Hilbert Scheme of Hypersurfaces in the Grassmannian LOCATION:CGP Main Hall DESCRIPTION:Speaker: See-Hak Seong\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will show that when $d \geq 3$ and $1 < k-1 < n$ then $Hilb_{dT+1-\binom{d-1}{2}}(G(k,n))$ has 2 connected components, even though elements in both components have the same cohomology class. Moreover, I will show that the Hilbert scheme associated to the Hilbert polynomial $\binom{T+m}{m}-\binom{T+m-d}{m}$ in Grassmannian has at most 2 connected components. At last, I will talk about the Nef cone of these Hilbert schemes by giving examples of generators of the Nef cone. END:VEVENT BEGIN:VEVENT DTSTART:20200716T133000 DTEND:20200716T153000 DTSTAMP:20200715T150000Z UID:5bb277c4cd23bee80ccabb764371ba17@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200723T133000 DTEND:20200723T153000 DTSTAMP:20200722T150000Z UID:6dd62d05740d3913c2d828a7e1eb896e@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200730T133000 DTEND:20200730T153000 DTSTAMP:20200729T150000Z UID:611da6c08fa519775bebd9fe59ed2069@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200806T133000 DTEND:20200806T153000 DTSTAMP:20200805T150000Z UID:89de5450e48b3e27cc9ba5051c69c644@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200813T133000 DTEND:20200813T153000 DTSTAMP:20200812T150000Z UID:266d9aba34f0e81728702c2b9ac230e7@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200820T133000 DTEND:20200820T153000 DTSTAMP:20200819T150000Z UID:a489346faa5afab596807cddf0df7ca0@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200827T133000 DTEND:20200827T153000 DTSTAMP:20200826T150000Z UID:36343565cc1312708dcd85c18dd48d40@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200811T160000 DTEND:20200811T180000 DTSTAMP:20200810T150000Z UID:7c776b905af02579e037abb7dc46c1bb@cgp.ibs.re.kr SUMMARY:Minimal degree rational curves on moduli space of symplectic and orthogonal bundles on a curve LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sanghyeon Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Moduli space of vector bundles on a curve is an object which has long history of researches from 1960s. X. Sun studied general minimal rational curves on vector bundles, and showed that they are Hecke curves. Moreover, their image of the tangent map(VMRT) is also studied by J.-M. Hwang and other researchers. As a generalization, we study minimal degree rational curves on moduli of symplectic and orthogonal bundles, and its application on geometry of these moduli spaces. This is based on a recent work joint with Insong Choe and Kiryong Chung. END:VEVENT BEGIN:VEVENT DTSTART:20200730T160000 DTEND:20200730T180000 DTSTAMP:20200729T150000Z UID:28d0513cacc66e8965816f1ea005376a@cgp.ibs.re.kr SUMMARY:Classification of hyperbolic Dehn fillings LOCATION:CGP Main Hall DESCRIPTION:Speaker: BoGwang Jeon\n\nEvent: CGP Seminar\n\nAbstract: Let M be a 2-cusped hyperbolic 3-manifold. By the work of Thurston, for each Dehn filling of M, the product of two core geodesics of the Dehn filling is an invariant of it. In this talk, I will explain how to classify Dehn fillings of M using this invariant. It will be further shown that, for any given two Dehn fillings of M, if their aforementioned invariants are the same, then their complex volumes are the same as well. END:VEVENT BEGIN:VEVENT DTSTART:20200818T140000 DTEND:20200818T150000 DTSTAMP:20200817T150000Z UID:0442269d3559622c536f82a2904f093e@cgp.ibs.re.kr SUMMARY:Arithmetic of the moduli of algebraic curves and Abelian varieties over global fields LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Highlighting the practical contexts for working with moduli stacks of algebraic curves and Abelian varieties, I will focus on concrete low genus/dimension examples with intuitive explanations. Further talks, I would like volunteers for various capacities, 'Reading seminars / Tangent connections / Problems briefings' are all welcome! END:VEVENT BEGIN:VEVENT DTSTART:20200901T130000 DTEND:20200901T150000 DTSTAMP:20200831T150000Z UID:f6a3b77a030fce855ecaec5f4197d8ae@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20200915T130000 DTEND:20200915T150000 DTSTAMP:20200914T150000Z UID:f9d45ddab8719a218c1af3d5995b603b@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20200924T130000 DTEND:20200924T150000 DTSTAMP:20200923T150000Z UID:2ba93f54baa6a26ab3f3d67e76759deb@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201008T130000 DTEND:20201008T150000 DTSTAMP:20201007T150000Z UID:f90f0a9b643a37e98c6b218cdb961844@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20200825T140000 DTEND:20200825T150000 DTSTAMP:20200824T150000Z UID:651c9cc9fdd1b3a1b80a564c1169c305@cgp.ibs.re.kr SUMMARY:Arithmetic of the moduli of fibrations & Number theory LOCATION:CGP Main Hall DESCRIPTION:Speaker: Jun Yong Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Continuing on, we will review the basic properties of Hom stacks, moduli stacks of higher genus algebraic curves and Abelian varieties. In the end, we will have a discussion about volunteers for various capacities, 'Reading seminars / Tangent connections / Problems briefings' are all welcome! END:VEVENT BEGIN:VEVENT DTSTART:20200921T160000 DTEND:20200921T170000 DTSTAMP:20200920T150000Z UID:9ee7b434bdb8c05a12c4d26616d494ca@cgp.ibs.re.kr SUMMARY:Deformation of complex structures via complete Kahler metrics I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: In this series of talks, we will study a deformation of complete Kahler manifolds including the non-compact case. First, we will survey the known results for the existence of Kahler-Einstein metrics and Kahler-Ricci flows. Then we will explain the variation of them on a family of canonically polarized compact manifolds, studied by Schumacher and Berman. Finally, we will discuss how to generalize their results to a family of non-compact Kahler manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20200923T160000 DTEND:20200923T170000 DTSTAMP:20200922T150000Z UID:472abfcf0da8fa102309af8edb9e47b7@cgp.ibs.re.kr SUMMARY:Deformation of complex structures via complete Kahler metrics II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: In this series of talks, we will study a deformation of complete Kahler manifolds including the non-compact case. First, we will survey the known results for the existence of Kahler-Einstein metrics and Kahler-Ricci flows. Then we will explain the variation of them on a family of canonically polarized compact manifolds, studied by Schumacher and Berman. Finally, we will discuss how to generalize their results to a family of non-compact Kahler manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20200925T160000 DTEND:20200925T170000 DTSTAMP:20200924T150000Z UID:fdf9253d7349e392ff760c0d599bc2aa@cgp.ibs.re.kr SUMMARY:Deformation of complex structures via complete Kahler metrics III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sungmin Yoo\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: In this series of talks, we will study a deformation of complete Kahler manifolds including the non-compact case. First, we will survey the known results for the existence of Kahler-Einstein metrics and Kahler-Ricci flows. Then we will explain the variation of them on a family of canonically polarized compact manifolds, studied by Schumacher and Berman. Finally, we will discuss how to generalize their results to a family of non-compact Kahler manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20200908T130000 DTEND:20200908T150000 DTSTAMP:20200907T150000Z UID:85e1ca3745bb7055dbe5e1f6213cce4e@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20200903T133000 DTEND:20200903T153000 DTSTAMP:20200902T150000Z UID:8e1578d73015c6c312bd3aa2a4683e24@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20200910T133000 DTEND:20200910T153000 DTSTAMP:20200909T150000Z UID:42c0e999c0dc3aa6fdec290bc2f20cc6@cgp.ibs.re.kr SUMMARY:(Reading Seminar) The Gross-Siebert program LOCATION:CGP Main Hall DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Seminar\n\nAbstract: The Gross-Siebert program is usually referred as an algebro-geometric approach to the SYZ conjecture in mirror symmetry. It gives an algebro-geometric way to construct mirror pairs. We will give an introduction to the GS program by reading through Chapter 6 of the book "Tropical geometry and mirror symmetry" by M. Gross. END:VEVENT BEGIN:VEVENT DTSTART:20201015T130000 DTEND:20201015T150000 DTSTAMP:20201014T150000Z UID:446a89c55330de683aee3bc3d2b96e43@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201022T130000 DTEND:20201022T150000 DTSTAMP:20201021T150000Z UID:d07f586b2e0f8260944a5e4d7a063379@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201105T130000 DTEND:20201105T150000 DTSTAMP:20201104T150000Z UID:45815782429d064c90af9e7dd8938185@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201112T130000 DTEND:20201112T150000 DTSTAMP:20201111T150000Z UID:6eee5d96b8086991f2daf761ee2100df@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201119T130000 DTEND:20201119T150000 DTSTAMP:20201118T150000Z UID:815cfcd60dc1c002355350a9e622b1c3@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201126T130000 DTEND:20201126T150000 DTSTAMP:20201125T150000Z UID:9481b6cbe97e5e250d944eb90395ed85@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201203T130000 DTEND:20201203T150000 DTSTAMP:20201202T150000Z UID:ba30c6aeab2f4a5dbde86843a55ba26c@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201210T130000 DTEND:20201210T150000 DTSTAMP:20201209T150000Z UID:1dfda42e9766b0e0b3b5b88c591a5a37@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201217T130000 DTEND:20201217T150000 DTSTAMP:20201216T150000Z UID:8bfe1179f9e02063ad1a2ede3c71a91f@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20201026T160000 DTEND:20201026T170000 DTSTAMP:20201025T150000Z UID:5ae8ddee2937f1cb08fcf9ef06c15cfa@cgp.ibs.re.kr SUMMARY:Introduction to topological Fukaya categories I LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: [Post-doc Lecture Series] Introduction to topological Fukaya categories\n\nAbstract: Fukaya category is one of the main themes in symplectic topology, but for a beginner, it is not easy to understand what it really means. This is because the definition of Fukaya categories hides many things behind moduli spaces, $A_\infty$-structures, or other complicated notions. Fortunately, there is a notion of topological Fukaya categories of surfaces, which is defined in a simpler way. In this lecture series, we will study the simpler version of Fukaya categories, by following the guidance of Haiden-Katzarkov-Kontesvich's paper "Flat surfaces and stability structures". If time permits, then we also will study their main result which gives stability conditions on Fukaya categories of surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20201028T160000 DTEND:20201028T170000 DTSTAMP:20201027T150000Z UID:744172086201d42dc9555bae9521aa26@cgp.ibs.re.kr SUMMARY:Introduction to topological Fukaya categories II LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: [Post-doc Lecture Series] Introduction to topological Fukaya categories\n\nAbstract: Fukaya category is one of the main themes in symplectic topology, but for a beginner, it is not easy to understand what it really means. This is because the definition of Fukaya categories hides many things behind moduli spaces, $A_\infty$-structures, or other complicated notions. Fortunately, there is a notion of topological Fukaya categories of surfaces, which is defined in a simpler way. In this lecture series, we will study the simpler version of Fukaya categories, by following the guidance of Haiden-Katzarkov-Kontesvich's paper "Flat surfaces and stability structures". If time permits, then we also will study their main result which gives stability conditions on Fukaya categories of surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20201030T160000 DTEND:20201030T170000 DTSTAMP:20201029T150000Z UID:6281b6565f63038c83fbcee2fa67af0b@cgp.ibs.re.kr SUMMARY:Introduction to topological Fukaya categories III LOCATION:CGP Main Hall DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: [Post-doc Lecture Series] Introduction to topological Fukaya categories\n\nAbstract: Fukaya category is one of the main themes in symplectic topology, but for a beginner, it is not easy to understand what it really means. This is because the definition of Fukaya categories hides many things behind moduli spaces, $A_\infty$-structures, or other complicated notions. Fortunately, there is a notion of topological Fukaya categories of surfaces, which is defined in a simpler way. In this lecture series, we will study the simpler version of Fukaya categories, by following the guidance of Haiden-Katzarkov-Kontesvich's paper "Flat surfaces and stability structures". If time permits, then we also will study their main result which gives stability conditions on Fukaya categories of surfaces. END:VEVENT BEGIN:VEVENT DTSTART:20201016T130000 DTEND:20201016T150000 DTSTAMP:20201015T150000Z UID:9e8ac81723eae27d010c0457fe84676b@cgp.ibs.re.kr SUMMARY:Adjoint Reidemeister torsion and 3D-3D correspondence LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dongmin Gang\n\nEvent: Mathematical Physics Seminar\n\nAbstract: '3D-3D' correspondence studies (2+1) dimensional quantum system, say T[M], associated to a 3-manifold M. After explaining how to count the ground states of T[M] put on compact Riemann surfaces from adjoint Reidemeister torsions on M twisted by irreducible flat connections, I will explain several non-trivial mathematical predictions on the topological invariants from the physics of T[M]. END:VEVENT BEGIN:VEVENT DTSTART:20201125T130000 DTEND:20201125T150000 DTSTAMP:20201124T150000Z UID:07c7bc5d7ada49a06a91e460b458bfe6@cgp.ibs.re.kr SUMMARY:Jacobi–Trudi formulas for flagged refined dual stable Grothendieck polynomials LOCATION:Online Streaming DESCRIPTION:Speaker: Jang Soo Kim\n\nEvent: CGP Seminar\n\nAbstract: Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The refined dual stable Grothendieck polynomials are defined as a generating function for reverse plane partitions of a given shape. They interpolate between Schur functions and dual stable Grothendieck polynomials introduced by Lam and Pylyavskyy in 2007. Flagged refined dual stable Grothendieck polynomials are a more refined version of refined dual stable Grothendieck polynomials, where lower and upper bounds are given for the entries of each row or column. In this talk we show Jacobi–Trudi-type formulas for flagged refined dual stable Grothendieck polynomials using plethystic substitution. This resolves a conjecture of Grinberg and generalizes a result by Iwao and Amanov–Yeliussizov. END:VEVENT BEGIN:VEVENT DTSTART:20210113T100000 DTEND:20210113T105000 DTSTAMP:20210112T150000Z UID:de41d1b84b719e9a270b9caf42b4a96d@cgp.ibs.re.kr SUMMARY:Newton-Okounkov bodies arising from cluster structures and mutations on polytopes LOCATION:Online (Zoom) DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A toric degeneration is a flat degeneration from a projective variety to a toric variety, which can be used to apply the theory of toric varieties to other projective varieties. In this talk, we discuss relations among the following three constructions of toric degenerations: representation theory, Newton-Okounkov bodies, and cluster algebras. More precisely, we construct Newton-Okounkov bodies using cluster structures, and realize representation-theoretic and cluster-theoretic toric degenerations using this framework. We also discuss its relation with combinatorial mutations which was introduced in the context of mirror symmetry for Fano varieties. More precisely, we relate Newton-Okounkov bodies of flag varieties arising from cluster structures by combinatorial mutations. This talk is based on joint works with Hironori Oya and Akihiro Higashitani. END:VEVENT BEGIN:VEVENT DTSTART:20210114T100000 DTEND:20210114T105000 DTSTAMP:20210113T150000Z UID:943400518765d05ac31088b4063b61d2@cgp.ibs.re.kr SUMMARY:Tropical Lagrangian multi-sections and smoothing of locally free sheaves on log Calabi-Yau surfaces LOCATION:Online (Zoom) DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Homological mirror symmetry suggests that Lagrangian multi-sections over an integral affine manifold with singularities $B$ should mirror to holomorphic vector bundles. In this talk, I will introduce the tropical version of Lagrangian multi-sections, called tropical Lagrangian multi-sections. I will mainly focus on dimension 2. To certain tropical Lagrangian multi-sections over $B$, I will construct a locally free sheaf $E_0$ on the log Calabi-Yau surface $X_0(B)$ associated to $B$ and study the smoothability of the pair $(X_0(B),E_0)$. This is a joint work with Kwokwai Chan and Ziming Ma. END:VEVENT BEGIN:VEVENT DTSTART:20210113T110000 DTEND:20210113T115000 DTSTAMP:20210112T150000Z UID:f65c34c049b4acdd44d3374f7eeaeb23@cgp.ibs.re.kr SUMMARY:SL3-laminations as bases for PGL3 cluster varieties for surfaces LOCATION:Online (Zoom) DESCRIPTION:Speaker: Hyun Kyu Kim\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: I will recall Fock-Goncharov's duality conjecture for cluster A- and X-varieties, and Fock-Goncharov's solution for the case of certain enhanced moduli spaces of G-local systems on a punctured surface when G is SL2 and PGL2. Then I will explain how Kuperberg's web can be used to extend this result to the case when G is SL3 and PGL3. END:VEVENT BEGIN:VEVENT DTSTART:20210106T090000 DTEND:20210106T100000 DTSTAMP:20210105T150000Z UID:3e186a728edbc9474241b2a3c2e50558@cgp.ibs.re.kr SUMMARY:An introduction to cluster algebras I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Linhui Shen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster algebras are commutative algebras equipped with remarkable combinatorial structures.Since its inception in 2000, the theory of cluster algebras has found numerous exciting applications in mathematics and physics. This series of lectures aim to provide an accessible introduction to cluster algebras for a general mathematical audience. In particular, we will investigate the following topics.
Lecture 1: Cluster algebras of rank 2: positive Laurent Phenomenon and greedy bases
This lecture will focus on cluster algebras of rank 2. Using elementary combinatorial tools, we will prove the positive Laurent Phenomenon and construct greedy bases for cluster algebras of rank 2. END:VEVENT BEGIN:VEVENT DTSTART:20210106T100000 DTEND:20210106T110000 DTSTAMP:20210105T150000Z UID:b1f8ebf9e7abff918248ec35053ceb20@cgp.ibs.re.kr SUMMARY:An introduction to cluster algebras II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Linhui Shen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster algebras are commutative algebras equipped with remarkable combinatorial structures.Since its inception in 2000, the theory of cluster algebras has found numerous exciting applications in mathematics and physics. This series of lectures aim to provide an accessible introduction to cluster algebras for a general mathematical audience. In particular, we will investigate the following topics.
Lecture 2: Cluster algebras and Finite type classifications
We begin with a rigorous definition of cluster algebras in terms of quiver mutations. We present a classification of cluster algebras of finite types by ADE quivers and explain their connections to generalized associahedra. END:VEVENT BEGIN:VEVENT DTSTART:20210107T090000 DTEND:20210107T100000 DTSTAMP:20210106T150000Z UID:ab7e2e25d26b4eb83636d9230b77435b@cgp.ibs.re.kr SUMMARY:An introduction to cluster algebras III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Linhui Shen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster algebras are commutative algebras equipped with remarkable combinatorial structures.Since its inception in 2000, the theory of cluster algebras has found numerous exciting applications in mathematics and physics. This series of lectures aim to provide an accessible introduction to cluster algebras for a general mathematical audience. In particular, we will investigate the following topics.
Lecture 3: Poisson geometry and quantization
Cluster varieties carry intrinsic Poisson structures. We present a quantization of cluster varieties and explore their connections with the theory of quantum groups. END:VEVENT BEGIN:VEVENT DTSTART:20210108T090000 DTEND:20210108T100000 DTSTAMP:20210107T150000Z UID:5332558be9f995918fae3e8d240ca2ad@cgp.ibs.re.kr SUMMARY:An introduction to cluster algebras IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Linhui Shen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster algebras are commutative algebras equipped with remarkable combinatorial structures.Since its inception in 2000, the theory of cluster algebras has found numerous exciting applications in mathematics and physics. This series of lectures aim to provide an accessible introduction to cluster algebras for a general mathematical audience. In particular, we will investigate the following topics.
Lecture 4: Categorification and Donaldson-Thomas theory
Every cluster variety can be categorized and gives rise to a 3d Calabi-Yau category with a generic stability condition. In this lecture, we will investigate their connections to the motivic Donaldson-Thomas theory. END:VEVENT BEGIN:VEVENT DTSTART:20210107T100000 DTEND:20210107T110000 DTSTAMP:20210106T150000Z UID:6fe52705f3a959c1c3f6d4ead00348aa@cgp.ibs.re.kr SUMMARY:Examples of cluster varieties from plabic graphs I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Daping Weng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster varieties were introduced by Fock and Goncharov as geometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply speaking, cluster varieties are algebraic varieties with an atlas of torus charts, whose transition maps are captured by certain combinatorial process called cluster mutations. Many interesting geometric objects turn out to be examples of cluster varieties, and one can then use cluster theoretical techniques to study these geometric objects. In this lecture series, we will discuss various examples of cluster varieties whose combinatorics can be captured by plabic graphs, including Grassmannians and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complementary to Linhui Shen’s lecture series on cluster theory.
Lecture 1: $Gr(2,n)$ and $M(0,n)$
We discuss the cluster structures on Grassmannian $Gr(2,n)$ and on the moduli space of n points in $\mathbb{P}^1$. These are examples of cluster varieties of Dynkin $A_{n-3}$ mutation type and their combinatorics are captured by triangulations of an n-gon. END:VEVENT BEGIN:VEVENT DTSTART:20210107T110000 DTEND:20210107T120000 DTSTAMP:20210106T150000Z UID:662b20df8a1586aea692beabf403b555@cgp.ibs.re.kr SUMMARY:Examples of cluster varieties from plabic graphs II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Daping Weng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster varieties were introduced by Fock and Goncharov as geometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply speaking, cluster varieties are algebraic varieties with an atlas of torus charts, whose transition maps are captured by certain combinatorial process called cluster mutations. Many interesting geometric objects turn out to be examples of cluster varieties, and one can then use cluster theoretical techniques to study these geometric objects. In this lecture series, we will discuss various examples of cluster varieties whose combinatorics can be captured by plabic graphs, including Grassmannians and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complementary to Linhui Shen’s lecture series on cluster theory.
Lecture 2: plabic graphs and $Gr(k,n)$
We introduce plabic (planar bicolor) graphs and use them to describe the cluster structures on Grassmannian $Gr(k,n)$ and on the moduli space of n points on $\mathbb{P}^{k-1}$. END:VEVENT BEGIN:VEVENT DTSTART:20210108T100000 DTEND:20210108T110000 DTSTAMP:20210107T150000Z UID:80a085757c87c45a35c9b0a100b09ad2@cgp.ibs.re.kr SUMMARY:Examples of cluster varieties from plabic graphs III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Daping Weng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster varieties were introduced by Fock and Goncharov as geometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply speaking, cluster varieties are algebraic varieties with an atlas of torus charts, whose transition maps are captured by certain combinatorial process called cluster mutations. Many interesting geometric objects turn out to be examples of cluster varieties, and one can then use cluster theoretical techniques to study these geometric objects. In this lecture series, we will discuss various examples of cluster varieties whose combinatorics can be captured by plabic graphs, including Grassmannians and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complementary to Linhui Shen’s lecture series on cluster theory.
Lecture 3: double Bruhat cells of $SL_n$
We introduce double Bruhat cells of a semisimple Lie group and discuss the cluster structures on double Bruhat cells of $SL_n$ in terms of plabic graphs. END:VEVENT BEGIN:VEVENT DTSTART:20210108T110000 DTEND:20210108T120000 DTSTAMP:20210107T150000Z UID:421f8b6c02321e1ffb4867173feefba2@cgp.ibs.re.kr SUMMARY:Examples of cluster varieties from plabic graphs IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Daping Weng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Cluster varieties were introduced by Fock and Goncharov as geometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply speaking, cluster varieties are algebraic varieties with an atlas of torus charts, whose transition maps are captured by certain combinatorial process called cluster mutations. Many interesting geometric objects turn out to be examples of cluster varieties, and one can then use cluster theoretical techniques to study these geometric objects. In this lecture series, we will discuss various examples of cluster varieties whose combinatorics can be captured by plabic graphs, including Grassmannians and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complementary to Linhui Shen’s lecture series on cluster theory.
Lecture 4: double Bott-Samelson cells of $SL_n$ and positive braid closures
We introduce double Bott-Samelson cells of $SL_n$ as a generalization of double Bruhat cells. We will describe their cluster structures and the connection to positive braid closures. END:VEVENT BEGIN:VEVENT DTSTART:20210111T090000 DTEND:20210111T095000 DTSTAMP:20210110T150000Z UID:12dd114a996fd0d430030cd2761db1a4@cgp.ibs.re.kr SUMMARY:Legendrian knots and their Lagrangian fillings: A conspectus on recent developments LOCATION:Online (Zoom) DESCRIPTION:Speaker: Roger Casals\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In this talk, I will survey some of the recent developments in the study of Lagrangian fillings of Legendrian knots. First, I will introduce and motivate the leading questions. Then, we will discuss the current methods and techniques available to tackle them. Finally, I will suggest some open problems that now seem at reach, along with some strategies to approach them. END:VEVENT BEGIN:VEVENT DTSTART:20210111T100000 DTEND:20210111T105000 DTSTAMP:20210110T150000Z UID:2bf91c157b3bb82d3b87685c3a4913c1@cgp.ibs.re.kr SUMMARY:Infinitely many fillings through augmentations LOCATION:Online (Zoom) DESCRIPTION:Speaker: Lenhard L. Ng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In 2020, a few groups of people proved that certain Legendrian links in $\mathbb{R}^3$ have infinitely many exact Lagrangian fillings that are distinct under Hamiltonian isotopy. These groups (Casals-Gao, Gao-Shen-Wang, Casals-Zaslow) used a variety of approaches involving microlocal sheaf theory and cluster structures. I'll describe a different, Floer-theoretic approach to the same sort of result, using integer-valued augmentations of Legendrian contact homology, and I'll discuss some examples that are amenable to the Floer approach but not (yet?) the other approaches. This is joint work with Roger Casals. END:VEVENT BEGIN:VEVENT DTSTART:20210104T090000 DTEND:20210104T100000 DTSTAMP:20210103T150000Z UID:ec45acc99e9314854dc0c66f7fdedb1e@cgp.ibs.re.kr SUMMARY:Sheaves in contact topology I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Honghao Gao\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Microlocal sheaf theory was introduced by Kashiwara-Schapira around 80s. With the notion of micro-support, one can use sheaves on smooth manifolds to access the geometry of their cotangent bundles. In recent years, microlocal sheaf theory entered contact and symplectic topology, and has been used to solve open problems. In this lecture series, we will introduce microlocal sheaf theory in the context of low-dimensional contact topology, and supply the audience with background for its applications such as producing non-classical invariants for Legendrian knots and distinguishing exact Lagrangian fillings.
Lecture 1: Legendrian knots and sheaves
Basics of Legendrian knots, sheaves and microsupport, local conditions at arcs, cusps, crossings. END:VEVENT BEGIN:VEVENT DTSTART:20210104T100000 DTEND:20210104T110000 DTSTAMP:20210103T150000Z UID:3ba63489e83943f123ec53d1251a5828@cgp.ibs.re.kr SUMMARY:Sheaves in contact topology II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Honghao Gao\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Microlocal sheaf theory was introduced by Kashiwara-Schapira around 80s. With the notion of micro-support, one can use sheaves on smooth manifolds to access the geometry of their cotangent bundles. In recent years, microlocal sheaf theory entered contact and symplectic topology, and has been used to solve open problems. In this lecture series, we will introduce microlocal sheaf theory in the context of low-dimensional contact topology, and supply the audience with background for its applications such as producing non-classical invariants for Legendrian knots and distinguishing exact Lagrangian fillings.
Lecture 2: invariance
Category of sheaves, non-classical invariants for Legendrian submanifolds (theorem by Guillermou-Kashiwara-Schapira), combinatorial verification under Reidemeister moves. END:VEVENT BEGIN:VEVENT DTSTART:20210105T090000 DTEND:20210105T100000 DTSTAMP:20210104T150000Z UID:a9fcf4e0ff537372085d34a9a3518ad2@cgp.ibs.re.kr SUMMARY:Sheaves in contact topology III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Honghao Gao\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Microlocal sheaf theory was introduced by Kashiwara-Schapira around 80s. With the notion of micro-support, one can use sheaves on smooth manifolds to access the geometry of their cotangent bundles. In recent years, microlocal sheaf theory entered contact and symplectic topology, and has been used to solve open problems. In this lecture series, we will introduce microlocal sheaf theory in the context of low-dimensional contact topology, and supply the audience with background for its applications such as producing non-classical invariants for Legendrian knots and distinguishing exact Lagrangian fillings.
Lecture 3: moduli space of sheaves
moduli space of sheaves for elementary tangles, microlocal rank 1 sheaves, positive braid Legendrian knots, flags and Bott-Samelson cells. END:VEVENT BEGIN:VEVENT DTSTART:20210105T100000 DTEND:20210105T110000 DTSTAMP:20210104T150000Z UID:d9cc0895a16354cb50ce547f507ffe78@cgp.ibs.re.kr SUMMARY:Sheaves in contact topology IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Honghao Gao\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Microlocal sheaf theory was introduced by Kashiwara-Schapira around 80s. With the notion of micro-support, one can use sheaves on smooth manifolds to access the geometry of their cotangent bundles. In recent years, microlocal sheaf theory entered contact and symplectic topology, and has been used to solve open problems. In this lecture series, we will introduce microlocal sheaf theory in the context of low-dimensional contact topology, and supply the audience with background for its applications such as producing non-classical invariants for Legendrian knots and distinguishing exact Lagrangian fillings.
Lecture 4: Lagrangian fillings
Singularities of Legendrian fronts, exact Lagrangian fillings and Legendrian weaves, sheaf quantization of Lagrangian fillings. END:VEVENT BEGIN:VEVENT DTSTART:20210114T090000 DTEND:20210114T095000 DTSTAMP:20210113T150000Z UID:94359f94e043e3a2d5f56e057896cc4d@cgp.ibs.re.kr SUMMARY:Mirror symmetry through perverse schobers LOCATION:Online (Zoom) DESCRIPTION:Speaker: Benjamin Gammage\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: We explain how the language of perverse schobers gives a natural tool for describing a generalization of the Seidel-Sheridan strategy for computing Fukaya categories to the non-Lefschetz situation. We apply this technique to calculate the Fukaya category of the Milnor fiber of a Berglund-Hübsch singularity, building on some earlier computations of David Nadler. This calculation proves a conjecture of Lekili-Ueda. END:VEVENT BEGIN:VEVENT DTSTART:20210115T100000 DTEND:20210115T105000 DTSTAMP:20210114T150000Z UID:d2946939c0e12acd82eba6606a874fca@cgp.ibs.re.kr SUMMARY:Dimers and Mirror Moduli LOCATION:Online (Zoom) DESCRIPTION:Speaker: Eric Zaslow\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: I will try to describe a counting problem that arises from considering mirror approaches to dimer integrable systems. Some of this talk is based on joint work with David Treumann and Harold Williams, and some is an ongoing project with Helge Ruddatand others. END:VEVENT BEGIN:VEVENT DTSTART:20210115T090000 DTEND:20210115T095000 DTSTAMP:20210114T150000Z UID:a1cb6d6e8547aab700c8b8fd797a817c@cgp.ibs.re.kr SUMMARY:Cluster coordinates from sheaf quantization of spectral curve LOCATION:Online (Zoom) DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A sheaf quantization is a sheaf associated to a Lagrangian brane. In this talk, I will explain my construction of sheaf quantization of the spectral curves of Schrodinger equations, which is a part of conjectural $\hbar$-Riemann—Hilbert correspondence. The construction is based on exact WKB analysis.I will also explain an application to cluster theory. Iwaki—Nakanishi have found cluster variables in exact WKB analysis. The construction of sheaf quantization gives a geometric explanation of Iwaki—Nakanishi’s cluster variables and their variants. A part of this talk is based on my joint work in progress with T. Ishibashi. END:VEVENT BEGIN:VEVENT DTSTART:20210104T153000 DTEND:20210104T163000 DTSTAMP:20210103T150000Z UID:869bf2aeb56638ebdfc9108e8987598d@cgp.ibs.re.kr SUMMARY:Mutations and toric degenerations I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: The aim of this lecture is to understand a relation between the wall crossing phenomenon of Lagrangians and the mutations in cluster theory via toric degenerations.Lecture 1 : Fano toric varieties and potentials
- A brief introduction to toric varieties
- Potential functions of smooth Fano toric varieties END:VEVENT BEGIN:VEVENT DTSTART:20210104T163000 DTEND:20210104T173000 DTSTAMP:20210103T150000Z UID:914bb67cb54677ea5a0e5d86535cc982@cgp.ibs.re.kr SUMMARY:Mutations and toric degenerations II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: The aim of this lecture is to understand a relation between the wall crossing phenomenon of Lagrangians and the mutations in cluster theory via toric degenerations.Lecture 2 : Toric degenerations, examples and construction
- Toric degenerations; definitions and examples
- Construction of toric degenerations
- Potential functions via toric degenerations END:VEVENT BEGIN:VEVENT DTSTART:20210105T153000 DTEND:20210105T163000 DTSTAMP:20210104T150000Z UID:e61aaeee0ffd7dfe2f4b3a6a8143831e@cgp.ibs.re.kr SUMMARY:Mutations and toric degenerations III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: The aim of this lecture is to understand a relation between the wall crossing phenomenon of Lagrangians and the mutations in cluster theory via toric degenerations.Lecture 3 : Mutations of potentials
- Mutations of Laurent polynomials, polytopes, and Lagrangian tori END:VEVENT BEGIN:VEVENT DTSTART:20210105T163000 DTEND:20210105T173000 DTSTAMP:20210104T150000Z UID:e0d6f31b6910dd41e6d832262d3f21cb@cgp.ibs.re.kr SUMMARY:Mutations and toric degenerations IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: The aim of this lecture is to understand a relation between the wall crossing phenomenon of Lagrangians and the mutations in cluster theory via toric degenerations.Lecture 4 : Examples: flag variety
- Toric degenerations of flag varieties
- Cluster structures of G/B and potential functions END:VEVENT BEGIN:VEVENT DTSTART:20210112T110000 DTEND:20210112T115000 DTSTAMP:20210111T150000Z UID:99a7eecf73f40456fb559e33920a3998@cgp.ibs.re.kr SUMMARY:Symplectic Structure on Augmentation Varieties LOCATION:Online (Zoom) DESCRIPTION:Speaker: Daping Weng\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In a recent joint project with H. Gao and L. Shen, we introduce a cluster K2 structure on the augmentation variety of the Chekanov-Eliashberg dga for the rainbow closure of any positive braid with marked point decorations. This cluster K2 structure defines a holomorphic presymplectic structure on the complex augmentation variety. Using a result of Goncharov and Kenyon on surface bipartite graphs, we prove that this holomorphic presymplectic structure becomes symplectic after we reduce the number of marked points to a single marked per link component. END:VEVENT BEGIN:VEVENT DTSTART:20210112T100000 DTEND:20210112T105000 DTSTAMP:20210111T150000Z UID:921722a2850c64f8a3e5f67c42a4c47d@cgp.ibs.re.kr SUMMARY:Quantum geometry of moduli spaces of local systems LOCATION:Online (Zoom) DESCRIPTION:Speaker: Linhui Shen\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Let G be a split semi-simple algebraic group over Q. We introduce a natural cluster structure on moduli spaces of G-local systems over surfaces with marked points. As a consequence, the moduli spaces of G-local systems admit natural Poisson structures, and can be further quantized. We will study the principal series representations of such quantum spaces. It will recover many classical topics, such as the q-deformed Toda systems, quantum groups, and the modular functor conjecture for such representations. This talk will mainly be based on joint work with A.B. Goncharov. END:VEVENT BEGIN:VEVENT DTSTART:20210114T110000 DTEND:20210114T115000 DTSTAMP:20210113T150000Z UID:79ad1d5f06703bfa3a85bfa6bb47aad0@cgp.ibs.re.kr SUMMARY:Orbifold Jacobian algebras and generalized Kodaira-Spencer maps LOCATION:Online (Zoom) DESCRIPTION:Speaker: Sangwook Lee\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Given an algebraic function, its Jacobian algebra encodes the information of the singularity. There is also a notion of orbifold Jacobian algebras for functions which admit finite (abelian) group actions. We give a construction of an orbifold Jacobian algebra as Floer cohomology of a Lagrangian submanifold which represents homological mirror functor. We also discuss generalized Kodaira-Spencer maps whose image is not necessarily an ordinary Jacobian algebra. This talk is based on the joint work with C.-H. Cho. END:VEVENT BEGIN:VEVENT DTSTART:20210104T130000 DTEND:20210104T140000 DTSTAMP:20210103T150000Z UID:e390730b405949bcff2765062b755537@cgp.ibs.re.kr SUMMARY:Homological mirror symmetry via Lagrangian Floer theory I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A version of homological mirror symmetry(HMS) conjecture relates the Fukaya category of a symplectic manifold and matrix factorization category of a mirror Landau-Ginzburg model. In this introductory lecture series, we illustrate geometric ideas behind such correspondences from a biased point of view of the theory of localized mirror functor in Lagrangian Floer theory.Lecture 1 : A-infinity category, HMS and localized mirror functor END:VEVENT BEGIN:VEVENT DTSTART:20210104T140000 DTEND:20210104T150000 DTSTAMP:20210103T150000Z UID:799ac25a8c8ab4f245e6b274d7aa4677@cgp.ibs.re.kr SUMMARY:Homological mirror symmetry via Lagrangian Floer theory II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A version of homological mirror symmetry(HMS) conjecture relates the Fukaya category of a symplectic manifold and matrix factorization category of a mirror Landau-Ginzburg model. In this introductory lecture series, we illustrate geometric ideas behind such correspondences from a biased point of view of the theory of localized mirror functor in Lagrangian Floer theory.Lecture 2 : Monotone Floer theory and its HMS END:VEVENT BEGIN:VEVENT DTSTART:20210105T130000 DTEND:20210105T140000 DTSTAMP:20210104T150000Z UID:715ad9079180021d2910562020adac53@cgp.ibs.re.kr SUMMARY:Homological mirror symmetry via Lagrangian Floer theory III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A version of homological mirror symmetry(HMS) conjecture relates the Fukaya category of a symplectic manifold and matrix factorization category of a mirror Landau-Ginzburg model. In this introductory lecture series, we illustrate geometric ideas behind such correspondences from a biased point of view of the theory of localized mirror functor in Lagrangian Floer theory.Lecture 3 : Fukaya category of surfaces and its HMS END:VEVENT BEGIN:VEVENT DTSTART:20210105T140000 DTEND:20210105T150000 DTSTAMP:20210104T150000Z UID:94786738c216a6188fed31a2472d8b9f@cgp.ibs.re.kr SUMMARY:Homological mirror symmetry via Lagrangian Floer theory IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: A version of homological mirror symmetry(HMS) conjecture relates the Fukaya category of a symplectic manifold and matrix factorization category of a mirror Landau-Ginzburg model. In this introductory lecture series, we illustrate geometric ideas behind such correspondences from a biased point of view of the theory of localized mirror functor in Lagrangian Floer theory.Lecture 4 : Singularities and its HMS END:VEVENT BEGIN:VEVENT DTSTART:20210107T140000 DTEND:20210107T150000 DTSTAMP:20210106T150000Z UID:f79c7a14a5541272f5c7af0a2b882e15@cgp.ibs.re.kr SUMMARY:Symplectic geometry in algebraic analysis I LOCATION:Online (Zoom) DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In these lectures, I will explain two ideas in algebraic analysis: sheaf quantization and exact WKB analysis, with emphasis on relations to symplectic geometry. The ideas presented in the lectures will be used in my talk in the workshop.Lecture 1: Sheaf quantization: basic ideas and examples END:VEVENT BEGIN:VEVENT DTSTART:20210107T150000 DTEND:20210107T160000 DTSTAMP:20210106T150000Z UID:af16e55c39ab8faaa756b2e17ab9d155@cgp.ibs.re.kr SUMMARY:Symplectic geometry in algebraic analysis II LOCATION:Online (Zoom) DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In these lectures, I will explain two ideas in algebraic analysis: sheaf quantization and exact WKB analysis, with emphasis on relations to symplectic geometry. The ideas presented in the lectures will be used in my talk in the workshop.Lecture 2: Sheaf quantization: continued END:VEVENT BEGIN:VEVENT DTSTART:20210108T140000 DTEND:20210108T150000 DTSTAMP:20210107T150000Z UID:5653854a71dea9e829d41b34d8f6bc22@cgp.ibs.re.kr SUMMARY:Symplectic geometry in algebraic analysis III LOCATION:Online (Zoom) DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In these lectures, I will explain two ideas in algebraic analysis: sheaf quantization and exact WKB analysis, with emphasis on relations to symplectic geometry. The ideas presented in the lectures will be used in my talk in the workshop.Lecture 3: Exact WKB analysis: basics END:VEVENT BEGIN:VEVENT DTSTART:20210108T150000 DTEND:20210108T160000 DTSTAMP:20210107T150000Z UID:43fdb82c9ed75c86fe7a9438f20b10ab@cgp.ibs.re.kr SUMMARY:Symplectic geometry in algebraic analysis IV LOCATION:Online (Zoom) DESCRIPTION:Speaker: Tatsuki Kuwagaki\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In these lectures, I will explain two ideas in algebraic analysis: sheaf quantization and exact WKB analysis, with emphasis on relations to symplectic geometry. The ideas presented in the lectures will be used in my talk in the workshop.Lecture 4: Exact WKB analysis: cluster algebra and local systems END:VEVENT BEGIN:VEVENT DTSTART:20210112T090000 DTEND:20210112T095000 DTSTAMP:20210111T150000Z UID:5aaaaa01a06cd1c803d55566444c5cd8@cgp.ibs.re.kr SUMMARY:Lagrangian fillings of Legendrian links of finite type LOCATION:Online (Zoom) DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: In this talk, we will focus on Legendrian links admitting cluster structures of finite type (via N-graph ways) and prove that those Legendrian links of type ADE have embedded exact Lagrangian fillings as many as the number of seeds in their cluster structures.Furthermore, we will describe the cluster structures of BCFG-type among Lagrangian fillings of ADE-type Legendrian links, which have certain partial symmetries.This is joint work with Youngjin Bae (Incheon National University) and Eunjeong Lee (IBS-CGP). END:VEVENT BEGIN:VEVENT DTSTART:20210111T110000 DTEND:20210111T115000 DTSTAMP:20210110T150000Z UID:083ae29f94977098a31899855401c9b1@cgp.ibs.re.kr SUMMARY:Infinitely many fillings through sheaves LOCATION:Online (Zoom) DESCRIPTION:Speaker: Honghao Gao\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: This talk will complement other talks in the day and present concrete examples. Specifically, I will construct infinitely many Lagrangian fillings for the Legendrian torus link (3,6), and explain how to distinguish them using sheaves and cluster algebras.Time permitting, I will discussion other torus links (joint work with R. Casals) and positive braid links (joint work with L. Shen and D. Weng). END:VEVENT BEGIN:VEVENT DTSTART:20210113T090000 DTEND:20210113T095000 DTSTAMP:20210112T150000Z UID:2f8f1a0a5bfdc86be37307e0eb08878a@cgp.ibs.re.kr SUMMARY:Positroid varieties and $q,t$-Catalan numbers LOCATION:Online (Zoom) DESCRIPTION:Speaker: Thomas Lam\n\nEvent: Legendrians, Cluster algebras, and Mirror symmetry\n\nAbstract: Positroid varieties are subvarieties of the Grassmannian defined as intersections of rotations of Schubert varieties in my work with Knutson and Speyer. They also appear in the work of Shende-Treumann-Williams-Zaslow as moduli spaces of constructible sheaves with microsupport in a Legendrian link.We show that the "top open positroid variety" has mixed Hodge polynomial given by the $q,t$-rational Catalan numbers (up to a simple factor). The $q,t$-rational Catalan numbers satisfy remarkable symmetry and unimodality properties, and we show that these follow from the curious Lefschetz phenomenon for cluster varieties. The cohomologies of open positroid varieties are shown to be related to Khovanov-Rosanzky knot homology.This talk is based on joint work with Pavel Galashin. END:VEVENT BEGIN:VEVENT DTSTART:20210121T130000 DTEND:20210121T150000 DTSTAMP:20210120T150000Z UID:a6f554e97760e519241fc43828b7bea1@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: \n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20210128T130000 DTEND:20210128T150000 DTSTAMP:20210127T150000Z UID:5e13576b9abf6bafe1a524ccb650c39a@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: \n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20210204T130000 DTEND:20210204T150000 DTSTAMP:20210203T150000Z UID:bd6b13aff1c8f27c7a3c49b6d7c8fa6f@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: \n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20210218T130000 DTEND:20210218T150000 DTSTAMP:20210217T150000Z UID:de75aa319c23ce224dc12df1684f75b0@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Reading Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20210225T130000 DTEND:20210225T150000 DTSTAMP:20210224T150000Z UID:3473dcc32a758ed2c9ca40ac4e4653c8@cgp.ibs.re.kr SUMMARY:(Reading Seminar) Algebraic aspects of contact topology LOCATION:Online Streaming DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Reading Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar. END:VEVENT BEGIN:VEVENT DTSTART:20210308T100000 DTEND:20210308T110000 DTSTAMP:20210307T150000Z UID:2343f3b5a24494bf4fb188d9e469fc45@cgp.ibs.re.kr SUMMARY:Mirror symmetry for Berglund-Hübsch Milnor fibers LOCATION:Online Streaming DESCRIPTION:Speaker: Benjamin Gammage\n\nEvent: Symplectic Monday Seminar\n\nAbstract: After recalling some joint work with Jack Smith proving homological Berglund-Hübsch mirror symmetry, we explain the calculation of the Fukaya category of a Berglund-Hübsch Milnor fiber, proving a conjecture of Yankı Lekili and Kazushi Ueda. The strategy of proof involves deforming the Fukaya category of an open ("very affine") subset, by calculating a contribution from disks passing through an affine normal crossings divisor. END:VEVENT BEGIN:VEVENT DTSTART:20210315T100000 DTEND:20210315T110000 DTSTAMP:20210314T150000Z UID:aaa2fb8ad5889c43845a6254af23d308@cgp.ibs.re.kr SUMMARY:Virtual fundamental chain in gauge theory LOCATION:Online Streaming DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The virtual fundamental chain technique is developed to study moduli space of pseudoholomorphic curve. In the case of moduli space appearing in gauge theory, the singularity appearing in the compactification is harder to work with and existing theory such as Kuranishi structure does not work. In this talk I explain certain stratified version of Kuranishi structure which works to find virtual fundamental chain in some easy case of gauge theory. This is a part of project I am working with A. Daemi and the motivation is to apply it to study certain SO(3) version of Atiyah Floer conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20210322T100000 DTEND:20210322T110000 DTSTAMP:20210321T150000Z UID:49a56e5268448dabb0b08cc44dfc7c9f@cgp.ibs.re.kr SUMMARY:Peterson conjecture via Lagrangian correspondences and wonderful compactifications LOCATION:Online Streaming DESCRIPTION:Speaker: Hanwool Bae\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Let G be a compact simply-connected semisimple Lie group and let T be a maximal torus subgroup of G. Peterson conjecture says that the homology of the based loop space of G and the quantum cohomology of the full flag variety G/T are isomorphic as rings after a localization. In a joint work with Naichung Conan Leung, we found a geometric proof of the conjecture using Floer theoretic techniques. In this talk, I will first introduce the moment Lagrangian correspondence from the cotangent bundle of G to the square (G/T)^2 of the flag variety G/T. Then I will discuss how to compute an A-infinity homomorphism associated to the Lagrangian correspondence and show that it induces the desired isomorphism. END:VEVENT BEGIN:VEVENT DTSTART:20210329T100000 DTEND:20210329T110000 DTSTAMP:20210328T150000Z UID:5d67810e8d8e23b16c2946e0f0932f49@cgp.ibs.re.kr SUMMARY:The Rabinowitz Fukaya category and applications LOCATION:Online Streaming DESCRIPTION:Speaker: Yuan Gao\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The goal of the talk is to introduce the Rabinowitz (wrapped) Fukaya category, as an open-string analogue of Rabinowitz Floer homology of (the boundary at infinity of) a Liouville manifold, which is a categorical invariant of exact cylindrical Lagrangians whose cohomology morphisms measure the failure of wrapped Floer cohomology to satisfy Poincare duality. The main result, answering a conjecture of Abouzaid, relates this category to the usual wrapped Fukaya category by a canonical algebraic formula, in terms of the categorical formal punctured neighborhood of infinity introduced by Efimov. As an application, we shall see a few new computations in Floer theory via homological mirror symmetry. In addition, we are going to explore the open-closed string relationship and derive structural and computational results in both Rabinowitz Floer homology and symplectic cohomology. This is based on joint work with Sheel Ganatra and Sara Venkatesh. END:VEVENT BEGIN:VEVENT DTSTART:20210405T100000 DTEND:20210405T110000 DTSTAMP:20210404T150000Z UID:3ce36d1a0eb1d635bcb56b5c8bbdfab5@cgp.ibs.re.kr SUMMARY:Floer Cohomology and Arc Spaces LOCATION:Online Streaming DESCRIPTION:Speaker: Mark Mclean\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Let f be a polynomial over the complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally, this corresponds to the space of d-jets of holomorphic disks in complex affine space whose boundary ‘wraps’ around the singularity d times. We show that Floer cohomology of the dth power of the Milnor monodromy map is isomorphic to compactly supported cohomology of the dth contact locus. This answers a question of Paul Seidel and it also proves a conjecture of Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê and Hong Duc Nguyen. The key idea of the proof is to use a jet space version of the PSS map together with a filtration argument. END:VEVENT BEGIN:VEVENT DTSTART:20210419T170000 DTEND:20210419T180000 DTSTAMP:20210418T150000Z UID:928076f49a4329fdb079953fbe060742@cgp.ibs.re.kr SUMMARY:Fukaya categories of quasihomogeneous polynomials LOCATION:Online Streaming DESCRIPTION:Speaker: Jack Smith\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Berglund-Hübsch mirror symmetry predicts that for certain 'transpose' pairs of quasihomogeneous polynomials, the Fukaya-Seidel category of one is equivalent to a category of matrix factorisations of the other. The difficulty in proving this is that the natural types of objects to consider on the two sides do not match up with each other. I will introduce an enlarged version of the Fukaya-Seidel category that contains the missing objects, and outline how this allows one to prove B-H mirror symmetry. This is joint work in progress with Benjamin Gammage. END:VEVENT BEGIN:VEVENT DTSTART:20210607T100000 DTEND:20210607T110000 DTSTAMP:20210606T150000Z UID:ed6251f2e2767bd00561c161a7238ea7@cgp.ibs.re.kr SUMMARY:Shifting numbers in triangulated categories LOCATION:Online Streaming DESCRIPTION:Speaker: Yu-Wei Fan\n\nEvent: Symplectic Monday Seminar\n\nAbstract: One can consider endofunctors of triangulated categories as dynamical systems, and study their long term behaviors under large iterations. There are (at least) three natural invariants that one can associate to endofunctors from the dynamical perspective: categorical entropy, and upper/lower shifting numbers. We will recall some background on categorical dynamical systems and categorical entropy, and introduce the notion of shifting numbers, which measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category. The shifting numbers are analogous to Poincare translation numbers. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Joint work with Simion Filip. END:VEVENT BEGIN:VEVENT DTSTART:20210309T160000 DTEND:20210309T170000 DTSTAMP:20210308T150000Z UID:9b4ede5b5bd77f1ffd10c341deb3f484@cgp.ibs.re.kr SUMMARY:Comparing numerical Iitaka dimensions LOCATION:Online Streaming DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In 1985, Kawamata defined the numerical Iitaka dimension of a nef divisor in order to study the abundance conjecture. In 2004, Boucksom-Demailly-Paun-Peternell introduced a numerical Iitaka dimension of a pseudoeffective divisor, which is a direct generalization of Kawamata's definition. Around the same time, Nakayama introduced two more numerical Iitaka dimensions of a pseudoeffective divisor, which are numerical variations of the Iitaka dimension. In 2013, Lehmann further introduced several more numerical Iitaka dimensions of a pseudoeffective divisor. Recently, Lesieutre proved that Boucksom-Demailly-Paun-Peternell's numerical Iitaka dimension can be different from one of Nakayama's numerical Iitaka dimension. In this talk, we review the definitions of numerical Iitaka dimensions, and we compare them. This is joint work with Sung Rak Choi.
END:VEVENT BEGIN:VEVENT DTSTART:20210316T160000 DTEND:20210316T170000 DTSTAMP:20210315T150000Z UID:5be6dd2c7d97d689dfcc532df4a61706@cgp.ibs.re.kr SUMMARY:Geometric quantization and canonical metrics on polarized manifolds LOCATION:Online Streaming DESCRIPTION:Speaker: Kewei Zhang\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk I will present a quantization approach which directly relates Fujita-Odaka's delta-invariant to the optimal exponent of certain Moser-Trudinger type inequality on polarized manifolds. As a consequence we obtain new criterions for the existence of twisted Kaehler-Einstein metrics or constant scalar curvature Kaehler metrics on possibly non-Fano manifolds.
END:VEVENT BEGIN:VEVENT DTSTART:20210330T160000 DTEND:20210330T170000 DTSTAMP:20210329T150000Z UID:2dcb4c7be4b312ab378e03c6c1f5e765@cgp.ibs.re.kr SUMMARY:Algebraic groups acting on the plane over a perfect field LOCATION:Online Streaming DESCRIPTION:Speaker: Susanna Zimmermann\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will give examples of algebraic groups acting birationally on the projective plane over different non-closed fields. It turns out that they act by automorphisms on a rational del Pezzo surface or a conic fibration. So, if we want to classify these algebraic groups, we have to classify these surfaces and get to know their automorphism groups. This is very hard in the automorphism group is finite, and the classification of finite groups acting birationally on the plane is open over a non-closed field.However, if the algebraic group is infinite, the del Pezzo surfaces are of large degree and the conic fibrations nice. I will explain their classification, and then the classification of the infinite maximal algebraic groups acting birationally on the plane.
END:VEVENT BEGIN:VEVENT DTSTART:20210412T100000 DTEND:20210412T110000 DTSTAMP:20210411T150000Z UID:5e6ae810afa7412ce210258d4a3ea9c4@cgp.ibs.re.kr SUMMARY:Scattering diagrams from blowups of toric surfaces LOCATION:Online Streaming DESCRIPTION:Speaker: Hansol Hong\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Gross-Hacking-Keel has shown that any cluster variety can be obtained by a sequence of (nontoric) blow-ups and blow-downs starting from a toric variety. Motivated by this, we study the effect of blowup on the Lagrangian torus fibration on a toric surface. In particular, we will see that if the blowup points lie over the codimension one strata of the toric variety, the resulting fibration on the blowup produces a scattering diagram that matches with the one constructed by Gross-Pandharipande-Siebert using algebraic curve counting. The talk is based on the work in progress jointly with Sam Bardwell-Evans, Man-Wai Mandy Cheung and Yu-Shen Lin. END:VEVENT BEGIN:VEVENT DTSTART:20210426T170000 DTEND:20210426T180000 DTSTAMP:20210425T150000Z UID:0f46c66c10cf800654a055c1f22c34f9@cgp.ibs.re.kr SUMMARY:Lagrangian Poincaré Recurrence via pseudoholomorphic foliations LOCATION:Online Streaming DESCRIPTION:Speaker: Georgios Dimitroglou Rizell\n\nEvent: Symplectic Monday Seminar\n\nAbstract: For any Hamiltonian displaceable closed curve inside a closed symplectic surface, there is a bound on the number of pairwise disjoint Hamiltonian isotopic copies of the curve that one can produce. This phenomenon is called Lagrangian Poincaré Recurrence, and it was only shown very recently by Polterovich and Shelukhin that there exist displaceable Lagrangians in higher dimension that satisfy the analogous property. In this work in progress joint with E. Opshtein, we use the technique of pseudoholomorphic foliations to show that the bound on the number of disjoint copies in the surface persists after increasing the dimension by the following stabilisation: take the cartesian product of the symplectic surface with a sufficiently small symplectic annulus, and take the product of the curve with the with the core of the annulus to produce a Lagrangian torus. END:VEVENT BEGIN:VEVENT DTSTART:20210503T100000 DTEND:20210503T110000 DTSTAMP:20210502T150000Z UID:32b1e310bb526b2ecbb8df5c64f0b0d6@cgp.ibs.re.kr SUMMARY:The symplectic (A-infinity,2)-category and a simplicial version of the 2D Fulton-MacPherson operad LOCATION:Online Streaming DESCRIPTION:Speaker: Nathaniel Bottman\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The symplectic (A-infinity,2)-category Symp, which is currently under construction by myself and my collaborators, is a 2-category-like structure whose objects are symplectic manifolds and where hom(M,N) := Fuk(M^- x N). Symp is a coherent algebraic structure which encodes the functoriality properties of the Fukaya category. This talk will begin with the following question: what can say about the part of Symp that knows only about a single symplectic manifold M, and the diagonal Lagrangian correspondence from M to itself? We expect that the answer to this question should be a chain-level algebraic structure on symplectic cohomology, and in this talk I will present progress toward confirming this. Specifically, I will present a "simplicial version" of the 2-dimensional Fulton-MacPherson operad. If there is time, I will discuss work-in-progress with Felix Janda and Paolo Salvatore that aims to complete this answer. END:VEVENT BEGIN:VEVENT DTSTART:20210304T160000 DTEND:20210304T180000 DTSTAMP:20210303T150000Z UID:48472aaf8bfb6d7a0ed1bb600680efa5@cgp.ibs.re.kr SUMMARY:Computation of categorical entropy via spherical functors LOCATION:Online Streaming DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: CGP Seminar\n\nAbstract: The notion of spherical functors (introduced by Anno$-$Logvinenko) generalizes that of spherical objects (introduced by Seidel$-$Thomas). A spherical functor gives rise to two exact autoequivalences: the twist and cotwist functors. In this talk, I will talk about the relationship between the categorical entropy (introduced by Dimitrov$-$Haiden$-$Katzarkov$-$Kontsevich) of the twist and cotwist functors. In particular, we will see that the categorical entropy of the twist functor coincides with that of the cotwist functor in certain circumstances and that our results generalize the computations of the categorical entropy of spherical twists and $\mathbb{P}$-twists by Ouchi and Fan. As an application, we will apply our results to the Gromov$-$Yomdin type conjecture by Kikuta$-$Takahashi.
END:VEVENT BEGIN:VEVENT DTSTART:20210413T160000 DTEND:20210413T170000 DTSTAMP:20210412T150000Z UID:089c05d8f31cbd6c1293a22a4e4d48fa@cgp.ibs.re.kr SUMMARY:Rationality of Fano 3-folds over nonclosed fields LOCATION:Online Streaming DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The rationality problem for smooth Fano threefolds over algebraically closed fields is basically solved. In this talk I will discuss rationality of forms of these Fanos over nonclosed fields of characteristic 0. I will concentrate on the case where the Picard number equals 1. The talk is based on joint works with Alexander Kuznetsov.
END:VEVENT BEGIN:VEVENT DTSTART:20210427T160000 DTEND:20210427T170000 DTSTAMP:20210426T150000Z UID:488319fd4a11578b6e517cecac71ba51@cgp.ibs.re.kr SUMMARY:Toric varieties of Catalan type and smooth toric Richardson varieties LOCATION:Online Streaming DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. Indeed, there are at least 214 different kinds of objects counted by them. For example, the enumeration of polygon triangulations or that of binary trees is given by Catalan numbers. In this talk, I will introduce an interesting family of smooth projective toric varieties each element of which will be called a toric variety $\textit{of Catalan type}$. As one may expect, there is a bijective correspondence between the set of toric varieties of Catalan type and that of polygon triangulations. And then, I will explain how they are related to smooth toric Richardson varieties, which are subvarieties of the flag variety. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.
END:VEVENT BEGIN:VEVENT DTSTART:20210312T170000 DTEND:20210312T180000 DTSTAMP:20210311T150000Z UID:6824e19680c73b90cc4e481594514bf3@cgp.ibs.re.kr SUMMARY:A noncommutative generalization of Witten's conjecture LOCATION:Online Streaming DESCRIPTION:Speaker: Alexandr Buryak\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The classical Witten conjecture says that the generating series of integrals over the moduli spaces of curves of monomials in the psi-classes is a solution of the Korteweg - de Vries (KdV) hierarchy. Together with Paolo Rossi, we present the following generalization of Witten's conjecture. On one side, let us deform Witten's generating series by inserting in the integrals certain naturally defined cohomology classes, the so-called double ramification cycles. It turns out that the resulting generating series is conjecturally a solution of a noncommutative KdV hierarchy, where one spatial variable is replaced by two spatial variables and the usual multiplication of functions is replaced by the noncommutative Moyal multiplication in the space of functions of two variables.
END:VEVENT BEGIN:VEVENT DTSTART:20210319T100000 DTEND:20210319T110000 DTSTAMP:20210318T150000Z UID:8c1c23b2a87c8128d52f1ff4d7419526@cgp.ibs.re.kr SUMMARY:Darboux coordinates for symplectic groupoid and cluster algebras LOCATION:Online Streaming DESCRIPTION:Speaker: Leonid Chekhov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The talk is based on Arxiv:2003:07499, joint work with Misha Shapiro. I will start with a short elementary excursion into cluster algebras $-$ a fascinating branch of modern algebra introduced by Fomin and Zelvinsky in 2000's $-$ and describe planar directed networks. We then concentrate on another interesting algebraic object $-$ the $\mathcal A_n$ groupoid of upper-triangular matrices, which has had many appearances in studies of algebras of monodromies of $SL_2$ Fuchsian systems and in geometry, including the celebrated Goldman bracket. I will show how we can use Fock-Goncharov higher Teichm\"uller space variables to derive canonical (Darboux) coordinate representation for entries of general symplectic leaves of the $\mathcal A_n$ groupoid and, in a more general setting, of higher-dimensional symplectic leaves for algebras governed by the quantum reflection equation with the trigonometric $R$-matrix. For the groupoid of upper-triangular matrices, we represent braid-group transformations via sequences of cluster mutations in the special $\mathbb A_n$-quiver. Time permitting, I will also describe a generalization of this construction to affine Lie-Poisson algebras and to quantum loop algebras (Arxiv:2012:10982).
END:VEVENT BEGIN:VEVENT DTSTART:20210326T100000 DTEND:20210326T110000 DTSTAMP:20210325T150000Z UID:5c382c292e6b7da0bc30d1840b678426@cgp.ibs.re.kr SUMMARY:Quenched free energy from spacetime D-branes LOCATION:Online Streaming DESCRIPTION:Speaker: Kazumi Okuyama\n\nEvent: Mathematical Physics Seminar\n\nAbstract: We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the generating function of correlators. It turns out that the resulting quenched free energy is a monotonically decreasing function of the temperature, as expected.
END:VEVENT BEGIN:VEVENT DTSTART:20210402T170000 DTEND:20210402T180000 DTSTAMP:20210401T150000Z UID:867d07eb6777ae71305bd75de15234dc@cgp.ibs.re.kr SUMMARY:Loop equations and integrable hierarchies for special cubic Hodge integrals LOCATION:Online Streaming DESCRIPTION:Speaker: Di Yang\n\nEvent: Mathematical Physics Seminar\n\nAbstract: By using the Virasoro constraints we derive the loop equations for the cubic Hodge partition function with three parameters p,q,r satisfying the Calabi-Yau condition pq + qr + rp = 0. We then show that the Hodge integrable hierarchy associated to the special cubic Hodge integrals is normal Miura equivalent to the fractional Volterra hierarchy. In the procedure of the proof, a particular tau-function for the fractional Volterra hierarchy is constructed, which we call the topological tau-function. Finally, when one of the three parameters p,q,r is equal to 1, we prove a certain gap condition for the logarithm of the topological tau-function. The talk is based on joint works with Si-Qi Liu, Youjin Zhang and Chunhui Zhou.
END:VEVENT BEGIN:VEVENT DTSTART:20210409T170000 DTEND:20210409T180000 DTSTAMP:20210408T150000Z UID:513d29674f21810e2faf89ca5af0a8d3@cgp.ibs.re.kr SUMMARY:The Alexander polynomial as a universal invariant LOCATION:Online Streaming DESCRIPTION:Speaker: Rinat Kashaev\n\nEvent: Mathematical Physics Seminar\n\nAbstract: I will explain how the reciprocal of the Alexander polynomial of a knot can be viewed as a universal (quantum) invariant associated to the Hopf algebra of regular functions on the group of affine linear transformations of the complex plane. This provides a conceptual interpretation for the Melvin--Morton--Rozansky conjecture proven by Bar-Nathan and Garoufalidis, and Garoufalidis and Le about the relation of the colored Jones polynomials to the reciprocal of the Alexander polynomial in a large color limit.
END:VEVENT BEGIN:VEVENT DTSTART:20210416T100000 DTEND:20210416T110000 DTSTAMP:20210415T150000Z UID:5fc73e2243f001c603f9648c763b93ee@cgp.ibs.re.kr SUMMARY:Abelianization, exact WKB and link invariants LOCATION:Online Streaming DESCRIPTION:Speaker: Andrew Neitzke\n\nEvent: Mathematical Physics Seminar\n\nAbstract: It has been understood in the last decade that various different problems, including
1) the exact WKB method for studying monodromy of linear ODEs,
2) the study of some link invariants, such as the Jones polynomial,
3) the computation of classical Chern-Simons invariants of flat connections,
can all be understood as aspects of a general strategy for reduction from a nonabelian Lie group to its maximal abelian subgroup. I will describe this point of view, emphasizing the common features of the three problems. Parts of the talk are a report of joint works with Dan Freed, Davide Gaiotto, Greg Moore, Lotte Hollands, and Fei Yan.
END:VEVENT BEGIN:VEVENT DTSTART:20210430T100000 DTEND:20210430T110000 DTSTAMP:20210429T150000Z UID:3c7e72b6d6062206583653cab389df7b@cgp.ibs.re.kr SUMMARY:Topological recursion for simple singularities LOCATION:Online Streaming DESCRIPTION:Speaker: Todor Milanov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: It is known that Givental's total ancestor potential of any semi-simple Frobenius manifold can be reconstructed via the so-called local Eynard--Orantin recursion. For the application to integrable systems and the representation theory of W-algebras however, it is important to determine whether the local recursion can be extended to a global one. In my talk, I would like to explain the problem of comparing local and global Eynard--Orantin recusrions and to explain the case of a Frobenius manifold corresponding to a simple singularity.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210510T100000
DTEND:20210510T110000
DTSTAMP:20210509T150000Z
UID:d34d500015b5905a912b8dad4c8c6d3e@cgp.ibs.re.kr
SUMMARY:Lagrangian configurations and Hamiltonian maps
LOCATION:Online Streaming
DESCRIPTION:Speaker: Egor Shelukhin\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofer's metric, showing in particular that this group is not quasi-isometric to a line. This answers a well-known question of Kapovich-Polterovich from 2006. We show that these flats in Ham(S^2) stabilize to certain product four-manifolds, prove constraints on Lagrangian packing, find new instances of Lagrangian Poincare recurrence, and present a new hierarchy of normal subgroups of area-preserving homeomorphisms of the two-sphere. The technology involves Lagrangian spectral invariants in symmetric product orbifolds. This is joint work with Leonid Polterovich.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210517T100000
DTEND:20210517T110000
DTSTAMP:20210516T150000Z
UID:af030004d15d2b2c17172c02cac329a7@cgp.ibs.re.kr
SUMMARY:Lifting cobordisms and Kontsevich-type recursions for counts of real curves
LOCATION:Online Streaming
DESCRIPTION:Speaker: Xujia Chen\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Kontsevich's recursion, proved in the early 90s, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation), signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon's approach).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210621T100000
DTEND:20210621T110000
DTSTAMP:20210620T150000Z
UID:c24fcab6fa3e21b10bd1c2b91b258398@cgp.ibs.re.kr
SUMMARY:Sharp Ellipsoid Embeddings and Toric Mutations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Renato Ferreira de Velloso VIANNA\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We will show how to construct volume filling ellipsoid embeddings in some 4-dimensional toric domainusing mutation of almost toric compactification of those. In particular we recover the results ofMcDuff-Schlenk for the ball, Fenkel-Müller for the product of symplectic disks and Cristofaro-Gardiner for E(2,3), giving a more explicit geometric perspective for these results. To be able to represent certain divisors, we develop the idea of symplectic tropical curves in almost toric fibrations, inspired by Mikhalkin's work for tropical curves.This is joint work with Roger Casals.
Obs: The same result appears in "On infinite staircases in toric symplectic four-manifolds", by Cristofaro-Gardiner -- Holm -- Mandini -- Pires.Both papers were posted simultaneously on arXiv.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210628T100000
DTEND:20210628T110000
DTSTAMP:20210627T150000Z
UID:53e806ce89e18ec705c5b7abbf631488@cgp.ibs.re.kr
SUMMARY:An algebraic model for smoothing Calabi-Yau varieties and its applications
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kwokwai Chan\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We are interested in smoothing of a degenerate Calabi-Yau variety or a pair (degenerate CY, sheaf). I will explain an algebraic framework for solving such smoothability problems. The idea is to glue local dg Lie algebras (or dg Batalin-Vilkovisky algebras), coming from suitable local models, to get a global object. The key observation is that while this object is only an almost dg Lie algebra (or pre-dg Lie algebra), it is sufficient to prove unobstructedness of the associated Maurer-Cartan equation (a kind of Bogomolov-Tian-Todorov theorem) under suitable assumptions, so the former can be regarded as a singular version of the Kodaira-Spencer DGLA. Our framework applies to degenerate CY varieties previously studied by Kawamata-Namikawa and Gross-Siebert, as well as a more general class of varieties called toroidal crossing spaces (by the recent work of Felten-Filip-Ruddat). This talk is based on various joint works with Conan Leung, Ziming Ma and Y.-H. Suen.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210511T100000
DTEND:20210511T110000
DTSTAMP:20210510T150000Z
UID:12c8f7a41854652871c5f6e182b21e01@cgp.ibs.re.kr
SUMMARY:Noether-Fano Inequalities and Canonical Thresholds on Fano Varieties
LOCATION:Online Streaming
DESCRIPTION:Speaker: Charles Stibitz\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, I will introduce a more precise and general version of the classical Noether-Fano inequalities for a birational map between Fano varieties. This will be applied to give a geometric description of global canonical thresholds on Fano varieties of Picard number one.
END:VEVENT BEGIN:VEVENT DTSTART:20210423T100000 DTEND:20210423T110000 DTSTAMP:20210422T150000Z UID:4470720d55de0010990f560c4c06643d@cgp.ibs.re.kr SUMMARY:Enumerative geometry via the moduli space of super Riemann surfaces LOCATION:Online Streaming DESCRIPTION:Speaker: Paul Norbury\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Mumford initiated the calculation of many algebraic topological invariants over the moduli space of Riemann surfaces in the 1980s, and Witten related these invariants to two dimensional gravity in the 1990s. This viewpoint led Wittento a conjecture, proven by Kontsevich, that a generating function for intersection numbers on the moduli space of curves is a tau function of the KdV hierarchy, now known as the Kontsevich-Witten tau function, which allowed their evaluation. In 2004, Mirzakhaniproduced another proof of Witten's conjecture via the study of Weil-Petersson volumes of the moduli space using hyperbolic geometry. In this lecture I will describe a new collection of integrals over the moduli space of Riemann surfaces whose generating functionis a tau function of the KdV hierarchy, known as the Brezin-Gross-Witten tau function. I will sketch a proof of this result that uses an analogue of Mirzakhani's argument applied to the moduli space of super Riemann surfaces - defined by replacing the fieldof complex numbers with a Grassman algebra - which uses recent work of Stanford and Witten. This appearance of the moduli space of super Riemann surfaces to solve a problem over the classical moduli space is deep and surprising.
END:VEVENT BEGIN:VEVENT DTSTART:20211022T100000 DTEND:20211022T110000 DTSTAMP:20211021T150000Z UID:34be0b8b5ab91f59a86ea6c9b0d28e48@cgp.ibs.re.kr SUMMARY:Bilinear expansions of lattices of KP $\tau$-functions in BKP $\tau$-functions, determinant and Pfaffian expressions of polynomial $\tau$-functions LOCATION:Online Streaming DESCRIPTION:Speaker: John Harnad\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The notion of Kadomtsev-Petviashvili (KP) and BKP $\tau$ functions will be recalled, together with their representations as fermionic expectation values. Schur-type lattices of KP and BKP $\tau$-functions will be defined, corresponding to a given infinite general linear or orthogonal group element, labelled by partitions and strict partitions respectively. A bilinear expansion expressing elements of these lattices of KP $\tau$-functions as sums over products of pairs of elements of associated lattices of BKP $\tau$-functions will be presented, generalizing earlier results relating determinants and Pfaffians of minors of skew symmetric matrices, with applications to Schur functions and Schur $Q$-functions. Further applications include determinantal and Pfaffian representations of all inhomogeneous polynomial $\tau$-functions of KP and BKP type.
END:VEVENT BEGIN:VEVENT DTSTART:20210514T170000 DTEND:20210514T180000 DTSTAMP:20210513T150000Z UID:5cc619dfdcf37fefb3c7b54039747d55@cgp.ibs.re.kr SUMMARY:On the rationality of MUMs and 2-functions LOCATION:Online Streaming DESCRIPTION:Speaker: Johannes Walcher\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Points of maximal unipotent monodromy in Calabi-Yau moduli space play a central role in mirror symmetry, and also harbor some interesting arithmetic. In the classic examples, suitable expansion coefficients of the (all-genus) prepotential (in polylogarithms) under the mirror map are integers with an enumerative interpretation on the mirror manifold. This correspondence should be expected to extend to periods relative to algebraic cycles capturing the enumerative geometry relative to Lagrangian submanifolds. This expectation is challenged, however, when the mixed degeneration is not defined over Q. After musing about compatibility with mirror symmetry, I will discuss two recent results that sharpen these questions further: The first is a theorem proven by Felipe Müller which states that the coefficients of rational 2-functions are necessarily contained in an abelian number field. (As defined in the talk, 2-functions are formal power series whose coefficients satisfy a natural Hodge theoretic supercongruence.) The second are examples worked out in collaboration with Bönisch, Klemm, and van Straten, of MUMs that are themselves not defined over Q.
END:VEVENT BEGIN:VEVENT DTSTART:20210521T100000 DTEND:20210521T110000 DTSTAMP:20210520T150000Z UID:b6bf44a7208e2221363fe2e7a5735f50@cgp.ibs.re.kr SUMMARY:New exact results for open enumerative invariants LOCATION:Online Streaming DESCRIPTION:Speaker: Sergei Gukov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Problems that involve bordered pseudoholomorphic curves with boundary on a Lagrangian submanifold in a Calabi-Yau 3-fold are usually called "open enumerative invariants." The analysis involved in such problems is extremely rich and interesting, which makes the study of open enumerative invariants challenging and complicated. Yet, over the past 30 years a lot of progress has been made, in part due to various "dualities" --- such as mirror symmetry --- that relate open enumerative problems to questions in other areas of mathematics. After a short survey of past developments, I will present a new class of Calabi-Yau 3-folds with Lagrangian submanifolds where the problem can be solved completely thanks to a new connection with quantum groups at generic values of the parameter q.
END:VEVENT BEGIN:VEVENT DTSTART:20210524T170000 DTEND:20210524T180000 DTSTAMP:20210523T150000Z UID:7eb54ab1b81c07e298c541f2ca7e32b2@cgp.ibs.re.kr SUMMARY:Lagrangian Cobordism and Lagrangian Surgery LOCATION:Online Streaming DESCRIPTION:Speaker: Jeff Hicks\n\nEvent: Symplectic Monday Seminar\n\nAbstract: A Lagrangian cobordism is a Lagrangian submanifold in X x C whose "ends" are Lagrangian submanifolds inside of X. We will show that the Lagrangian cobordisms associated to the Lagrangian surgery operation provide the building blocks for all Lagrangian cobordisms. Finally, we will discuss some of the Floer theoretic implications of this decomposition, extending previous work of Biran and Cornea. This is based on work from arxiv:2102.10197. END:VEVENT BEGIN:VEVENT DTSTART:20210531T100000 DTEND:20210531T110000 DTSTAMP:20210530T150000Z UID:f124d1ea3e34b66b3864cd1d144ea148@cgp.ibs.re.kr SUMMARY:Real Lagrangian tori in monotone symplectic 4-manifolds LOCATION:Online Streaming DESCRIPTION:Speaker: Joontae Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: By a real Lagrangian, we mean the fixed point set of an anti-symplectic involution in a symplectic manifold. In this talk, we explore the topology of real Lagrangian tori in monotone symplectic 4-manifolds. They are very rare in the sense that all known exotic monotone Lagrangian tori cannot be real, but they exist exactly when no topological obstructions occur. The disc potential plays an intriguing role in our voyage. END:VEVENT BEGIN:VEVENT DTSTART:20210614T100000 DTEND:20210614T110000 DTSTAMP:20210613T150000Z UID:9c69515316eb17c1ff11cd347097c632@cgp.ibs.re.kr SUMMARY:Noncompact description for Fukaya-Seidel categories of invertible curve singularities LOCATION:Online Streaming DESCRIPTION:Speaker: Wonbo Jeong\n\nEvent: Symplectic Monday Seminar\n\nAbstract: For given invertible polynomial W, we consider two types of Fukaya category. One is the usual Fukaya-Seidel category from Lefschetz fibration structure of W. For the maximal symmetry group G of W, we can construct the other Fukaya category of the pair (W,G) from wrapped Fukaya category of the Milnor fiber and quantum cap action of monodromy orbit. In this talk, we compare the equivariant lift of the latter with the Fukaya-Seidel category and prove its derived equivalence for invertible curve singularities. In particular, directedness of the category is obtained from quantum cap action and related constructions. This talk is based on the joint work (in progress) with Cheol-hyun Cho (SNU) and Dongwook Choa (KIAS). END:VEVENT BEGIN:VEVENT DTSTART:20210427T100000 DTEND:20210427T110000 DTSTAMP:20210426T150000Z UID:29abb3b8ffd7d4b429cc16c4e497e3e6@cgp.ibs.re.kr SUMMARY:A double Johnson filtration for the mapping class group and the Goeritz group of the sphere LOCATION:Online Streaming DESCRIPTION:Speaker: Anderson Vera\n\nEvent: Seminar\n\nAbstract: This talk will be about a double-indexed Johnson filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of S^3. In particular we will explain how this double filtration allows us to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (joint work K. Habiro) END:VEVENT BEGIN:VEVENT DTSTART:20210506T160000 DTEND:20210506T170000 DTSTAMP:20210505T150000Z UID:bf1eeb27c24db93ffe61d3cd8e11461d@cgp.ibs.re.kr SUMMARY:Topologies on the exponential LOCATION:Online Streaming DESCRIPTION:Speaker: Damien Lejay\n\nEvent: CGP Seminar\n\nAbstract: Yes, you have read correctly.In this talk we shall endow the exponential with several topologies, compare them and explain why it's interesting.This is joint work with Anna Cepek.There are no special prerequisites to attend this talk; it is intended to be accessible to all CGP members. END:VEVENT BEGIN:VEVENT DTSTART:20210429T160000 DTEND:20210429T180000 DTSTAMP:20210428T150000Z UID:9aea7da5fc25807d67d5566254ca3697@cgp.ibs.re.kr SUMMARY:Invariants of non-arborescent knots, links & topological entanglement LOCATION:Online Streaming DESCRIPTION:Speaker: Saswati Dhara\n\nEvent: CGP Seminar\n\nAbstract: Computing invariants for knots and links carrying arbitrary representation of $SU(N )$ needs diverse approaches. Chern-Simons field theory provides an approach to write the invariants of arborescent knots and links in terms of exclusive quantum Racah matrices $U_e$ and braiding matrices.As the closed form for $U_e$ are known for all symmetric representations belonging to $SU(N )$ group, the [r]-colored HOMFLY-PT polynomial is available in the literature. For the class of non-arborescent knots and links, the invariants involve inclusive quantum Racah matrices. Hence, our aim was to work on the colored HOMFLY-PT for non-arborescent knots and links using the highest weight approach and eigenvalue hypothesis approach that will be explained. The next problem was to generalise some works on multi-boundary entanglement of three manifolds with torus boundaries using Chern-Simons theory based on a generic gauge group $G$. The multi-colored link invariants are needed to compute entanglement entropy and Rényi entropy. Finally, I will project an idea to study the entanglement amongst multiple $S^2$ boundaries with or without punctures END:VEVENT BEGIN:VEVENT DTSTART:20210504T100000 DTEND:20210504T110000 DTSTAMP:20210503T150000Z UID:0a3012ecc9f12eb39e45b6eac4a91cff@cgp.ibs.re.kr SUMMARY:On (-1) curves in $P^n$ and geometry of Mori Dream Spaces LOCATION:Online Streaming DESCRIPTION:Speaker: Olivia Dumitrescu\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The notion of (-1) curves was analyzed in the early days of mirror symmetry by Maxim Kontsevich. In this talk we classify (-1) curves in Mori Dream spaces of type $X^n_s$, the projective space $P^n$ blown up in s general points. If the number of points is at least n+5 we prove there are infinitely many (-1) curves. As applications, we show that (0) and (1)-curves determine the faces of the cone of effective divisors in $X^n_{n+3}$.
We further present the necessary techniques for computing Weyl orbits of linear cycles in dimension 4, and we determine the varieties that determine combinatorial data describing the birational geometry of $X^4_8$. This is talk is based on joint work with Rick Miranda.
END:VEVENT BEGIN:VEVENT DTSTART:20210608T160000 DTEND:20210608T170000 DTSTAMP:20210607T150000Z UID:b72dcb4b948d0f444d36fcaebaf6e21e@cgp.ibs.re.kr SUMMARY:Some applications of Jordan algebras in geometry LOCATION:Online Streaming DESCRIPTION:Speaker: Nicolas Perrin\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will present some relation between Jordan algebras and homogeneous or symmetric spaces and describe some applications towards the study of VMRT or of deformations.
END:VEVENT BEGIN:VEVENT DTSTART:20210601T160000 DTEND:20210601T170000 DTSTAMP:20210531T150000Z UID:87ae790c6c77553b7569d99738f607cf@cgp.ibs.re.kr SUMMARY:Minimal rational curves on Schubert varieties and their desingularizations LOCATION:Online Streaming DESCRIPTION:Speaker: Michel Brion\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Minimal rational curves on a uniruled projective algebraic variety X are generalizations of lines. They feature prominently in the intrinsic geometry of X, as demonstrated by work of Mok, Hwang and others. The talk will first introduce the notion of minimal rational curves, and present some general results in the setting where X has an action of a linear algebraic group with an open orbit. Then we will discuss the case where X is a Schubert variety or a Bott-Samelson desingularization, based on joint work with S. S. Kannan.
END:VEVENT BEGIN:VEVENT DTSTART:20210528T170000 DTEND:20210528T180000 DTSTAMP:20210527T150000Z UID:90b2b86d5673e97ee06f8fba52268e15@cgp.ibs.re.kr SUMMARY:Fluxes, Holomorphic Anomalies and Elliptic Genera in d=4 LOCATION:Online Streaming DESCRIPTION:Speaker: Wolfgang Lerche\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Motivated by tests of Weak Gravity Conjectures, we investigate properties of elliptic genera of string theories that arise in large distance limits of the moduli space of F-theory compactifications. This allows for a non-perturbative definition of elliptic genera that goes beyond the ordinary world-sheet description. While thisconstruction has been known for six-dimensional theories, we find the four-dimensional variant to be surprisingly complex. The essential new ingredient is background fluxes, and these lead to different sectors of the elliptic genus with different modular properties. Crucial is the appearance of derivatives which leadsto novel modular (and hence, holomorphic) anomalies that are much worse than expected. We also give a physical interpretation of these phenomena.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210531T160000
DTEND:20210531T180000
DTSTAMP:20210530T150000Z
UID:873c8adfb55c09435a33d6e030d81378@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory I
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210602T160000
DTEND:20210602T180000
DTSTAMP:20210601T150000Z
UID:75110870fc4d1bb4ebc4bd37cf824733@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory II
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210603T160000
DTEND:20210603T180000
DTSTAMP:20210602T150000Z
UID:580687e9e410a3e978d3c6dff5e25816@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory III
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210607T160000
DTEND:20210607T180000
DTSTAMP:20210606T150000Z
UID:f72f2132b636f3a8843f01c7f8aa5955@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory IV
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210609T160000
DTEND:20210609T180000
DTSTAMP:20210608T150000Z
UID:374935f009abf4d03887ba8397a834b9@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory V
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210622T160000
DTEND:20210622T170000
DTSTAMP:20210621T150000Z
UID:547280f06d655143dcfabf91893a643d@cgp.ibs.re.kr
SUMMARY:Tropical varieties and integral affine manifolds with singularities
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yuto Yamamoto\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: There are two types of spaces which we study in tropical geometry. One is tropical varieties which appear as tropicalizations of algebraic varieties over valuation fields. They are polyhedral complexes equipped with some kind of affine structures. The other one is integral affine manifolds with singularities which arise as dual intersection complexes of toric degenerations in the Gross$-$Siebert program. They are also expected to be base spaces of Lagrangian torus fibrations in Strominger$-$Yau$-$Zaslow conjecture, and Gromov$-$Hausdorff limits of maximally degenerating families of Calabi$-$Yau manifolds with Ricci-flat Kähler metrics. In this talk, we discuss relations between these two different types of tropical spaces. We construct contraction maps between them in the case of Calabi$-$Yau varieties, and compare some of their invariants such as tropical cohomology groups.
END:VEVENT BEGIN:VEVENT DTSTART:20210618T100000 DTEND:20210618T110000 DTSTAMP:20210617T150000Z UID:5225efd2026371ec4bc7b5e49ed4efec@cgp.ibs.re.kr SUMMARY:KP integrability of triple Hodge integrals LOCATION:Online Streaming DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In my talk, I will describe a relation between the Givental group of rank one and the Heisenberg-Virasoro symmetry group of the KP integrable hierarchy. It appears that only a two-parameter family of the Givental operators can be identified with elements of the Heisenberg-Virasoro symmetry group. This family describes triple Hodge integrals satisfying the Calabi-Yau condition. Using the identification of the elements of two groups it is possible to prove that the generating function of triple Hodge integrals satisfying the Calabi-Yau condition and its $\Theta$-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in the case of linear Hodge integrals. I will also describe the relation of this family of tau-functions with the deformation of the Kontsevich matrix model. My talk is based on two papers, arXiv:2009.01615 and arXiv:2009.10961.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210712T100000
DTEND:20210712T105000
DTSTAMP:20210711T150000Z
UID:d52e053b89a30debb93a0e3f89f9d7a4@cgp.ibs.re.kr
SUMMARY:Scalar curvature and moment map in Generalized Kähler geometry
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ryushi GOTO\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: We introduce a notion of scalar curvature of a twisted generalized Kähler manifold in terms of pure spinors formalism. A moment map framework on an arbitrary compact twisted generalized Kähler manifold is provided and then it turns out that a moment map is given by the scalar curvature under the certain condition, which is a generalization of the result of the scalar curvature as a moment map in the ordinary Kähler geometry, due to Fujiki and Donaldson. A noncommutative compact Lie group G does not have any Kähler structure. However, we show that a compact Lie group has a family of generalized Kähler structures twisted by the Cartan 3-form, which is constructed by the action of the real Pin group of the double of Cartan subalgebra. Then we show that an arbitrary compact Lie group admits generalized Kähler structures with constant scalar curvature. In particular, generalized Kähler structures with constant scalar curvature on the standard Hopf surface are explicitly given.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210712T111000
DTEND:20210712T120000
DTSTAMP:20210711T150000Z
UID:8dc0e8a8824904c64f6b6c9048a90a9d@cgp.ibs.re.kr
SUMMARY:Augmentations and ruling polynomials for Legendrian graphs
LOCATION:Online Streaming
DESCRIPTION:Speaker: Byunghee AN\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: In this talk, we will show the equivalence between two Legendrian isotopy invariants of Legendrian graphs: (i) augmentation number via point-counting over a finite field for the augmentation variety of the associated Chekanov-Eliashberg DGA, and (ii) the ruling polynomial via combinatorics of the decompositions of the associated front projections.This is a joint work with Youngjin Bae(Incheon National University) and Tao Su(Yau Mathematical Sciences Center, Tsinghua University).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210713T093000
DTEND:20210713T102000
DTSTAMP:20210712T150000Z
UID:3b6ab7a674ce26a2804d88b0f493704e@cgp.ibs.re.kr
SUMMARY:Seeds many Lagrangian fillings for Legendrian links
LOCATION:Online Streaming
DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: I will introduce Legendrian links of finite and affine Dynkin diagrams, and then argue that there are at least as many Lagrangian fillings as seeds in the corresponding cluster structure. The main ingredients are N-graphs developed by Casals-Zaslow, and cluster structures by Fomin-Zelevinsky. This is a joint work with Byung Hee An and Eunjeong Lee.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210713T114000
DTEND:20210713T123000
DTSTAMP:20210712T150000Z
UID:334b52b10b7fadbfcce531f5d9823bab@cgp.ibs.re.kr
SUMMARY:Structure of high genus Gromov Witten invariants
LOCATION:Online Streaming
DESCRIPTION:Speaker: Huai-Liang CHANG\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: Gromov Witten invariants Fg encodes the numbers of genus g curves in Calabi Yau threefolds and play an important role in enumerative geometry. In 1993, Bershadsky, Cecotti, Ooguri, Vafa exhibited a hidden ``Feynman structure” governing all Fg’s at once,using path integral methods. The counterpart in mathematics has been missing for many years. After a decades of search, in 2018, a mathematical approach: Mixed Spin P field (MSP) moduli, is finally developed to provide the wanted ``Feynman structure”, for quintic CY 3fold. Instead of enumerating curves in the quintic 3fold, MSP enumerate curves in a large N dimensional singular space with quintic-3-fold boundary. The “P fields” and “cosections” are used to formulate counting in the singular space via a Landau Ginzburg type construction. In this talk, I shall focus on geometric ideas behind the MSP moduli. The results follows from a decade of joint works with Jun Li, Shuai Guo, Young Hoon Kiem, Weiping Li, Melissa C.C. Liu, Jie Zhou, and Yang Zhou.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210713T103500
DTEND:20210713T112500
DTSTAMP:20210712T150000Z
UID:5c778c64fd5c75f01e3cc792b9a72225@cgp.ibs.re.kr
SUMMARY:Non-invariant deformations of left-invariant complex structures on compact Lie groups
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hisashi KASUYA\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: It is known that every compact Lie group of even dimension admits left-invariant complex structures. We study deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are non-invariant. We compute cohomology of vector bundles for such non-invariant complex structures and see the difference between invariant complex structures and non-invariant complex structures. This talk is a joint work with Hiroaki Ishida (Kagoshima).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210714T100000
DTEND:20210714T105000
DTSTAMP:20210713T150000Z
UID:77e5288745e9359894f93b00e7d842a0@cgp.ibs.re.kr
SUMMARY:Limits of canonical metrics in low-dimensions
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hyungryul Baik\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: For a tower of finite normal covers of graphs or surfaces, one can consider a sequence of metrics on the base given by pull-back of canonical metrc of the covers. We show that such a sequence has a limit and it depends only on the cover approximated by the tower up to scaling. The case of compact Riemann surface where the tower approximates the universal cover is due to Kazhdan. In this talk, we will mostly focus on the surface case and explain how the L^2-theory can be applied. This talk is based on a joint work with Farbod Shokrieh and Chenxi Wu.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210714T111000
DTEND:20210714T120000
DTSTAMP:20210713T150000Z
UID:bbb35df4fe412925adb3369a48145964@cgp.ibs.re.kr
SUMMARY:Degenerations of Hilbert schemes of points on K3 surfaces
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ziyu ZHANG\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: It is a widely open problem to understand the degenerations of higher dimensional hyperkähler manifolds. The simplest case would be the degenerations of Hilbert schemes of points on K3 surfaces. Given a simple degeneration family of K3 surfaces, there are two existing constructions of the degenerations of the Hilbert schemes of its fibers in the literature, due to Nagai and Gulbrandsen-Halle-Hulek respectively. I will compare the two constructions with an emphasis on the geometry of the latter. Based on joint work with M.G.Gulbrandsen, L.H.Halle and K.Hulek.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210715T093000
DTEND:20210715T102000
DTSTAMP:20210714T150000Z
UID:d887b69d56832dbc768d69d4cb2caedb@cgp.ibs.re.kr
SUMMARY:Continuous solutions to Monge-Amp ere equations on Hermitian manifolds for measures dominated by capacity
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ngoc Cuong Nguyen\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: We prove the existence of a continuous quasi-plurisubharmonic solution to the Monge-Amp ere equation on a compact Hermitian manifold for a very general measre on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh-Nguyen-Sibony. As a consequence, we give a characterization of measures admitting Holder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh-Nguyen. This is joint work with S lawomir Ko lodziej.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210715T103500
DTEND:20210715T112500
DTSTAMP:20210714T150000Z
UID:944349d85e09d8f2a8b1e1ba53696098@cgp.ibs.re.kr
SUMMARY:Complex structures on Einstein four-manifolds of positive scalar curvature
LOCATION:Online Streaming
DESCRIPTION:Speaker: Peng WU\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: The question that when a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, LeBrun classified Hermitian, Einstein four-manifolds of positive scalar curvature. In this talk we consider the inverse problem, that is, when a simply connected four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210715T114000
DTEND:20210715T123000
DTSTAMP:20210714T150000Z
UID:e01250a272a2b90ab0e370d1157b93f3@cgp.ibs.re.kr
SUMMARY:On Berndtsson-Lempert's proof of optimal $L^2$ extension theorem and extension from non-reduced varieties
LOCATION:Online Streaming
DESCRIPTION:Speaker: Genki HOSONO\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: I'd like to talk about the proof of an optimal version of the Ohsawa-Takegoshi $L^2$ extension theorem and its application to an extension theorem from non-reduced varieties.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210716T100000
DTEND:20210716T105000
DTSTAMP:20210715T150000Z
UID:03aa2928cc9905915fc5adff39fd92f8@cgp.ibs.re.kr
SUMMARY:Some geometric flow approaches for deformed Hermitian-Yang-Mills equation
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ryosuke TAKAHASHI\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: On SYZ mirror symmetry, a deformed Hermitian-Yang-Mills (dHYM) metric is a fiber metric on a holomorphic line bundle, which is the mirror object to a special Lagrangian section of the dual torus fibration. As a parabolic analogue, Jacob-Yau introduced the Line Bundle Mean Curvature Flow (LBMCF) as the mirror of the Lagrangian Mean Curvature Flow. In this talk, we explore some geometric flow approaches for dHYM metrics:(A) On K\”ahler surfaces, it is known that the existence of dHYM metrics is equivalent to a K\”ahler condition for a certain cohomology class. We relax this condition and study how the LBMCF blows up.(B) Recently, Collins-Yau discovered a new variational characterization for dHYM metrics. Motivated by this, we introduce a new geometric flow which is designed to deform a given metric to a dHYM one. Then we show that this new flow potentially has more global existence and convergence properties than the LBMCF.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210716T111000
DTEND:20210716T120000
DTSTAMP:20210715T150000Z
UID:32081e6062423472283ffca5b6721fbf@cgp.ibs.re.kr
SUMMARY:Translators of the Gauss curvature flow
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kyeongsu CHOI\n\nEvent: 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\nAbstract: We begin by reviewing the blow-up analysis for the minimal surfaces at isolated singularities, and will quickly discuss about some related recent developments in the singularity analysis for the mean curvature flow. Then, we will classify the translating surfaces under the flows by sub-affine-critical powers of the Gauss curvature, which is a Liouville theorem for a class of Monge-Ampere equations. We will put an emphasis on the divergence free property of the linearized operator of the Monge-Ampere equation. This is a joint work with Beomjun Choi and Soojung Kim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210610T160000
DTEND:20210610T180000
DTSTAMP:20210609T150000Z
UID:a6bf88bd752ae9206a688a4b97cf6fc3@cgp.ibs.re.kr
SUMMARY:The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory VI
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: The Le-Murakami-Ohtsuki invariant and Johnson-Morita theory\n\nAbstract: Registration: Link
After the discovery of the Jones polynomial for knots and its physical interpretation by Witten a new kind of invariants for links and 3-manifolds were defined, the so-called "quantum invariants". The first quantum invariants for 3-manifolds were defined by Reshetikhin and Turaev using quantum groups and their representations. There is an alternative approach developed byLe-Murakami-Ohtsuki which gave rise to the LMO invariant. The LMO invariant was extended to cobordisms between surfaces with one boundary component by Cheptea, Habiro and Massuyeau, giving rise to the so-called LMO functor. The LMO invariant and the LMO functor are very strong invariants taking values in some spaces of graphs known as Jacobi diagrams. The LMO invariant and LMO functor are universal among quantum invariants, in particular, all Reshetikhin-Turaev invariants can be recovered from them.
The construction of the LMO invariant and LMO functor is quite sophisticated, so an important effort is made into finding relationships with classical invariants.
In this series of lectures, we give a survey of the construction of the LMO invariant and the LMO functor and we focus on the relationships with some algebraic invariants defined on the mapping class group of a surface with one boundary component. We will start by reviewing some combinatorial presentations of 3-manifolds (surgery presentations) and then we will see the spaces involved in the definition of the Kontsevich integral, LMO invariant and LMO functor as well as the precise definition of these invariants. Finally, we will study some notions about the mapping class group and the Johnson-Morita theory to conclude with the explicit relationships between the LMO functor and several kinds of Johnson-type homomorphisms.
References
[1] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on S 3 . Sel. math., New ser. 8, 315–339 (2002).
[2] Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002).
[3] Cheptea, Dorin; Habiro, Kazuo; and Massuyeau, Gwénaël, "A functorial LMO invariant for Lagrangian cobordisms." Geometry & Topology 12.2, 1091-1170 (2008).
[4] Habegger, Nathan, and Masbaum, Gregor. "The Kontsevich integral and Milnor’s invariants." Topology 39.6 1253-1289 (2000).
[5] Massuyeau, Gwénaël. "Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant." Bulletin de la société mathématique de France 140.1 (2012): 101-161.
[6] Ohtsuki, Tomotoda, Quantum invariants: A study of knots, 3-manifolds, and their sets. Vol. 29. World Scientific, 2002.
[7] Vera, Anderson. "Johnson–Levine homomorphisms and the tree reduction of the LMO functor." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 170. No. 2. Cambridge University Press, 2021.
[8] Vera, Anderson. "Alternative versions of the Johnson homomorphisms and the LMO functor." arXiv preprint arXiv:1902.10012 (2019).
END:VEVENT
BEGIN:VEVENT
DTSTART:20210701T160000
DTEND:20210701T180000
DTSTAMP:20210630T150000Z
UID:84a8f6dc24b458de3780a1ccbdffa76e@cgp.ibs.re.kr
SUMMARY:Tropical Lagrangian multi-sections and toric vector bundles
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: CGP Seminar\n\nAbstract: It is well-known that toric line bundles on a toric variety correspond to piecewise linear functions on the fan. For toric vector bundles, Payne constructed a branched covering over the fan and a piecewise linear function on the domain. We think of these objects as the tropicalization of Lagrangian multi-sections and therefore, deserve the name tropical Lagrangian multi-sections. In this talk, we will discuss the reconstruction problem of toric vector bundles from a given tropical Lagrangian multi-section. Those tropical Lagrangian multi-sections that arise from toric vector bundles are called unobstructed. We reformulate Kaneyama's classification of toric vector bundles in terms of the language of tropical Lagrangian multi-sections. We also provide a "SYZ-type" approach to construct toric vector bundles from tropical Lagrangian multi-sections. In dimension 2, such "mirror-symmetric" approach provides us a combinatorial condition for checking which rank 2 tropical Lagrangian multi-section is unobstructed. If time allows, I will discuss an application in the Gross-Siebert program.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210713T100000
DTEND:20210713T120000
DTSTAMP:20210712T150000Z
UID:e47b20768c6605db94ebb6e26a223849@cgp.ibs.re.kr
SUMMARY:Basic knot theory and some knot invariants
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210720T100000
DTEND:20210720T120000
DTSTAMP:20210719T150000Z
UID:8d970b5210bb12d206f00b004ef7770a@cgp.ibs.re.kr
SUMMARY:Braids and its R-matrix representations
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Minkyoung Song\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210727T100000
DTEND:20210727T120000
DTSTAMP:20210726T150000Z
UID:0fc4c1dce9bc2e37d88e53618ca7711b@cgp.ibs.re.kr
SUMMARY:Knot invariants through R-matrix representations
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210803T100000
DTEND:20210803T120000
DTSTAMP:20210802T150000Z
UID:976e2c55ee08eaea62798a69351ad4ce@cgp.ibs.re.kr
SUMMARY:Operator invariants of tangles
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Yifan Li\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210810T100000
DTEND:20210810T120000
DTSTAMP:20210809T150000Z
UID:22365cf54a651135951e71a9e7dd3005@cgp.ibs.re.kr
SUMMARY:Ribbon Hopf algebras I
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210817T100000
DTEND:20210817T120000
DTSTAMP:20210816T150000Z
UID:65583eb42d6d832490ab03baec5404bb@cgp.ibs.re.kr
SUMMARY:Ribbon Hopf algebras II
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants”2) “Quantum Invariants” by Tomotada Ohstuki
END:VEVENT
BEGIN:VEVENT
DTSTART:20210714T160000
DTEND:20210714T180000
DTSTAMP:20210713T150000Z
UID:f40c46bb51b0f0ce19832692c2876d02@cgp.ibs.re.kr
SUMMARY:(Reading Seminar) Algebraic aspects of contact topology
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Reading Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210721T140000
DTEND:20210721T160000
DTSTAMP:20210720T150000Z
UID:6d81192450db03299bcb9a324bb6db59@cgp.ibs.re.kr
SUMMARY:(Reading Seminar) Algebraic aspects of contact topology
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Reading Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210728T140000
DTEND:20210728T160000
DTSTAMP:20210727T150000Z
UID:a419704945ea3d27a3139cc8a31765f7@cgp.ibs.re.kr
SUMMARY:(Reading Seminar) Algebraic aspects of contact topology
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: Reading Seminar\n\nAbstract: In the reading seminar, we will study some algebraic aspects of contact topology. As you know, contact topology is a sibling of symplectc topology. In symplectic topology, there is a helpful algebraic tool, Fukaya category. Thus, it is natural to expect that there is an algebraic tool for studying contact topology. Based on this, we will study Legendrian DGA and contact homology in the reading seminar.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210928T100000
DTEND:20210928T110000
DTSTAMP:20210927T150000Z
UID:47f863880be17c429ae2d1d9880e75bd@cgp.ibs.re.kr
SUMMARY:Seshadri constants and K-stability of Fano manifolds
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ziquan Zhuang\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Seshadri constants were originally introduced by Demailly to measure the local positivity of ample line bundles and may be vaguely thought of as an algebraic version of curvature. In this talk, I will explain how they can be used to detect K-stability of Fano manifolds and thereby prove existence of Kähler-Einstein metrics in various cases. Based on joint work with Hamid Ahmadinezhad.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210914T160000
DTEND:20210914T170000
DTSTAMP:20210913T150000Z
UID:c4172af3e505c33d55fc0caf9e1d9a4b@cgp.ibs.re.kr
SUMMARY:Kahler-Einstein smooth Fano threefolds
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract:
A smooth Fano manifold X admits a Kahler-Einstein metric if and only if X is K-polystable (K-stable if the automorphism group of X is finite).For smooth del Pezzo surfaces (two-dimensional Fano manifolds), Tian proved that the K-polystability is equivalent to the reductivity of the automorphism group.In this talk, I will explain which smooth Fano threefolds (three-dimensional Fano manifolds) are K-polystable.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210824T100000
DTEND:20210824T120000
DTSTAMP:20210823T150000Z
UID:6e746547fe733b5007aea7c18f95df47@cgp.ibs.re.kr
SUMMARY:Ribbon Hopf algebras III
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 213 & Online streaming (Zoom: ID: 330 113 4642, Password: postech)
END:VEVENT
BEGIN:VEVENT
DTSTART:20210831T100000
DTEND:20210831T120000
DTSTAMP:20210830T150000Z
UID:f3046f6b625a086129d4a64c8383f6bf@cgp.ibs.re.kr
SUMMARY:Turaev-Reshetikhin Invariants
LOCATION:Math. Bldg. #213
DESCRIPTION:Speaker: Yifan Li\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 213 & Online streaming (Zoom: ID: 330 113 4642, Password: postech)
END:VEVENT
BEGIN:VEVENT
DTSTART:20211012T160000
DTEND:20211012T170000
DTSTAMP:20211011T150000Z
UID:2b2ad4a7ddf6cb1f0f5e00c4bd74c692@cgp.ibs.re.kr
SUMMARY:Birational geometry of sextic double solids with cA points
LOCATION:Online Streaming
DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: A sextic double solid is a Fano 3-fold which is a double cover of the projective 3-space branched along a sextic surface. Iskovskikh proved that a smooth sextic double solid is birationally superrigid, that is, it does not admit a non-biregular birational map to a Mori fiber space. Later on Cheltsov and Park showed that the same conclusion holds for sextic double solids with ordinary double points. In this talk I will explain birational (non-)superrigidity of sextic double solids with cA points. This talk is based on a joint work with Krylov and Paemurru.
END:VEVENT BEGIN:VEVENT DTSTART:20211102T160000 DTEND:20211102T170000 DTSTAMP:20211101T150000Z UID:ee7af4efffec91a4b104786155439217@cgp.ibs.re.kr SUMMARY:Intermediate Jacobians of Gushel-Mukai varieties LOCATION:Online Streaming DESCRIPTION:Speaker: Alexander Kuznetsov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The subject of this talk are Gushel-Mukai threefolds $-$ prime Fano threefolds of genus 6, and their higher dimensional analogues. Geometry of GM varieties is controlled by the data of a Lagrangian subspace in acertain 20-dimensional symplectic vector space and by the associated double EPW sextic and EPW surface. I will explain how the intermediate Jacobians of GM threefolds and fivefolds can be identified with the Albanese varieties of double EPW surfaces and discuss implications of this for the period map of GM varieties. This is joint work with Olivier Debarre.
END:VEVENT BEGIN:VEVENT DTSTART:20210924T100000 DTEND:20210924T110000 DTSTAMP:20210923T150000Z UID:bac43f28a85460ce35ab041818cb4adb@cgp.ibs.re.kr SUMMARY:Whittaker vectors for W-algebras from topological recursion LOCATION:Online Streaming DESCRIPTION:Speaker: Vincent Bouchard\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of G-bundles over $P^2$, for G a complex simple Lie group, are Whittaker vectors for modules of W-algebras. In this work we identify these Whittaker vectors with partition functions of quantum Airy structures, which means that they can be calculated by topological recursion methods. On the physics side, it means that the Nekrasov partition function for pure N=2 4d supersymmetric gauge theories can be accessed via a topological recursion à la Chekhov-Eynard-Orantin. We formulate the connection for Gaiotto vectors of type A, B, C, and D. For those interested in topological recursion, the type A case at arbitrary level gives rise to a new non-commutative formulation of topological recursion.
This is joint work with Gaetan Borot, Nitin K. Chidambaram, and Thomas Creutzig.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210906T100000
DTEND:20210906T110000
DTSTAMP:20210905T150000Z
UID:2a97397359db50a9ba187f21a44d9711@cgp.ibs.re.kr
SUMMARY:Mirror Symmetry Correspondence between Indecomposable Cohen-Macaulay Modules over Degenerate Cusps and Immersed Lagrangians on Surfaces
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kyungmin Rho\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Burban and Drozd (2017) classified all indecomposable maximal Cohen-Macaulay modules over degenerate cusps. For the degenerate cusp defined by xyz, its mirror is given by a pair of pants (Abouzaid, Auroux, Efimov, Katzarkov and Orlov). We find explicit objects in the Fukaya category of a pair of pants, which correspond to every indecomposable Cohen-Macaulay modules in Burban and Drozd's list under the localized mirror functor. This is a joint work in progress with Cheol-Hyun Cho, Wonbo Jeong and Kyoungmo Kim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210913T170000
DTEND:20210913T180000
DTSTAMP:20210912T150000Z
UID:5e84e1fb779cc8266508dacbb9e53c11@cgp.ibs.re.kr
SUMMARY:The algebraic structure of groups of area-preserving homeomorphisms
LOCATION:Online Streaming
DESCRIPTION:Speaker: Sobhan Seyfaddini\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will review recent joint work with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak and Ivan Smith constructing a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, we resolve several open questions from topological surface dynamics and continuous symplectic topology: 1. We show that the group of Hamiltonian homeomorphisms of any compact surface with (possibly empty) boundary is not simple2. We extend the Calabi homomorphism to the group of Hameomorphisms constructed by Oh-Müller.3. We construct an infinite dimensional family of quasimorphisms on the group of area and orientation preserving homeomorphisms of the two-sphere. Our invariants are inspired by recent work of Polterovich and Shelukhin defining and applying spectral invariants for links in the two-sphere consisting of parallel circles.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210927T170000
DTEND:20210927T180000
DTSTAMP:20210926T150000Z
UID:d2d41b9c60878f094c1db9b3db667cd4@cgp.ibs.re.kr
SUMMARY:Skein valued curve counts, basic holomorphic disks, and HOMFLY homology
LOCATION:Online Streaming
DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We describe invariant counts of holomorphic curves in a Calabi-Yau 3-fold with boundary in a Lagrangian in the skein module of that Lagrangian. We show how to turn this into concrete counts for the toric brane in the resolved conifold. This leads to a notion of basic holomorphic disks for any knot conormal in the resolved conifold. These basic holomorphic disks seem to generate HOMFLY homology in the basic representation. We give a conjectural description of similar holomorphic object generating parts of higher symmetric representation HOMFLY homology and verify some predictions coming from this conjecture in examples.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211018T100000
DTEND:20211018T110000
DTSTAMP:20211017T150000Z
UID:73db0b40835bd300e574099b969d6f93@cgp.ibs.re.kr
SUMMARY:Noncommutative deformations of crepant resolutions via mirror symmetry
LOCATION:Online Streaming
DESCRIPTION:Speaker: Siu-Cheong Lau\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Noncommutative crepant resolutions of singularities formulated by Van den Bergh admit interesting quantization deformations. On the other hand, nc deformations can also be constructed via a local-to-global approach using the notion of an algebroid stack. In this talk, I will explain a mirror method of constructing explicit nc deformed crepant resolutions, and a Fourier-Mukai transform between these two notions. An important ingredient is a certain class of Lagrangian objects in the mirror side, whose (higher) morphisms can be found via a 3d enhancement of the corresponding objects in Riemann surfaces.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211025T100000
DTEND:20211025T110000
DTSTAMP:20211024T150000Z
UID:0d84a90ca5c68966639d8f3bf552f56a@cgp.ibs.re.kr
SUMMARY:Categorical non-properness in wrapped Floer theory
LOCATION:Online Streaming
DESCRIPTION:Speaker: Sheel Ganatra\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We will explain why a global variant of this observed phenomenon holds in broad generality: the wrapped Fukaya category of any positive-dimensional Weinstein (or non-degenerate Liouville) manifold is always either non-proper or zero, as is any quotient thereof. Moreover any non-compact connected exact Lagrangian is always either a "non-proper object" or zero in such a wrapped Fukaya category, as is any idempotent summand thereof. We will examine where the argument could break if one drops exactness, which is consistent with known computations of non-exact wrapped Fukaya categories which are smooth, proper, and non-vanishing (e.g., work of Ritter-Smith). We will also give a perspective on the proof in terms of "properness obstruction" invariants of certain categories, which can be related for wrapped Fukaya categories to closed and open-string versions of Rabinowitz Floer theory (the latter by joint work in progress with Y. Gao and S. Venkatesh).
END:VEVENT
BEGIN:VEVENT
DTSTART:20211101T100000
DTEND:20211101T110000
DTSTAMP:20211031T150000Z
UID:b84743877c4ae2e00fdabe317aa8c78c@cgp.ibs.re.kr
SUMMARY:The Simplicity Conjecture
LOCATION:Online Streaming
DESCRIPTION:Speaker: Daniel Cristofaro-Gardiner\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In the 60s and 70s, there was a flurry of activity concerning the question of whether or not various subgroups of homeomorphism groups of manifolds are simple, with beautiful contributions by Fathi, Kirby, Mather, Thurston, and many others. A funnily stubborn case that remained open was the case of area-preserving homeomorphisms of surfaces. For example, for balls of dimension at least 3, the relevant group was shown to be simple by work of Fathi from the 1970s, but the answer in the two-dimensional case was not known. I will explain recent joint work proving that the group of compactly supported area preserving homeomorphisms of the two-disc is in fact not a simple group, which answers the "Simplicity Conjecture” in the affirmative. Our proof uses a new tool for studying area-preserving surface homeomorphisms, called periodic Floer homology (PFH) spectral invariants; these recover the classical Calabi invariant in their asymptotic limit.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211108T100000
DTEND:20211108T110000
DTSTAMP:20211107T150000Z
UID:dd87023f4a5eb066123e355ec75bec6a@cgp.ibs.re.kr
SUMMARY:Complex cobordism and Hamiltonian fibrations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will discuss joint work with McLean and Smith, lifting the results of Seidel, Lalonde, and McDuff concerning the topology of Hamiltonian fibrations over the 2-sphere from rational cohomology to complex cobordism. In addition to the use of Morava K-theory (as in the recent work with Blumberg on the Arnold Conjecture), the essential new ingredient is the construction of global Kuranishi charts of genus 0 pseudo-holomorphic curves; i.e. their realisation as quotients of zero loci of equivariant vector bundles on manifolds
END:VEVENT
BEGIN:VEVENT
DTSTART:20211115T100000
DTEND:20211115T110000
DTSTAMP:20211114T150000Z
UID:c3f1a3f7e471f176a0de1a66009a5ce8@cgp.ibs.re.kr
SUMMARY:Interlevel persistence and Floer theory
LOCATION:Online Streaming
DESCRIPTION:Speaker: Michael Usher\n\nEvent: Symplectic Monday Seminar\n\nAbstract: There is a rich history in symplectic topology of using the filtration structures on Floer complexes to extract geometrically interesting information, in a way that formally mimics the relations between the homologies of sublevel sets of a Morse function on a finite-dimensional manifold. In the finite-dimensional case, it can be useful to consider homologies not just of sublevel sets but of interlevel sets (preimages of general intervals, including singletons); however, in the Floer-theoretic context it is not so obvious what the analogue of the homology of an interlevel set is. I will explain a general algebraic framework---applicable for instance to Hamiltonian Floer theory---for obtaining interlevel persistence-type barcodes from the sorts of complexes that arise in Floer theory; these barcodes carry somewhat more information than the more conventional sublevel persistence barcodes.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211122T100000
DTEND:20211122T110000
DTSTAMP:20211121T150000Z
UID:ad6377c9c0855ef7c34cae53c865df9d@cgp.ibs.re.kr
SUMMARY:Smooth closing lemmas for area-preserving surface diffeomorphisms
LOCATION:Online Streaming
DESCRIPTION:Speaker: Michael Hutchings\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We show that an area-preserving diffeomorphism of a closed surface satisfying a "rationality" property has the "C^\infty closing property". The latter property asserts that for any nonempty open set, one can make a C^\infty small Hamiltonian perturbation supported in the open set to obtain a periodic orbit intersecting the open set. Moreover we obtain quantitative results, asserting roughly speaking that during a given Hamiltonian isotopy, within time \delta a periodic orbit must appear of period at most O(\delta^{-1}). The proof uses spectral invariants in periodic Floer homology. This is a joint work with Oliver Edtmair.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211129T100000
DTEND:20211129T110000
DTSTAMP:20211128T150000Z
UID:438e81cd3d9db104e2eb5242bbc4ccce@cgp.ibs.re.kr
SUMMARY:Moduli of Calabi-Yau pairs and secondary fans
LOCATION:Online Streaming
DESCRIPTION:Speaker: Tony Yue Yu\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We conjecture that the moduli space of smooth polarized Calabi-Yau pairs is unirational. More precisely, we consider its natural compactification inside the KSBA stable pair moduli space, and conjecture that the compactification admits a finite cover by a complete toric variety. We construct the associated complete toric fan, generalizing the Gelfand-Kapranov-Zelevinski secondary fan for reflexive polytopes. Inspired by mirror symmetry, we speculate a synthetic construction of the universal family over this toric variety, as the Proj of a sheaf of graded algebras with a canonical basis, whose structure constants are given by counts of non-archimedean analytic disks. In the Fano case and under the assumption that the mirror variety contains a Zariski open torus, we construct the conjectural universal family, generalizing the families of Kapranov-Sturmfels-Zelevinski and Alexeev in the toric case. In the case of del Pezzo surfaces with an anti-canonical cycle of (-1)-curves, we prove the full conjecture. Joint work with Hacking and Keel.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211206T170000
DTEND:20211206T180000
DTSTAMP:20211205T150000Z
UID:d752254616fc2af328e471ca68f674a1@cgp.ibs.re.kr
SUMMARY:The topology of the Gelfand–Zeitlin fiber
LOCATION:Online Streaming
DESCRIPTION:Speaker: Jeffrey Carlson\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Gelfand–Zeitlin systems are a well-known family of examples in symplectic geometry, singular Lagrangian torus fibrations whose total spaces are coadjoint orbits of an action of a unitary or special orthogonal group and whose base spaces are certain convex polytopes. They are easily defined in terms of matrices and their truncations, but do not fit into the familiar framework of integrable systems with nondegenerate singularities, and hence are studied as a sort of edge case.
It is known that the fibers of these systems are determined as iterated pullbacks by the combinatorics of joint eigenvalues of systems of truncated matrices, but the resulting expressions can be rather inexplicit. We provide a new interpretation of Gelfand–Zeitlin fibers as balanced products of Lie groups (or biquotients), and pursue these viewpoints to a determination of their cohomology rings and low-dimensional homotopy groups which can be read transparently off of the combinatorics.
This all represents joint work with Jeremy Lane.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211213T100000
DTEND:20211213T110000
DTSTAMP:20211212T150000Z
UID:30f6cd4575d7909664a7960ca34690dc@cgp.ibs.re.kr
SUMMARY:Semi-toric degenerations of Richardson varieties from cluster algebras
LOCATION:Online Streaming
DESCRIPTION:Speaker: Naoki Fujita\n\nEvent: Symplectic Monday Seminar\n\nAbstract: A toric degeneration is a flat degeneration into an irreducible normal toric variety. In the case of a flag variety, its toric degeneration with desirable properties induces degenerations of Richardson varieties into unions of irreducible toric subvarieties, called semi-toric degenerations. Semi-toric degenerations are closely related to Schubert calculus. For instance, Kogan-Miller constructed semi-toric degenerations of Schubert varieties from Knutson-Miller's semi-toric degenerations of matrix Schubert varieties which give a geometric proof of the pipe dream formula of Schubert polynomials. In this talk, we construct a toric degeneration of a flag variety using its cluster structure, and see that it induces semi-toric degenerations of Richardson varieties, which can be regarded as generalizations of Kogan-Miller's semi-toric degeneration. This talk is partly based on a joint work with Hironori Oya.
END:VEVENT
BEGIN:VEVENT
DTSTART:20210906T133000
DTEND:20210906T153000
DTSTAMP:20210905T150000Z
UID:6484aea5d041251044820d96ce90954b@cgp.ibs.re.kr
SUMMARY:Fundamentals of Vassiliev Invariants
LOCATION:Online Streaming
DESCRIPTION:Speaker: Minkyoung Song\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20210913T133000
DTEND:20210913T153000
DTSTAMP:20210912T150000Z
UID:506468404cd3e2d8eb29905f81bef5cb@cgp.ibs.re.kr
SUMMARY:Chord diagrams I
LOCATION:Online Streaming
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20210927T133000
DTEND:20210927T153000
DTSTAMP:20210926T150000Z
UID:a16faf99f5b48d1887e07a99d8b38d84@cgp.ibs.re.kr
SUMMARY:Chord diagrams II
LOCATION:Online Streaming
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20211018T133000
DTEND:20211018T153000
DTSTAMP:20211017T150000Z
UID:10ca4dfcb0859c688ee11f3b4b0382b2@cgp.ibs.re.kr
SUMMARY:Jacobi diagrams I
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yifan Li\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20211025T133000
DTEND:20211025T153000
DTSTAMP:20211024T150000Z
UID:77430adc458ff65a85a5581cbbe044e5@cgp.ibs.re.kr
SUMMARY:Jacobi diagrams II
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20211101T133000
DTEND:20211101T153000
DTSTAMP:20211031T150000Z
UID:891a8a9ba23c67d8b1f4b4f8c6227430@cgp.ibs.re.kr
SUMMARY:Lie algebra weight systems I
LOCATION:Online Streaming
DESCRIPTION:Speaker: Myeong-Sang Cho\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20211108T133000
DTEND:20211108T153000
DTSTAMP:20211107T150000Z
UID:e2b5d3838d4d4c5cf573df31a4ac1418@cgp.ibs.re.kr
SUMMARY:Lie algebra weight systems II
LOCATION:Online Streaming
DESCRIPTION:Speaker: Myeong-Sang Cho\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
Math Bldg 404 & Online streaming
Zoom Link: https://zoom.us/j/4564461054?pwd=cHArY3dIUlNQT3RSZjR3STk5RVZNUT09
Zoom ID: 456 446 1054, Password: POSTECH
END:VEVENT
BEGIN:VEVENT
DTSTART:20211109T160000
DTEND:20211109T170000
DTSTAMP:20211108T150000Z
UID:82309e9986a2089e55606819baa24dd6@cgp.ibs.re.kr
SUMMARY:Greatest Ricci lower bounds of smooth Fano horospherical varieties and equivariant group compactifications
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kyeong-Dong Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract:
The greatest Ricci lower bound of a Fano manifold X is defined as the supremum of real numbers t such that Ric(w) - t w is positive for some Kahler form w in the first Chern class of X. This invariant was first studied by Tian, and was explicitely defined by Rubinstein, where it was called Tian's beta-invariant. Szekelyhidi later showed that it is the same as the maximum existence time in Aubin and Yau's continuity method. Recently, Cheltsov-Rubinstein-Zhang and Berman-Boucksom-Jonsson show that this analytic invariant coincides with the basis log canonical threshold introduced by Fujita-Odaka if X is K-unstable.
In this talk, I will explain how to compute the greatest Ricci lower bounds of smooth Fano horospherical varieties of Picard number one and equivariant group compactifications with rank two, via the barycenter of each algebraic moment polytope with respect to the Duistermaat-Heckman measure from a recent work of Delcroix and Hultgren. This talk is based on joint works with DongSeon Hwang, Shin-Young Kim; Jae-Hyouk Lee and Sungmin Yoo.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211119T170000
DTEND:20211119T180000
DTSTAMP:20211118T150000Z
UID:809a19c2572125cdeb5351675d468e99@cgp.ibs.re.kr
SUMMARY:Cohomological field theories and BKP integrability: Omega classes times Witten-classes
LOCATION:Online Streaming
DESCRIPTION:Speaker: Danilo Lewański\n\nEvent: Mathematical Physics Seminar\n\nAbstract: There is a deep interaction between Cohomological field theories (CohFTs), introduced by Kontsevich and Manin, and integrable hierarchies. For instance, the celebrated Witten-Kontsevich result shows that the trivial CohFT gives rise to a solution of the KdV integrable hierarchy. As another example, Kazarian’s theorem shows that the Hodge CohFT gives rise to a solution of the KP hierarchy, and so do Hurwitz numbers, which by ELSV formula are descendant integrals of the Hodge CohFT. The change of variable which carries the partition function of Hurwitz numbers into the partition function of pure descendant Hodge integrals is triangular and KP-preserving, it is in fact essentially given by the Topological Recursion spectral curve in the sense of Eynard and Orantin.
We study spin-Hurwitz numbers (not to be confused with completed cycles Hurwitz numbers) enumerating branches Riemann covers weighted by the parity of theta characteristics. They obey the BKP integrable hierarchy. We prove that the Topological Recursion conjecture for these numbers is equivalent to their underlying CohFT to be an explicit product between Witten’s class and Omega-classes computed by Chiodo. The Topological Recursion conjecture has recently been proved by Alexandrov and Shadrin in a more general framework for BKP integrability.
END:VEVENT BEGIN:VEVENT DTSTART:20211008T170000 DTEND:20211008T180000 DTSTAMP:20211007T150000Z UID:bad0375387562bacbf8a535da7944c69@cgp.ibs.re.kr SUMMARY:Topological recursion for generalized Hurwitz numbers LOCATION:Online Streaming DESCRIPTION:Speaker: Maxim Kazarian\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The topological recursion or Chekhov-Eunard-Orantin recursion is an inductive procedure for an explicit computation of correlator functions appearing in a large number of problems in mathematical physics, from matrix integrals and Gromov-Witten invariants to enumerations of maps and meromorphic functions with prescribed singularities. In spite of existence of a huge number of known cases where this procedure does work, its validity and universality still remains mysterious in much extend.
We develop a new tool based on the theory of KP hierarchy that allows one not only formally prove it in a unified way for a wide class of problems but also to understand its true nature and the origin. These problems include enumeration various kinds of Hurwitz numbers: ordinary ones, orbifold, double, monotone, r-spin Hurwitz numbers, as well as enumeration of (hyper) maps and extends much beyond. The talk is based on a joint work with B. Bychkov, P. Dunin-Barkowski, S. Shadrin.END:VEVENT BEGIN:VEVENT DTSTART:20211112T170000 DTEND:20211112T180000 DTSTAMP:20211111T150000Z UID:12ad4a3e4248be75869eec9929f66183@cgp.ibs.re.kr SUMMARY:Correlation functions for unitary invariant ensembles and Hurwitz numbers LOCATION:Online Streaming DESCRIPTION:Speaker: Tamara Grava\n\nEvent: Mathematical Physics Seminar\n\nAbstract: We provide effective formulae for generating functions of multipoint correlators for unitary invariants ensembles.As an application we show that the multipoint correlators of the Laguerre and the Jacobi ensembles are obtained in terms of Hahn polynomials and Wilson polynomials generalising earlier formula for one-point correlators. Finally we provide an enumerative interpretation of the topological expansion of these multipoint correlators. This is a joint work with M. Gisonni and G. Ruzza.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211029T170000
DTEND:20211029T180000
DTSTAMP:20211028T150000Z
UID:56a5ddbc496da1e3fb269848a853bde8@cgp.ibs.re.kr
SUMMARY:Quantum T-Q and KZ equations in gauge theory
LOCATION:Online Streaming
DESCRIPTION:Speaker: Nikita Nekrasov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Baxter's T-Q equation is a main instrument in the functional and algebraic Bethe ansatz approach to quantum spin chains. Knizhnik-Zamolodchikov equation is obeyed by the conformal blocks of the two dimensional current algebra. Remarkably, the analytic continuation of the latter, and a deformation of the former can be found in the realm of the four dimensional supersymmetric gauge theories with matter.
Based on the recent work with Saebyeok Jeong and Norton Lee.
END:VEVENT BEGIN:VEVENT DTSTART:20211130T170000 DTEND:20211130T180000 DTSTAMP:20211129T150000Z UID:ac9726988db581e12c05a924ec0377e2@cgp.ibs.re.kr SUMMARY:Automorphisms of algebraic surfaces LOCATION:Online Streaming DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I will discuss boundedness properties for finite subgroups in the groups of (birational) automorphisms of algebraic surfaces. The main focus will be on the Jordan property of such groups and its analogs suitable for fields of positive characteristic.
END:VEVENT BEGIN:VEVENT DTSTART:20211126T170000 DTEND:20211126T180000 DTSTAMP:20211125T150000Z UID:815aafdfd8ce6bd521973db8e09483c2@cgp.ibs.re.kr SUMMARY:CFT from Topological Recursion LOCATION:Online Streaming DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Conformal Field Theories, can be "defined" by the bootstrap axioms. The main axioms are that we have a set of functions (amplitudes) that should satisfy OPE (short distance asymptotic behaviour), Ward identities (reflecting conformal invariance) and crossing-symmetry (all possible ways of computing an amplitude should give the same answer).Topological Recursion is a recursive recipe that associates to a spectral curve S (an algebraic plane curve with some additional features), a sequence of n-forms, denoted $\omega_{g,n}(S)$, $g=0,\dots,\infty$, $n=0,\dots,\infty$. These n-forms naturally allow to define amplitudes (as formal series) that do satisfy OPE and Ward Identities axioms. Moreover, there is a way to adapt them to also satisfy crossing symmetry. This last statement is presently a conjecture, not yet proved in all cases, but belived to be true.We shall also discuss the link to integrable systems and algebraic geometry.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211203T102000
DTEND:20211203T110000
DTSTAMP:20211202T150000Z
UID:b73f62fd47dcc27afdf03fbea6718797@cgp.ibs.re.kr
SUMMARY:Hochschild homology for matrix factorization categories of Deligne-Mumford Stacks
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Sai Somanjana Sreedhar Bhamidi\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In this talk we will prove a Hirzebruch-Riemann-Roch (HRR) type theorem for matrix factorization categories of Deligne-Mumford stacks. We firstly discuss a construction of a Hochschild-Kostant-Rosenberg type isomorphism and show how it can be used to define a Chern character formula which allows us to prove the HRR type theorem. This talk is based on a joint work with Dongwook Choa and Bumsig Kim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211202T144000
DTEND:20211202T152000
DTSTAMP:20211201T150000Z
UID:20112e8a5d2cf2a76bf70f86ac182fc8@cgp.ibs.re.kr
SUMMARY:CG coefficients, Vertex Model & Knots/Links
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Saswati Dhara\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In physics, the Clebsch–Gordan (CG) coefficients are used to expand the coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.They are also used in representation theory to represent the basis in the case of decomposition of the tensor product of two irreducible representation. So, these coefficients can be used for the calculation of knot/lin invariants. There are various methods to obtain knot/link invariants. In this talk, I will discuss a method to calculate knot/link invariants using CG coefficients through a solvable model known as vertex model.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211204T092000
DTEND:20211204T100000
DTSTAMP:20211203T150000Z
UID:3fcdd5939f19eac938fe36157e32842a@cgp.ibs.re.kr
SUMMARY:Cluster Algebras, Crystals and Combinatorics
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Volker Genz\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: We introduce certain operators on tropical points of cluster algebras generalizing the crystal operators due to Kashiwara/Lusztig. On the one hand, crystal operators provide a tool for calculations in the category of finite dimensional representations of semi-simple Lie algebras. On the other hand, cluster algebras are a certain class of algebras with favourable combinatorial properties. Furthermore, due to the work of Kontsevich-Soibelman and Gross-Hacking-Keel-Kontsevich cluster algebras are linked to the concept of mirror symmetry appearing in physics. Motivated by this we are interested in understanding the role of our operators in these worlds.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211202T092000
DTEND:20211202T100000
DTSTAMP:20211201T150000Z
UID:3412a7ff9f7fd92222374bc573d19ff1@cgp.ibs.re.kr
SUMMARY:Involutive techniques in Heegaard Floer theory
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Sungkyung Kang\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: Heegaard Floer theory can often be endowed with involutions, induced either by intrinsic or topologicaly symmetry. Exploiting such symmetries gives us new topological invariants, which were used to solve several problems in knot theory and 3-dimensional topology. In this talk, we will review some recent results regarding involutive techniques in Heegaard Floer homology and discuss related open problems.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211203T092000
DTEND:20211203T100000
DTSTAMP:20211202T150000Z
UID:d4fab0c02f7cd5a18e2b94dbfa8c2765@cgp.ibs.re.kr
SUMMARY:Homotopy colimits of semifree DG categories.
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In the category of DG categories, it is hard to take homotopy colimits. In this talk, I will introduce a joint work with Dogancan Karabas, which reduces the difficulty of taking homotopy colimits. Also, I will introduce an application of the work in symplectic topology.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211203T102000
DTEND:20211203T110000
DTSTAMP:20211202T150000Z
UID:059afd51063b28aa426d3f89f9ff9ada@cgp.ibs.re.kr
SUMMARY:An overview of my research works: Categorical Algebra and Absolute Algebraic Geometry
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Samarpita Ray\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In this talk, I will give an overview of my research interests / works which lie in the area of Category Theory and Algebraic Geometry. For half of my talk, I will discuss some of my works that build connections between enriched category theory and Hopf algebra theory (or broadly, coalgebra theory). Such works are motivated by the idea of obtaining an algebraic geometry like categorical framework which studies both modules and comodules. For the other half of my talk, I will discuss my works related to the field of Absolute Algebraic Geometry. If time permits, I will also touch upon my ongoing work related to tensor triangular geometry, in which I have developed interest since last year.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211202T134000
DTEND:20211202T142000
DTSTAMP:20211201T150000Z
UID:b1cd48b16fac8cf529c3f4f6cbcafc40@cgp.ibs.re.kr
SUMMARY:Black hole horizons
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Abbas Mohamed Sherif\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In this talk I briefly introduce the history behind the mathematical theory of black holes. An overview of their horizons is then given. A covariant (and hence gauge invariant) approach recently applied to the study of black hole horizons is introduced, and various works by me and my coauthors on the evolution, geometry and existence of horizons are presented. Finally, our recent works on conformal geometry and admittance of Ricci soliton structure on hypersurfaces in spacetimes - using this covariant approach - are discussed.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211204T102000
DTEND:20211204T110000
DTSTAMP:20211203T150000Z
UID:2ce5294a9168b91d9dad87b226580e00@cgp.ibs.re.kr
SUMMARY:The Jacobian of modular forms.
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Haowu Wang\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: In this talk I introduce the modular Jacobian approach which gives a necessary and sufficient condition for an algebra of modular forms on a Hermitian symmetric domain being free. Many interesting examples will be presented.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211202T102000
DTEND:20211202T110000
DTSTAMP:20211201T150000Z
UID:78ffddd0af74fb425d50b6d0d4d5a031@cgp.ibs.re.kr
SUMMARY:Double lower central series and a double Johnson filtration for the Goeritz group of the sphere
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: For a triple (K,X,Y) consisting of a group K and two normal subgroups X and Y of K, we introduce a double-indexed family of normal subgroups of K which we call the double lower central series. In particular, if K=XY we show that this family allows us to recover the lower central series of K. If G is a group acting on K preserving X and Y, we show that the double lower central series induces a double-indexed filtration of G. We apply this theory to the group of isotopy classes of self-homeomorphisms of the 3-sphere S^3 which preserves the standard decomposition of S^3 as the gluing of two handlebodies. (Joint work with Kazuo Habiro.)
END:VEVENT
BEGIN:VEVENT
DTSTART:20211202T112000
DTEND:20211202T120000
DTSTAMP:20211201T150000Z
UID:1be80db53e58b68e1e2e814c807dea1f@cgp.ibs.re.kr
SUMMARY:Liouville theorem for surfaces translating by sub-affine-critical powers of Gauss curvature
LOCATION:Avani Central Busan
DESCRIPTION:Speaker: Beomjun Choi\n\nEvent: 2021 Pohang Mathematics Workshop\n\nAbstract: We classify the translators to the flows by sub-affine-critical powers of Gauss curvature in $\mathbb{R}^3$. If $\alpha$ denotes the power, this is a Liouville theorem for degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^{2-\frac{1}{2\alpha}}$ for $0<\alpha<1/4$. For the affine-critical-case $\det D^2u =1$, the classical result by Jorgens, Calabi and Pogorelov shows the level curves of given solution are homothetic ellipses. In our case, the level curves converge asymptotically to a round circle or a curve with $k$-fold symmetry for some $k>2$. More precisely, these curves are closed shrinking curves to the $\frac {\alpha}{1-\alpha}$-curve shortening flow that were previously classified by B. Andrews in 2003. This is a joint work with K. Choi and S. Kim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20211213T133000
DTEND:20211213T153000
DTSTAMP:20211212T150000Z
UID:1ddba56ae9f9598b0996d272b2acb03a@cgp.ibs.re.kr
SUMMARY:Construction of the Kontsevich Integral
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yifan Li\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
https://zoom.us/j/97265865548?pwd=UmVGc2U4VFhPd3RsYWh2UVB2ekZWQT09
Zoom ID: 972 6586 5548, Password: postech
END:VEVENT
BEGIN:VEVENT
DTSTART:20211220T133000
DTEND:20211220T153000
DTSTAMP:20211219T150000Z
UID:e85f2f6d561173d36375a792dad58270@cgp.ibs.re.kr
SUMMARY:Universality properties of the Kontsevich invariant
LOCATION:Online Streaming
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This will be an informal and convivial space whose main goal is to learn about low-dimensional topology and quantum topology. People who are completely new to this subject are very welcome. The goal is basically to study the books. 1) “An introduction to Quantum and Vassiliev Knot invariants” 2) “Quantum Invariants” by Tomotada Ohstuki
https://zoom.us/j/97265865548?pwd=UmVGc2U4VFhPd3RsYWh2UVB2ekZWQT09
Zoom ID: 972 6586 5548, Password: postech
END:VEVENT
BEGIN:VEVENT
DTSTART:20211221T100000
DTEND:20211221T120000
DTSTAMP:20211220T150000Z
UID:e95e34ab34ea9355f4a978c359b64985@cgp.ibs.re.kr
SUMMARY:The KZ equations and the Drinfel’d associator I
LOCATION:Online Streaming
DESCRIPTION:Speaker: Xinxing Tang\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: First, I will introduce the monodromy representations of the braid group alongthe solutions of KZ equations. In particular I will analyze the monodromies of KZ equationon the Confn(C) when n = 3, 4. I will explain that the corresponding ΦKZ serves asan associator for the quasi-bialgebra. Combined with the corresponding R matrix RKZ,(Ug[[~]],Δ,ΦKZ,RKZ) forms a quasi-triangular quasi-bialgebra. Finally, I will talk aboutthe equivalence between two representations of the braid group, one is the above monodromyrepresentation and the other is the representation provided by the universal Rmatrix of the quantum group.
https://us06web.zoom.us/j/83077134179?pwd=RlJPY2NzVFlVcHh5Z1hvd1cwLzdRQT09
Zoom ID: 830 7713 4179, Password: postech
END:VEVENT
BEGIN:VEVENT
DTSTART:20211222T100000
DTEND:20211222T120000
DTSTAMP:20211221T150000Z
UID:0dffe1e787790ee4c162d8512115b0ed@cgp.ibs.re.kr
SUMMARY:The KZ equations and the Drinfel’d associator II
LOCATION:Online Streaming
DESCRIPTION:Speaker: Xinxing Tang\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: First, I will introduce the monodromy representations of the braid group alongthe solutions of KZ equations. In particular I will analyze the monodromies of KZ equationon the Confn(C) when n = 3, 4. I will explain that the corresponding ΦKZ serves asan associator for the quasi-bialgebra. Combined with the corresponding R matrix RKZ,(Ug[[~]],Δ,ΦKZ,RKZ) forms a quasi-triangular quasi-bialgebra. Finally, I will talk aboutthe equivalence between two representations of the braid group, one is the above monodromyrepresentation and the other is the representation provided by the universal Rmatrix of the quantum group.
https://us06web.zoom.us/j/83077134179?pwd=RlJPY2NzVFlVcHh5Z1hvd1cwLzdRQT09
Zoom ID: 830 7713 4179, Password: postech
END:VEVENT
BEGIN:VEVENT
DTSTART:20220113T160000
DTEND:20220113T170000
DTSTAMP:20220112T150000Z
UID:e41c7a6cd83fade7f1155296aeaece5b@cgp.ibs.re.kr
SUMMARY:Seiberg-Witten Floer K-theory for knots
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hokuto Konno\n\nEvent: CGP Seminar\n\nAbstract: This talk is based on joint work with Jin Miyazawa and Masaki Taniguchi (arXiv:2110.09258) where we established a version of Seiberg-Witten Floer K-theory for knots. This framework is used to prove a version of “10/8-inequality for knots”, which effectively extracts difference between topological and smooth categories in knot theory. I will explain concrete applications, such as relative genus bounds and stabilization numbers, as well as how we construct this framework.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220217T170000
DTEND:20220217T180000
DTSTAMP:20220216T150000Z
UID:a721c317acc7c2d5bd1fa6bd522425ef@cgp.ibs.re.kr
SUMMARY:Symmetries and Knot Floer homology
LOCATION:Online Streaming
DESCRIPTION:Speaker: Abhishek Mallick\n\nEvent: CGP Seminar\n\nAbstract: Given an equivariant knot, we study the induced action of the symmetry on the knot Floer chain complex. We relate this action with the induced action of the symmetry on the Heegaard Floer homology of large surgeries on K. This identification can be regarded as the equivariant surgery formula in Heegaard Floer homology. We then define two invariants of the equivariant knot concordance group which can be thought of as the correction terms stemming from the surgery formula and use them to give the first known examples of strongly invertible slices knots with arbitrary large equivariant genus. Using the invariants we also show that knot Floer homology can be used to detect exotic pairs of slice disks (parts of this talk is joint work with Irving Dai and Matthew Stoffregen).
END:VEVENT
BEGIN:VEVENT
DTSTART:20220228T100000
DTEND:20220228T110000
DTSTAMP:20220227T150000Z
UID:ddb3ba03cccc1d9338596eb6a7c83d2b@cgp.ibs.re.kr
SUMMARY:Complex cobordism and Hamiltonian fibrations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will discuss joint work with McLean and Smith, lifting the results of Seidel, Lalonde, and McDuff concerning the topology of Hamiltonian fibrations over the 2-sphere from rational cohomology to complex cobordism. In addition to the use of Morava K-theory (as in the recent work with Blumberg on the Arnold Conjecture), the essential new ingredient is the construction of global Kuranishi charts of genus 0 pseudo-holomorphic curves; i.e. their realisation as quotients of zero loci of equivariant vector bundles on manifolds
END:VEVENT
BEGIN:VEVENT
DTSTART:20220307T100000
DTEND:20220307T110000
DTSTAMP:20220306T150000Z
UID:2d264527bbefafe12864fc20b4c7b824@cgp.ibs.re.kr
SUMMARY:Gluing theories of contact instantons and of pseudoholomorphic curves in symplectic buildings
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Symplectic Monday Seminar\n\nAbstract: We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the study of (virtually) smooth moduli space of(bordered) contact instantons needed for the construction of contact instanton Floer cohomology and more generally for the construction of Fukaya-type category of Legendrian submanifolds in contact manifold $(Q,\xi)$. As an application, we also apply this gluing theory to that of moduli spaces of holomorphic buildings arising in Symplectic Field Theory (SFT), by canonically lifting the former to that of the latter.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220502T100000
DTEND:20220502T110000
DTSTAMP:20220501T150000Z
UID:fdfcbed02146ae6a7ae29588439489d0@cgp.ibs.re.kr
SUMMARY:Topological entropy, barcodes and Floer theory
LOCATION:Online Streaming
DESCRIPTION:Speaker: Viktor Ginzburg\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Topological entropy is one of the fundamental invariants of a dynamical system, measuring its complexity. In this talk, we discuss a connection between the topological entropy of compactly supported Hamiltonian diffeomorphisms and Floer theory. We introduce a new invariant associated with the Floer complexes of the iterates of such a diffeomorphism, which we call barcode entropy. We show that barcode entropy is closely related to topological entropy and that these invariants are equal in dimension two. The talk is based on joint work with Erman Cineli and Basak Gurel.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220328T170000
DTEND:20220328T180000
DTSTAMP:20220327T150000Z
UID:0b694067fcc2ed662644aa1c2b2c195e@cgp.ibs.re.kr
SUMMARY:Hofer's geometry and entropy
LOCATION:Online Streaming
DESCRIPTION:Speaker: Matthias Meiwes\n\nEvent: Symplectic Monday Seminar\n\nAbstract: A central object in the study of Hamiltonian diffeomorphisms on a symplectic manifold is Hofer's metric, a bi-invariant metric on the group of Hamiltonian diffeomorphisms. In my talk, I will address a question of Polterovich on the stability of topological entropy for Hamiltonian diffeomorphisms with respect to Hofer's metric. I will focus on some results in dimension two. First I discuss examples for which positive entropy persists under large perturbations. Then I present a braid stability result in the context of Hofer's geometry, and explain what it implies for the question of entropy stability. This is based on joint works with Arnon Chor, and Marcelo R.R. Alves.
END:VEVENT
BEGIN:VEVENT
DTSTART:19700101T090000
DTEND:19700101T090000
DTSTAMP:19700101T000000Z
UID:82dfd6c7e9f2921bf26cc8af856214a0@cgp.ibs.re.kr
SUMMARY:The B-model for singular spectral curves and its enumerative interpretation
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Mathematical Physics Seminar\n\nAbstract: I will discuss the definition of B-model/topological recursion for spectral curves and explain the obstructions to the well-posedness of this definition for arbitrary spectral curves. The question can be approached by the representation theory of W-algebras, and I will describe the largest known class of admissible spectral curves (including singular cases) that has been obtained in this way. Each case is expected to have an enumerative interpretation in a sense that I will specify. In particular l will describe possible applications in open r-spin intersection theory.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220318T170000
DTEND:20220318T180000
DTSTAMP:20220317T150000Z
UID:2a8fddb1c46392152d931cb43569a8bb@cgp.ibs.re.kr
SUMMARY:b-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and O(N)-BGW integral
LOCATION:Online Streaming
DESCRIPTION:Speaker: Guillaume Chapuy\n\nEvent: Mathematical Physics Seminar\n\nAbstract:
My talk will be an introduction to (part of) my recent paper arXiv:2109.01499 written jointly with Valentin Bonzom and Maciej Dołęga. We study a b-deformation of monotone Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. It is a special case of the b-deformed weighted Hurwitz numbers recently introduced by Dołęga and myself and is related branched coverings of the sphere by non-oriented surfaces.
We give an evolution (cut-and-join) equation for the model and we derive, by a method of independent interest, explicit Virasoro constraints from it, for arbitrary values of the deformation parameter b. For b=1 the model is related to the (large) BKP hierarchy and an O(N) version of the BGW integral. The talk will not assume previous knowledge, I will try in particular to explain where the interest of combinatorialists for these deformations come from, and in particular the Goulden-Jackson b-conjecture.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220308T160000
DTEND:20220308T170000
DTSTAMP:20220307T150000Z
UID:14a5ce2bc5d0304a272a07530453876f@cgp.ibs.re.kr
SUMMARY:On K-stability of Fano weighted hypersurfaces
LOCATION:Online Streaming
DESCRIPTION:Speaker: Taro Sano\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Weighted complete intersections are a rich source of examples of varieties. K-stability (or existence of Kähler-Einstein metrics) of explicit Fano varieties has been studied for a long time. In this talk, I will explain our results on the K-stability of some Fano weighted hypersurfaces and the application.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220322T170000
DTEND:20220322T180000
DTSTAMP:20220321T150000Z
UID:3a4002f49ac428b2ca11c1f4aa6ab455@cgp.ibs.re.kr
SUMMARY:On K-stability of Fano varieties
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hamid Abban\n\nEvent: Algebraic Geometry Seminar\n\nAbstract:
K-stability is an algebraic notion that detects the existence of Kahler-Einstein metrics on Fano varieties. I will give an overview of the theory of K-stability from a birational geometer’s perspective. Then I go through the existing methods of verifying K-stability for a given Fano variety before introducing the new method (joint work with Ziquan Zhuang) which is based on linear algebra and induction. Several results will be illustrated.
1. the equivalence between certain open Gromov-Witten invariants and the log Gromov-Witten invariants with maximal tangency in algebraic geometry for $\mathbb{P}^2$.
2. Equivalence of counting special Lagrangians in mirror and counting semi-stable sheaves on $\mathbb{P}^2$ . Part of the talk will be based on the joint work with S.-C. Lau, T.-J. Lee. END:VEVENT BEGIN:VEVENT DTSTART:20220425T100000 DTEND:20220425T110000 DTSTAMP:20220424T150000Z UID:6f714c69e870a2386c9df7538dc4b978@cgp.ibs.re.kr SUMMARY:Equivariant Lagrangian Floer cohomology over integers via semi-global Kuranishi structures LOCATION:Online Streaming DESCRIPTION:Speaker: Erkao Bao\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will explain the definition of the equivariant Lagrangian Floer cohomology over integers of a pair of Lagrangian submanifolds that are fixed under a finite symplectic group action and satisfy certain simplifying assumptions that excludes bubbles. I will explain the usage of the semi-global Kuranishi structures for the equivariant transversality issue. This is based on a joint work with Ko Honda. END:VEVENT BEGIN:VEVENT DTSTART:20220429T150000 DTEND:20220429T160000 DTSTAMP:20220428T150000Z UID:db9847d59960b026176f7856df2d6eb4@cgp.ibs.re.kr SUMMARY:Quantum trace map for 3-manifolds and a 'length conjecture' LOCATION:CGP Main Hall DESCRIPTION:Speaker: Dongmin Gang\n\nEvent: Mathematical Physics Seminar\n\nAbstract: After giving a review on the Kauffman Bracket Skein Module (KBSM) of 3-manifolds, I will introduce a quantum trace map for a hyperbolic knot complement S3\K. The map assigns a quantum operator to each element in KBSM of the knot complement. Then, I will explain how the map determines the full expansion of the colored Jones polynomial of a link composed of the K and another knot K' in a certain asymptotic limit. END:VEVENT BEGIN:VEVENT DTSTART:20220325T170000 DTEND:20220325T180000 DTSTAMP:20220324T150000Z UID:6e2ccb1927b5d459b6b4dbad08463263@cgp.ibs.re.kr SUMMARY:Mirror symmetry for a cusp polynomial Landau-Ginzburg orbifold LOCATION:Online Streaming DESCRIPTION:Speaker: Alexey Basalaev\n\nEvent: Mathematical Physics Seminar\n\nAbstract:
We will establish mirror symmetry between the cusp polynomials considered with a nontrivial symmetry group and Geigle-Lenzing orbifold projective lines. In particular, we will introduce Dubrovin-Frobenius manifold of equivariant Saito theory of any cusp polynomial and show that it is isomorphic to Dubrovin-Frobenius manifold of the respective Geigle-Lenzing orbifold.We will also show that in the case of simple-elliptic singularities this mirror isomorphism is equivalent the certain relations in the ring of modular forms.This is a joint work with A.Takahashi (Osaka). END:VEVENT BEGIN:VEVENT DTSTART:20220405T100000 DTEND:20220405T110000 DTSTAMP:20220404T150000Z UID:f78c7c6df578a8fe1b34e879bc5aac6e@cgp.ibs.re.kr SUMMARY:Geometry of algebraic surfaces via their Cox rings LOCATION:Online Streaming DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Cox ring is an important tool in modern algebraic geometry and several other branches of mathematics. In the first part of this talk, I will briefly review basic theory of Cox ring and explain how it connects birational geometry and geometric invariant theory. Then I will discuss how we can use Cox rings to study geometry of certain algebraic surfaces. The second part of this talk is based on several joint works (some in progress) with JongHae Keum and Davide Frapporti. END:VEVENT BEGIN:VEVENT DTSTART:20220516T170000 DTEND:20220516T180000 DTSTAMP:20220515T150000Z UID:b588ed70980533590b88978595c6282c@cgp.ibs.re.kr SUMMARY:Floer homology and right-veering monodromy LOCATION:Online Streaming DESCRIPTION:Speaker: Steven Sivek\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Right-veering maps are a widely studied class of diffeomorphisms of surfaces with boundary. They were introduced by Honda, Kazez, and Matić, who proved that a contact structure on a closed 3-manifold is tight if and only if every supporting open book has right-veering monodromy. In this talk I will explain how Heegaard Floer homology can detect whether or not a given surface diffeomorphism is right-veering, by making use of its relationship to the symplectic Floer homology of that diffeomorphism. This is joint work with John Baldwin and Yi Ni. END:VEVENT BEGIN:VEVENT DTSTART:20220401T170000 DTEND:20220401T180000 DTSTAMP:20220331T150000Z UID:d348a17a386adeeaf5daffb54378ccd0@cgp.ibs.re.kr SUMMARY:Moduli spaces of residueless meromorphic differentials and the KP hierarchy LOCATION:Online Streaming DESCRIPTION:Speaker: Paolo Rossi\n\nEvent: Mathematical Physics Seminar\n\nAbstract: I'll present a recent joint work with A. Buryak and D. Zvonkine, where we study the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of prescribed orders of a meromorphic differential with vanishing residues. Our main result is that intersection theory on these spaces is controlled by an integrable system containing the celebrated Kadomtsev-Petviashvili (KP) hierarchy as a reduction to the case of differentials with exactly two zeros and any number of poles. This fact has several deep consequences and in particular it relates the aforementioned moduli spaces with Hurwitz theory, representation theory of sl2(C), integrability and a conjecture of Schmitt and Zvonkine on the r=0 limit of Witten's r-spin classes.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220304T090000
DTEND:20220304T100000
DTSTAMP:20220303T150000Z
UID:8015bd98db969a1517ee7ba4dd277c54@cgp.ibs.re.kr
SUMMARY:Introduction to Topological Quantum Field Theories
LOCATION:Online Streaming
DESCRIPTION:Speaker: Vladimir Turaev\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: The lecture will be an introduction to quantum topology for beginners (including undergraduates). I will start by a brief description of the Alexander and Jones polynomials of knots and links in the 3-dimensional sphere. Then I will introduce the concept of an n-dimensional topological quantum field theory (TQFT) and discuss algebraic sources of such theories for n=2 and n=3. Preliminary knowledge of the following notions is required: a manifold of a given dimension n=1,2,3, ... a manifold with boundary, a homeomorphism of manifolds, an algebra, a module over an algebra, a group, a category, a knot in the 3-dimensional sphere, a link in the 3-dimensional sphere, a braid on n strings.
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220307T150000
DTEND:20220307T170000
DTSTAMP:20220306T150000Z
UID:453a28a10ea8e18c833f66c625ab9ddc@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Anderson Vera\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220314T150000
DTEND:20220314T170000
DTSTAMP:20220313T150000Z
UID:2d34b71b2d4d4a7444fd46823096fc3b@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yifan Li\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220321T150000
DTEND:20220321T170000
DTSTAMP:20220320T150000Z
UID:7f76b4a2e5625a6980a6829c153d9315@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Minkyoung Song\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220328T150000
DTEND:20220328T170000
DTSTAMP:20220327T150000Z
UID:bd8da0d6e51d2767514744c2cb97277e@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220404T150000
DTEND:20220404T170000
DTSTAMP:20220403T150000Z
UID:06b2442b9b40660c2ee733772baae16b@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220411T150000
DTEND:20220411T170000
DTSTAMP:20220410T150000Z
UID:2fbbebc8265f705a3d2fd3aedbdaf6e1@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Myeong-Sang Cho\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220418T150000
DTEND:20220418T170000
DTSTAMP:20220417T150000Z
UID:1496ee3c906dcc51898a6274f60122fa@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Eric Rubiel Dolores Cuenca\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220425T150000
DTEND:20220425T170000
DTSTAMP:20220424T150000Z
UID:7eb261b226a3fd3f79cfe6c671af95e7@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220502T150000
DTEND:20220502T170000
DTSTAMP:20220501T150000Z
UID:e0e5bf13aca72efd02644e9c95f313c2@cgp.ibs.re.kr
SUMMARY:The geometry of q-6j-symbols
LOCATION:Online Streaming
DESCRIPTION:Speaker: Nicolai Reshetikhin\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: $6j$-symbols, also known as Racah-Wigner coefficients first appeared in representation theory of $SU(2)$, or, as it is called in physics, the theory of quantum angular momentum. They are given by special values of hypergeometric functions ${}_4F_3$ and have a geometric limit which relates them with the geometry of coadjoint orbits in the dual space to the Lie algebra $su(2)$.Their $q$-analogs appear in the representation theory of quantum universal enveloping algebra of $sl(2)$. They are given by special values of $q$-hypergeometric functions ${}_4\phi_3$ and are instrumental in topological quantum field theory and corresponding conformal field theories. They also have a geometric limit and are related to the geometry of $SU(2)$ conjugation orbits.In this talk I will start with the definition of $q$-$6j$ symbols, and explain how to express colored Jones polynomials in terms of these objects. Then I will focus on the relation of $q$-$6j$ symbols with the Clebsch-Gordan integrable system for $su(2)$ and will compute their semiclassical asymptotic. At the end I will review the results of Q. Chen, J. Murakami, T. Yang and others on the relation between this semiclassical asymptotic and the volume conjecture.
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 15 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220509T150000
DTEND:20220509T170000
DTSTAMP:20220508T150000Z
UID:342f032cebba9c3d6d03d96f53d2d476@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220516T150000
DTEND:20220516T170000
DTSTAMP:20220515T150000Z
UID:d35bc24eea9e5ffcc893919311575055@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220523T150000
DTEND:20220523T170000
DTSTAMP:20220522T150000Z
UID:421717bb6120e733b6ff8c984b61ed0e@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: \n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220613T150000
DTEND:20220613T170000
DTSTAMP:20220612T150000Z
UID:7906fa79fa692bfa1867b854a1b204b4@cgp.ibs.re.kr
SUMMARY:Learning Seminar on Quantum Topology and related topics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Eric Rubiel Dolores Cuenca\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: During this season of the Learning seminar we will focus on the study of quantum invariants of 3-manifolds by using Temperley-Lieb algebras. We will closely follow the book: “Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds” by Louis H. Kauffman and Sóstenes L. Lins). Our main goal is understanding the definition of Turaev-Viro and Reshetikhin-Turaev invariants and their explicit computation. In particular we will learn about: Kauffman bracket and Temperley-Lieb algebras, Triangulations, spines and Heegaard splittings of 3-manifolds, Turaev-Viro invariants, Reshetikhin-Turaev invariants.
For detailed information, please visit Homepage: Learning seminar on quantum topology and related topics
Zoom link: https://us05web.zoom.us/j/5411347674?pwd=LytHY25CcWdCMG1jUnN1NGNUaVpDQT09
(The link will open 30 minutes before the Seminar starts.)
◎ Meeting ID: 541 134 7674
◎ Password: CRTZOOM
END:VEVENT
BEGIN:VEVENT
DTSTART:20220422T100000
DTEND:20220422T110000
DTSTAMP:20220421T150000Z
UID:94e58fd8886b26aff9fb6095fbdc6a44@cgp.ibs.re.kr
SUMMARY:Hall-Littlewood functions and Virasoro constraints
LOCATION:Online Streaming
DESCRIPTION:Speaker: Xiaobo Liu\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Hall-Littlewood functions are generalizations of Schur Q-functions which have been used to study Kontsevich-Witten and Brezin-Gross-Witten tau functions. Recently Mironov and Morozov proposed to use Hall-Littlewood functions specialized at roots of unity to study generalized Kontsevich matrix models. Virasoro constraints are powerful tools in the study of matrix models and Gromov-Witten invariants. In this talk, I will describe how Virasoro operators act on Hall-Littlewood functions and applications of such formulas. This is based on joint works with Chenglang Yang.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220426T160000
DTEND:20220426T170000
DTSTAMP:20220425T150000Z
UID:08f974ebdc04c53bbd8959c0e09ab8c7@cgp.ibs.re.kr
SUMMARY:A birational Torelli theorem for parabolic symplectic bundles
LOCATION:Online Streaming
DESCRIPTION:Speaker: Sumit Roy\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: A parabolic bundle over a compact Riemann surface $X$ is a vector bundle together with a weighted flag over a fixed finite set $D$. In this talk, I will consider parabolic symplectic bundles over $X$ of genus $g > 3$ which are parabolic bundles together with a non-degenerate skew-symmetric form taking values in a line bundle. First I will prove a Torelli theorem for the moduli space of parabolic symplectic bundles, which states that if two such moduli spaces $\mathcal{M}_{(X,D)}$ and $\mathcal{M}_{(X',D')}$ over $X$ and $X'$ are isomorphic then there exists an isomorphism between $X$ and $X'$ sending $D$ to $D'$. Using this result I will prove a birational version of the Torelli theorem, which states that if there exist an isomorphism between two open sets $U \subset \mathcal{M}_{(X,D)}$ and $U' \subset \mathcal{M}_{(X',D')}$ whose respective compliments have codimension $\geq 3$ then there exists an isomorphism $X \cong X'$ sending $D$ to $D'$.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220517T100000
DTEND:20220517T110000
DTSTAMP:20220516T150000Z
UID:93cc266318daa0f732a78977f32f3d67@cgp.ibs.re.kr
SUMMARY:Compact Moduli of K3 surfaces with a prescribed nonsymplectic cyclic action
LOCATION:Online Streaming
DESCRIPTION:Speaker: Changho Han\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Observe that any construction of "meaningful" compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g, and Satake used the periods from Hodge theory to compactify the same moduli space. After a brief review of the elliptic curve case (how those notions are the same), I will generalize into looking at various compactifications of Kondo's moduli space of lattice polarized K3 surfaces (which are of degree 6) with nonsymplectic Z/3Z group action; this involves periods and genus 4 curves by Kondo's birational period map in 2002. Then, I will extend Kondo's birational map to describe birational relations between different compactifications by using the slc compactifications (also known as KSBA compactifications) of moduli of surface pairs. The main advantage of this approach is that we obtain an explicit classification of degenerate K3 surfaces, which is used to find geometric meaning of points parametrized by Hodge-theoretic compactifications. This comes from joint works (in progress) with Valery Alexeev, Anand Deopurkar, and Philip Engel.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220415T170000
DTEND:20220415T180000
DTSTAMP:20220414T150000Z
UID:dbc94b0db70512b2a7b97077930eb005@cgp.ibs.re.kr
SUMMARY:The B-model for singular spectral curves and its enumerative interpretation
LOCATION:Online Streaming
DESCRIPTION:Speaker: Gaëtan Borot\n\nEvent: Mathematical Physics Seminar\n\nAbstract: I will discuss the definition of B-model/topological recursion for spectral curves and explain the obstructions to the well-posedness of this definition for arbitrary spectral curves. The question can be approached by the representation theory of W-algebras, and I will describe the largest known class of admissible spectral curves (including singular cases) that has been obtained in this way. Each case is expected to have an enumerative interpretation in a sense that I will specify. In particular l will describe possible applications in open r-spin intersection theory.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220509T100000
DTEND:20220509T110000
DTSTAMP:20220508T150000Z
UID:ae5cedff9cb7eb75d7cd006f42e3fe70@cgp.ibs.re.kr
SUMMARY:Mirror symmetry of Fano manifolds via toric degenerations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Fumihiko Sanda\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Let X be a Fano manifold and L be a monotone Lagrangian in X. Then (a chart of) a Landau-Ginzburg mirror of X is a Laurent polynomial f which is computed by counting holomorphic disks bounded by L. Suppose that X admits a toric degeneration to a normal toric Fano variety X′. In this talk, I will explain that the Newton polytope of f is equal to the fan polytope of X′.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220321T100000
DTEND:20220321T110000
DTSTAMP:20220320T150000Z
UID:8fa3f5871cc2a9f4a4eb10a850914837@cgp.ibs.re.kr
SUMMARY:Polyhedral Liouville domains
LOCATION:Online Streaming
DESCRIPTION:Speaker: Marco Castronovo\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In the early 2000s, Hori-Vafa proposed a Landau-Ginzburg model on a complex torus for any smooth toric Fano variety, whose potential was later interpreted in terms of Lagrangian Floer theory of a moment fiber by Cho-Oh. More recent work of Rietsch gives a realistic Landau-Ginzburg model for homogeneous varieties, that however contains many complex torus charts. I will describe the first step of a program aimed at interpreting each local potential in terms of Lagrangian Floer theory of a moment fiber in a toric Fano variety with arbitrary singularities.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220406T133000
DTEND:20220406T153000
DTSTAMP:20220405T150000Z
UID:03390f261e3b71f5f17829501ee26802@cgp.ibs.re.kr
SUMMARY:Open Gromov-Witten invariants: their definition, obstruction and wall-crossing
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: The following is the overall abstract of this seminar series.
Cohomological field theories were introduced by Kontsevich and Manin to describe the universal properties of the Gromov-Witten theory. They are given by the families of cohomological classes on the moduli spaces of punctured Riemann surfaces, these families satisfy certain consistency conditions.The Givental-Teleman construction describes the all-genera generating functions of the semisimple cohomological field theories in terms of the Givental group. The main building block of this construction is the Kontsevich-Witten tau-function, the generating function for the Gromov-Witten invariants of a point.
Starting with general introduction of defintion, obstruction and wall crossing phenomenaon of open Gromov-Witten invariants, and recalling some elements of Givental-Teleman construction from the point of view of a mathematical physicist, we will learn about recent work of Alexandrov, Basalaev and Buryak on an open analog of total descendant and total ancestor potentials via an "open version'' of Givental's action. The construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a flat unit. In addition to the Kontsevich-Witten tau-function, this construction needs its open analog, a generating function introduced by Buryak-Pandharipande-Solomon-Tessler.
The construction only partially inherits nice properties of Givental's description but satisfies a number of non-trivial properties expected for the general open Gromov-Witten invariants.Namely, the open total descendant potentials we define satisfy the open topological recursion relations in genus 0 and 1, the open string and open dilaton equations.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220413T133000
DTEND:20220413T153000
DTSTAMP:20220412T150000Z
UID:c03498a9d2d28e739ec5609cfa4b3782@cgp.ibs.re.kr
SUMMARY:On construction of open descendant potentials in all genera
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Director's Seminar\n\nAbstract: The following is the overall abstract of this seminar series.
Cohomological field theories were introduced by Kontsevich and Manin to describe the universal properties of the Gromov-Witten theory. They are given by the families of cohomological classes on the moduli spaces of punctured Riemann surfaces, these families satisfy certain consistency conditions.The Givental-Teleman construction describes the all-genera generating functions of the semisimple cohomological field theories in terms of the Givental group. The main building block of this construction is the Kontsevich-Witten tau-function, the generating function for the Gromov-Witten invariants of a point.
Starting with general introduction of defintion, obstruction and wall crossing phenomenaon of open Gromov-Witten invariants, and recalling some elements of Givental-Teleman construction from the point of view of a mathematical physicist, we will learn about recent work of Alexandrov, Basalaev and Buryak on an open analog of total descendant and total ancestor potentials via an "open version'' of Givental's action. The construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a flat unit. In addition to the Kontsevich-Witten tau-function, this construction needs its open analog, a generating function introduced by Buryak-Pandharipande-Solomon-Tessler.
The construction only partially inherits nice properties of Givental's description but satisfies a number of non-trivial properties expected for the general open Gromov-Witten invariants.Namely, the open total descendant potentials we define satisfy the open topological recursion relations in genus 0 and 1, the open string and open dilaton equations.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220420T133000
DTEND:20220420T153000
DTSTAMP:20220419T150000Z
UID:e86a4ab9a62c1ffb9075237c1f94c445@cgp.ibs.re.kr
SUMMARY:On construction of open descendant potentials in all genera II
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Director's Seminar\n\nAbstract: The following is the overall abstract of this seminar series.
Cohomological field theories were introduced by Kontsevich and Manin to describe the universal properties of the Gromov-Witten theory. They are given by the families of cohomological classes on the moduli spaces of punctured Riemann surfaces, these families satisfy certain consistency conditions.The Givental-Teleman construction describes the all-genera generating functions of the semisimple cohomological field theories in terms of the Givental group. The main building block of this construction is the Kontsevich-Witten tau-function, the generating function for the Gromov-Witten invariants of a point.
Starting with general introduction of defintion, obstruction and wall crossing phenomenaon of open Gromov-Witten invariants, and recalling some elements of Givental-Teleman construction from the point of view of a mathematical physicist, we will learn about recent work of Alexandrov, Basalaev and Buryak on an open analog of total descendant and total ancestor potentials via an "open version'' of Givental's action. The construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a flat unit. In addition to the Kontsevich-Witten tau-function, this construction needs its open analog, a generating function introduced by Buryak-Pandharipande-Solomon-Tessler.
The construction only partially inherits nice properties of Givental's description but satisfies a number of non-trivial properties expected for the general open Gromov-Witten invariants.Namely, the open total descendant potentials we define satisfy the open topological recursion relations in genus 0 and 1, the open string and open dilaton equations.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220414T100000
DTEND:20220414T110000
DTSTAMP:20220413T150000Z
UID:9dcf5c1065e914be4fee209aae336c2f@cgp.ibs.re.kr
SUMMARY:New developments in involutive Heegaard Floer homology
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ian Zemke\n\nEvent: CGP Seminar\n\nAbstract: Involutive Heegaard Floer homology is a refinement of Ozsvath and Szabo's Heegaard Floer homology which keeps track of an additional Pin(2) symmetry in the theory. In this talk, we will talk about some basic properties of involutive Heegaard Floer homology, as well as some new properties, such as the surgery exact triangle, naturality, and functoriality. The work in the talk is joint with K. Hendricks, J. Hom and M. Stoffregen.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220411T100000
DTEND:20220411T110000
DTSTAMP:20220410T150000Z
UID:5fcc34a63d7adf9b333acf25b18f593a@cgp.ibs.re.kr
SUMMARY:Mutations and flat families with toric fibers
LOCATION:Online Streaming
DESCRIPTION:Speaker: Nathan Ilten\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Mutation is a combinatorial operation on Laurent polynomials related to mirror symmetry and wall-crossing. In this talk, I will discuss an old result of mine that connects mutation with deformation theory: given a mutation from a Laurent polynomial $f$ to $g$, there is a corresponding flat projective family over the projective line with the toric varieties associated to the Newton polytopes of $f$ and $g$ appearing as special fibers. Time permitting, I will also discuss recent related work connecting mutation to wall-crossing between Newton-Okounkov bodies.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220418T100000
DTEND:20220418T110000
DTSTAMP:20220417T150000Z
UID:564cd10186d62e8ce6a557976e9d2387@cgp.ibs.re.kr
SUMMARY:Complex Lagrangian vector spaces and representations of the Heisenberg Lie algebra
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hyunmoon Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Smooth functions on a real vector space are representations of the abelian Lie algebra of partial derivatives. In this talk, we will pick up a classical perspective by Grossman and consider representations of the Heisenberg Lie algebra as analogs of this object for suitably defined analytic functions on a real symplectic vector space. A new feature is that there is a homogeneous space of choices rather than a distinguished choice for the representation. We will describe this homogeneous space as the set of pairs of transverse complex Lagrangian subspaces, and show how each pair gives a representation of the Heisenberg Lie algebra. We will show how different subsets are associated with previously constructed families of representations by Satake, Grossman-Daubechies, and Lion-Vergne. We will briefly discuss relations with Jacobi forms and information geometry in the two dimensional case, based on discussions with Gabriel Khan.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220523T100000
DTEND:20220523T110000
DTSTAMP:20220522T150000Z
UID:2ab8b5e796d236656a00f133bd890aee@cgp.ibs.re.kr
SUMMARY:Compactification of Popsicles with interior insertions
LOCATION:Online Streaming
DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Popsicles are discs with a constraint that their interior marked points lie on the geodesics between one of the input and output boundary marked points.These structures were developed by Abouzaid-Seidel. We introduce a new compactification of popsicles when interior marked points are not allowed to coincide.Stable map compactification is not enough and it requires additional data, which we call alignment data. These can be used to define a new A-infinity structure related to a quantum cap action under suitable index conditions.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220404T100000
DTEND:20220404T110000
DTSTAMP:20220403T150000Z
UID:c023d567fd4f2ebd7b2e8bbf5fb8117e@cgp.ibs.re.kr
SUMMARY:On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity
LOCATION:Online Streaming
DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In topological dynamics, the Gromov-Yomdin theorem states that the topological entropy of a holomorphic automorphism $f$ of a smooth projective variety is equal to the logarithm of the spectral radius of the pullback $f^*$ induced on cohomology. In order to establish a categorical analogue of the Gromov-Yomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this talk, we propose a notion that categorifies and generalizes that of a holomorphic automorphism and prove that the Gromov-Yomdin type theorem holds for them. The key is to make use of stability conditions and a conjectural description of stability conditions on Fukaya category due to Bridgeland and Joyce. This talk is based on a joint work with Federico Barbacovi.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220531T100000
DTEND:20220531T110000
DTSTAMP:20220530T150000Z
UID:237664bc852217f0fddffb281db65c10@cgp.ibs.re.kr
SUMMARY:Double lines in the quintic del Pezzo fourfold
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kiryong Chung\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Let $Y$ be the del Pezzo 4-fold defined by the linear section $\mathrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this talk, we classify the type of normal bundles of lines in $Y$ and describe its parameter space. As a corollary, we obtain the desigularized model of the moduli space of stable maps in $Y$. Also we compute the intersection Poincar\'e polynomial of the stable maps space. This talk is based on the preprint: arXiv:2204.02014.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220614T170000
DTEND:20220614T180000
DTSTAMP:20220613T150000Z
UID:66c16d03fffa74599d4e71a497eb7b5b@cgp.ibs.re.kr
SUMMARY:Gorenstein spherical Fano varieties
LOCATION:Online Streaming
DESCRIPTION:Speaker: Giuliano Gagliardi\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, I will introduce spherical varieties and explain how they are described combinatorially in terms of colored fans and spherical systems. Then I will present joint work with Johannes Hofscheier on the combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano varieties by reflexive polytopes.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220519T160000
DTEND:20220519T170000
DTSTAMP:20220518T150000Z
UID:948f7ac4ad1aae94988f809123dce3d5@cgp.ibs.re.kr
SUMMARY:Groups of area-preserving homeomorphisms, spectral estimators, and Sikorav's trick
LOCATION:Online Streaming
DESCRIPTION:Speaker: Lev Buhovsky\n\nEvent: CGP Seminar\n\nAbstract: The celebrated Fathi question asked about the simplicity of the group of Hamiltonian homeomorphisms of a symplectic surface. The recent solution of the question introduced the group of finite energy Hamiltonian homeomorphisms which was shown to bea non-trivial normal subgroup, thus giving the negative answer to the question. That group of finite energy Hamiltonian homeomorphisms contains in itself the group of Oh-Müller Hamiltonian homeomorphisms. In my talk I will try to explain how one can compare between these groups and show that their quotient is large from the perspective of Hofer's geometry.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220616T160000
DTEND:20220616T180000
DTSTAMP:20220615T150000Z
UID:1ac2b4d46cb89b66ef0d4c46dac6127a@cgp.ibs.re.kr
SUMMARY:Strong Suslin reciprocity, additive dilogarithms, and a family of algebraic curves
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Jinhyun Park\n\nEvent: CGP Seminar\n\nAbstract: The sum of the residues of a rational differential form on a smooth projective curve is zero. It is often called the residue theorem, or the Tate reciprocity. The Weil reciprocity is its multiplicative version for two arguments (e.g. Tame symbols), and this traces back to the quadratic reciprocity of Gauss. In modern terms, it is elegantly expressed in terms of the second Milnor K-groups. Its generalization to higher Milnor K-theory version was proven by Suslin.
An extension of the Suslin’s reciprocity was proposed by Goncharov about 20 years ago (called Strong Suslin reciprocity), and this conjecture was recently resolved by Rudenko. This allowed a different description of the Bloch-Winger dilogarithm function, that offers the volumes of the ideal tetrahedra in the solid 3-sphere with the hyperbolic metric. Its analogue for schemes smooth over the truncated polynomials k[t]/(t^m) of relative dimension 1, were studied recently by Ünver in terms of the additive dilogarithm.
In this talk, let me sketch my work in-progress, that extends it and answers a related problem for proper family of algebraic curves.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220726T160000
DTEND:20220726T180000
DTSTAMP:20220725T150000Z
UID:243b28ac7dca52468ee44646f1ea68c6@cgp.ibs.re.kr
SUMMARY:Counting divisorial contractions with centre a cA_n-singularity
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Erik Paemurru\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: First, we simplify the existing classification due to Kawakita and Yamamoto of 3-dimensional divisorial contractions with centre a cA_n-singularity. Next we consider divisorial contractions of discrepancy at least 2 to a fixed variety with centre a cA_n-singularity. We show that if there exists one such divisorial contraction, then there exist uncountably many such divisorial contractions.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220714T160000
DTEND:20220714T180000
DTSTAMP:20220713T150000Z
UID:1bbd26019750363d688cd075b9eb9761@cgp.ibs.re.kr
SUMMARY:Compactness results of Hamiltonian stationary Lagrangian submanifolds in symplectic manifold
LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium
DESCRIPTION:Speaker: Man Shun Ma\n\nEvent: CGP Seminar\n\nAbstract: In this talk, we discuss some recent results on the compactness of the space of Hamiltonian stationary Lagrangian immersions with bounded area and total curvatures. This is a joint work with Jingyi Chen.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220705T160000
DTEND:20220705T170000
DTSTAMP:20220704T150000Z
UID:6c0738e0b166a0e3b99d349d14c452b4@cgp.ibs.re.kr
SUMMARY:On toric Schubert varieties
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Schubert varieties are some of the most interesting subvarieties of the flag variety. A maximal (complex) torus $T$ acts on the flag variety and these subvarieties are stable under the action. In this talk, we consider \textit{toric} Schubert varieties (with respect to the action of $T$) and their isomorphism classes. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220719T160000
DTEND:20220719T180000
DTSTAMP:20220718T150000Z
UID:6f8d3b456b8b878b8d402caf3bb2fdd6@cgp.ibs.re.kr
SUMMARY:Families of simple subgroups in the Cremona group arising from del Pezzo fibrations
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Igor Krylov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Cremona group of rank nis the group of birational self-maps of the projective space of dimension n. For any subgroup Gof Cremona group there is a rational variety on which G acts regularly. This allows to translate the study of subgroups of the Cremona group into the study of G-equivariant geometry of rational varieties. In this talk I will describe some continuous families of rational threefolds with an action of alternating group of rank 5. I will also explain why the corresponding subgroups of the Cremona group are not pair-wise conjugate.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220819T100000
DTEND:20220819T113000
DTSTAMP:20220818T150000Z
UID:c0e92583a790135603f94accfab8b62e@cgp.ibs.re.kr
SUMMARY:Temperley-Lieb Recoupling Theory and Invariants of Classical and Virtual Knots and Links
LOCATION:Online Streaming
DESCRIPTION:Speaker: Louis H. Kauffman(University of Illinois at Chicago)\n\nEvent: Learning Seminar on Quantum Topology\n\nAbstract: This talk will review the structure of the Temperley-Lieb Recoupling Theory and describe some of its applications, including the Fibonacci model for topological quantum computation, invariants of three manifolds and recent work by the speaker and Heather Dye and Eiji Ogasa on invariants of virtual knots and links and associated three manifolds.For registration, please fill in the google form.https://forms.gle/UAFKY4e5i5Ko14Sx8
END:VEVENT
BEGIN:VEVENT
DTSTART:20221004T093000
DTEND:20221004T102000
DTSTAMP:20221003T150000Z
UID:b71c46ce842a579ccc9525c07fdf082c@cgp.ibs.re.kr
SUMMARY:Birational involutions of the real projective plane
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Ivan Cheltsov\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: We present classification of birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which includes 4 different classes of involutions, there are 12 different classes over the reals. In this talk, I will describe these classes explicitly, and explain how to classify birational involutions of the real projective plane up to conjugation. This is a joint work with Frederic Mangolte, Egor Yasinsky and Susanna Zimmermann.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221006T113000
DTEND:20221006T122000
DTSTAMP:20221005T150000Z
UID:73a595e479a6cd46ac2663631346e792@cgp.ibs.re.kr
SUMMARY:Nonequilibrium theomodynamics and relative information entropy
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Starting from the first principle of statistical physics and kinetic theory, we canonically derive theormodynamic phase space (TPS) for nonequilibrium thermodynamics as a contact manifold through Marsden-Weinstein reduction. We then explain how the relative information entropy canonically define a thermodynamic equilibrium of a given statistical system as a Legendrian submanifold which is not necessarily holonomic. We then interpret Maxwell construction as the process of finding a continuous, not necessarily differentiable, thermodynamic potential and explain the associated phase transition in this framework. This is based on the joint work with Jin-Wook Lim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221004T113000
DTEND:20221004T122000
DTSTAMP:20221003T150000Z
UID:be440c1b51a9043d724afa9d9196a538@cgp.ibs.re.kr
SUMMARY:Volumes of moduli spaces of super hyperbolic surfaces.
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Paul Norbury\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Mirzakhani produced recursion relations between polynomials that give Weil-Petersson volumes of moduli spaces of hyperbolic surfaces. Stanford and Witten described an analogous construction for moduli spaces of super hyperbolic surfaces producing Mirzakhani-like recursion relations between polynomials that give super volumes. This was achieved in the so-called Neveu-Schwarz case. Both of these stories have an algebro-geometric description, and in particular this led Mirzakhani to a new proof of Witten's conjecture on intersection numbers over the moduli space of stable curves. In this lecture, via the algebro-geometric description, I will describe what occurs in the Ramond case of the super construction. It produces deformations of the Neveu-Schwarz polynomials again satisfying Mirzakhani-like recursion relations.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221005T093000
DTEND:20221005T102000
DTSTAMP:20221004T150000Z
UID:68a72e3daf466bfe7483de3dea2f9148@cgp.ibs.re.kr
SUMMARY:Twisted String Theory
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Philsang Yoo\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: String theory is a framework of physics which among other things gives rise to various interesting predictions in mathematics. Some of these predictions are derived from S-duality that provides a non-trivial equivalence of two physical theories. The main aim of the talk is to explain how to mathematically understand aspects of string theory, focusing on topological strings, and discuss S-duality in this context. A large part of the talk will be devoted to providing a dictionary for string theory and mathematical objects in this restricted context of topological string theory. This talk is based on a joint work in progress with Surya Raghavendran.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221005T103000
DTEND:20221005T112000
DTSTAMP:20221004T150000Z
UID:655defc24d981fc019af5cb33a6b8779@cgp.ibs.re.kr
SUMMARY:Reflection vectors for semi-simple Frobenius manifolds
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Todor Milanov\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Let M be a semi-simple Frobenius manifold and H be the space of flat vector fields on M. The monodromy group of the so-called second structure connection is a reflection group generated by a certain set of reflections. Each reflection is determined by a corresponding vector in H which we call a reflection vector. In the first part of my talk I would like to explain the importance of the reflection vectors from the point of view of integrable systems. Furthermore, the set of reflection vectors can be viewed as a generalized root system. One of my long term goals is to obtain a classification of generalized root systems that can be identified with the set of reflection vectors in quantum cohomology and singularity theory. The second part of my talk is partially motivated by this problem and I would like to explain my current progress. This part of the talk will be based on joint work with my students Chenghan Zha and Xiaokun Xia.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221005T113000
DTEND:20221005T122000
DTSTAMP:20221004T150000Z
UID:34aec813fd39445fce8958044eb462d9@cgp.ibs.re.kr
SUMMARY:Geometry of flag varieties and string polytopes
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: For a semisimple algebraic group $G$ and a Borel subgroup $B$, the homogeneous space $G/B$, called the flag variety, is a smooth projective variety that has a fruitful connection with $G$-representations. On the other hand, string polytopes are combinatorial objects which encode the characters of irreducible $G$-representations. The flag variety and the string polytopes are related via the theory of Newton--Okounkov bodies. It has been known that two string polytopes can have different combinatorics even though they encode the same data of an irreducible $G$-representation. In this talk, we will study a family of string polytopes in type A which are unimodularly equivalent to the Gelfand--Cetlin polytope. Moreover, we will present small toric resolutions of certain string polytopes using blowing-ups of Bott manifolds that are smooth projective toric varieties. This talk is based on joint works with Yunhyung Cho, Yoosik Kim, and Kyeong-Dong Park.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221005T140000
DTEND:20221005T145000
DTSTAMP:20221004T150000Z
UID:5e70d1804a8be82252d68b47e97bf129@cgp.ibs.re.kr
SUMMARY:The (2,1)-cable of the figure-eight knot is not smoothly slice
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Sungkyung Kang\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice, thereby solving a question posed by Kawauchi in 1980. While doing so, we will review the involutive and equivariant actions in Heegaard Floer homology, and how one can use those symmetries to tackle various knot slicing problems in the smooth category. This is a joint work with Irving Dai, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221005T153000
DTEND:20221005T162000
DTSTAMP:20221004T150000Z
UID:d79161b74d9b6f631c2f292ea549dcf9@cgp.ibs.re.kr
SUMMARY:Variation operator and Fukaya category of singularity
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Cheol-Hyun Cho\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: For a weighted homogeneous polynomial of Fano or Calabi-Yau type or for a general polynomial of a two variable, we define a new Fukaya category, using the global monodromy of the singularity and the wrapped Fukaya category of the Milnor fiber. Variation operator in singularity theory is categorified as a quantum cap action of a monodromy Hamiltonian orbit in this construction. A-infinity operations are defined from J-holomorphic popsicles with interior insertions ofmonodromy orbits. This is a joint work in progress with Hanwool Bae, Dongwook Choa and Wonbo Jeong.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221006T093000
DTEND:20221006T102000
DTSTAMP:20221005T150000Z
UID:5d1d35355492c455fd76f0d7cfa3cfcb@cgp.ibs.re.kr
SUMMARY:The Calabi problem for Fano threefolds
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Kento Fujita\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: There are 105 irreducible families of smooth Fano threefolds,which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kaehler-Einstein metric or not.This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov,Hendrik Suess and Nivedita Viswanathan.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221006T103000
DTEND:20221006T112000
DTSTAMP:20221005T150000Z
UID:989a8faa2f5748d3f6acd49a79a05459@cgp.ibs.re.kr
SUMMARY:Birational geometry of varieties with effective anticanonical divisors.
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Fano varieties are fundamental objects in algebraic geometry. These can be considered as the unique output of the -K -minimal model program on the varieties with effective anticanonical divisors. Thus the initial models should encode the information of their resulting Fano varieties. In this talk, I will present some results related to the -K-MMP.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221004T103000
DTEND:20221004T112000
DTSTAMP:20221003T150000Z
UID:ff5dd3e0344dbf8d5ccf5f08e88fabee@cgp.ibs.re.kr
SUMMARY:Vector bundles on elliptic surfaces and logarithmic transformations
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Logarithmic transformation is an important operation introduced by Kodaira in the 1960s. One can obtain an elliptic surface with multiple fibers by performing logarithmic transformations on an elliptic surface without multiple fibers. On the other hand, vector bundles on elliptic surfaces are important objects in many branches of mathematics, e.g., algebraic geometry, gauge theory, mathematical physics, etc. In this talk, I will discuss how certain vector bundles on elliptic surfaces are changed via logarithmic transformations. This talk is based on a joint work with Ludmil Katzarkov.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221006T140000
DTEND:20221006T145000
DTSTAMP:20221005T150000Z
UID:45defaf2c1b507a03e8ff00cea15a011@cgp.ibs.re.kr
SUMMARY:Higher-dimensional Heegaard Floer homology and Hecke algebras
LOCATION:POSCO International Center
DESCRIPTION:Speaker: Ko Honda\n\nEvent: IBS Center for Geometry and Physics 10th Anniversary Conference\n\nAbstract: Given a closed oriented surface $\Sigma$ of genus greater than zero, we construct an $A_\infty$ map from the higher-dimensional Heegaard Floer homology of the cotangent fibers of $T^*\Sigma$ to the Hecke algebra associated to $\Sigma$ and show that it is an isomorphism of algebras. For example, when $\Sigma$ is the 2-torus, the surface Hecke algebra is a double affine Hecke algebra. This is joint work with Yin Tian and Tianyu Yuan.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220919T170000
DTEND:20220919T180000
DTSTAMP:20220918T150000Z
UID:0a9adfb1152caccd11a6f0e6ec88ebf1@cgp.ibs.re.kr
SUMMARY:Groups of area preserving homeomorphisms and subleading asymptotics of link spectral invariants
LOCATION:Online Streaming
DESCRIPTION:Speaker: Vincent Humilière\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Whether the group G of area preserving homeomorphisms of the 2-sphere is simple remained an open question for a long time, but was finally answered in the negative a couple of years ago by Dan Cristofaro-Gardiner, Sobhan Seyfaddini and myself. The proof shows in particular that the normal subgroup of "hameomorphisms" (denoted Hameo) introduced in the 2000s by Yong-Geun Oh and Stefan Müller is proper. To pursue the study of the group G, a central open question was then whether Hameo was the smallest normal subgroup in G. I will report on very recent joint work with Dan Cristofaro-Gardiner, Cheuk-Yu Mak, Sobhan Seyfaddini and Ivan Smith, which in particular answers this question in the negative as well.This is based on a study of a sequence of invariants extracted from a version of Floer homology on symmetric products of a surface (which we developed in our previous work) that might be of independent interest, and raises new questions about these invariants.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220916T170000
DTEND:20220916T180000
DTSTAMP:20220915T150000Z
UID:f82840690e3f46bcb251da6e7d8dea97@cgp.ibs.re.kr
SUMMARY:Defect in gauge theory and quantum spin chains
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The N=2 supersymmetric gauge theories in four dimensions have intrinsic connection to algebraic integrable systems. The gauge theory of interests, the asymptotically superconformal N=2 SQCD in four dimensions, reveals a structure which has dual descriptions. On the one hand it is the complex generalization of the Heisenberg XXX spin chain, based on the Lie algebra sl_2. On the other hand is the Gaudin model (a special type of Hitchin system), based on the Lie algebra sl_N. In this talk I will focus on the spin chain side. I will show that by introducing BPS surface defects, we find observables in the gauge theory that satisfy difference equations called fractional quantum T-Q equation. The observables represents states of the XXX Heisenberg spin chain of N Heisenberg-Weyl modules over Y(sl_2). We also exploited to find the the explicit formula for the Jost function of the XXX Heisenberg spin chain from gauge theory.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220923T170000
DTEND:20220923T180000
DTSTAMP:20220922T150000Z
UID:6bb4824c71661a0e3082be6d094276aa@cgp.ibs.re.kr
SUMMARY:The spin Gromov-Witten/Hurwitz correspondence
LOCATION:Online Streaming
DESCRIPTION:Speaker: Reinier Kramer\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In 2006, Okounkov and Pandharipande established a correspondence between two theories of counting maps between curves. Gromov-Witten theory constructs a moduli space of stable maps and considers intersection numbers of natural classes on this space. Hurwitz theory counts the number of maps with given ramification data over all points in the target.The Gromov-Witten theory of a surface with positive geometric genus can be localised to a curve in that surface, and this obtains a spin structure, leading to spin Gromov-Witten theory of curves. The Hurwitz side also has a natural spin analogue, and Lee conjectured these theories correspond in a similar manner.In this talk, I will introduce the notions of spin Gromov-Witten theory and spin Hurwitz theory and give an outline of the spin Gromov-Witten/Hurwitz correspondence for the projective line. I will also explain relations to the (small) 2BKP integrable hierarchy, which is the analogue of the 2D Toda lattice hierarchy in the non-spin case.This talk is based on joint work with Alessandro Giacchetto, Danilo Lewański, and Adrien Sauvaget.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221024T100000
DTEND:20221024T110000
DTSTAMP:20221023T150000Z
UID:6e03375d6bb5cc9f47209d7c625a6e39@cgp.ibs.re.kr
SUMMARY:Strong closing property of contact forms and action selecting functors
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kei Irie\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I introduce a notion of strong closing property of contact forms, inspired by the $C^\infty$-closing lemma for Reeb flows in dimension three.The goal of this talk is to formulate (and discuss its applications) a sufficient criterion for the strong closing property by using an abstract notion of action selecting functors, which is a generalization of quantitative (embedded) contact homology.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221117T170000
DTEND:20221117T180000
DTSTAMP:20221116T150000Z
UID:f9f8a640aab446327f7b9f6598b2bfc1@cgp.ibs.re.kr
SUMMARY:Natural differentiable structures on statistical models and the Fisher metric
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hong Van Le\n\nEvent: CGP Seminar\n\nAbstract: In my talk I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of measures, $k$-integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.
END:VEVENT
BEGIN:VEVENT
DTSTART:20220930T170000
DTEND:20220930T180000
DTSTAMP:20220929T150000Z
UID:ebf7399627cccd473409b9f1298d5139@cgp.ibs.re.kr
SUMMARY:Fractional quantum Hall effect via the Grothendieck-Riemann-Roch formula
LOCATION:Online Streaming
DESCRIPTION:Speaker: Dimitri Zvonkine\n\nEvent: Mathematical Physics Seminar\n\nAbstract: We study the fractional quantum Hall effect on a Riemann surface of genus g traversed by a magnetic field of total flux d. The wave functions of charged particles have a semi-phenomenological description by Laughlin states. These states can be studied by methods of algebraic geometry: they form a holomorphic vector bundle over the d-th Picard group of the Riemann surface. The Chern characters of this vector bundle can be computed by the Grothendieck-Riemann-Roch formula. In a fully filled state the Chern character we obtain is compatible with the existence of a projectively flat connection on the vector bundle. In a state with quasiholes our computation implies that no such connection can exist. This is joint work with Semyon Klevtsov.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221014T100000
DTEND:20221014T110000
DTSTAMP:20221013T150000Z
UID:43da6164c51fc068eab376e92a84a232@cgp.ibs.re.kr
SUMMARY:Integrable Systems and mirror symmetry in probability theory and combinatorics
LOCATION:Online Streaming
DESCRIPTION:Speaker: Jian Zhou\n\nEvent: Mathematical Physics Seminar\n\nAbstract: We will first explain how any moment sequence leads to a sequence of tau-functions of the KP hierarchy, which can be interpreted in terms of weighted counts of nonintersecting lattice paths. We will also explain how various lattice counting problems and some other problems in combinatorics lead to probability measures on the real line, and surprising mirror symmetry among them.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221021T170000
DTEND:20221021T180000
DTSTAMP:20221020T150000Z
UID:08ea34809af1681883bec015d5b9cab1@cgp.ibs.re.kr
SUMMARY:Perturbative connection formulas for Heun equations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Oleg Lisovyi\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Connection formulas relating Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed in terms of the large order asymptotics of the corresponding power series. I will show that for the Heun equation and some of its confluent versions, the series expansion of the relevant asymptotic amplitude in a suitable parameter can be systematically computed to arbitrary order. This allows to check a recent conjecture of Bonelli-Iossa-Panea-Tanzini expressing the Heun connection matrix in terms of quasiclassical Virasoro conformal blocks.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221028T170000
DTEND:20221028T180000
DTSTAMP:20221027T150000Z
UID:71e17708d5e48548626313ede8de6df5@cgp.ibs.re.kr
SUMMARY:Superintegrability: new and old meanings and techniques
LOCATION:Online Streaming
DESCRIPTION:Speaker: Aleksandr Popolitov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The goal of this talk is to review the topic of superintegrability/character expansion which recently enjoyed very rapid development and discovery of new techniques and is on the verge of becoming a systematic approach to matrix models.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221017T100000
DTEND:20221017T110000
DTSTAMP:20221016T150000Z
UID:b8c2979e16c1d96bfedfa9dd8ab956a1@cgp.ibs.re.kr
SUMMARY:Contact Hamiltonian Floer homology and Eliashberg-Polterovich’s orderability
LOCATION:Online Streaming
DESCRIPTION:Speaker: Jun Zhang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In this talk, we will elaborate on a Hamiltonian Floer homology in the set-up of a contact manifold. Different from many other versions of contact homology, this homology theory depends on a given contact Hamiltonian function (so it is a more direct analogue of the symplectic version of Hamiltonian Floer homology). However, different from the symplectic situation, the Floer continuation maps are not necessarily isomorphisms. Moreover, we will see that non-isomorphic Floer continuation maps are closely related to the orderability property defined by Eliashberg-Polterovich, which is a peculiar phenomenon in contact geometry that characterizes the rigidity of positive loops in the contactomorphism group. Finally, we will briefly explain how quantitative studies can be extracted from this version of the Floer theory. This talk is based on joint work with Igor Uljarević.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221031T170000
DTEND:20221031T180000
DTSTAMP:20221030T150000Z
UID:0ef511dba8334ea2591847762fed07ed@cgp.ibs.re.kr
SUMMARY:Symplectic blowing down in dimension six
LOCATION:Online Streaming
DESCRIPTION:Speaker: Weiyi Zhang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Symplectic blowing down is a fundamental operation in symplectic birational geometry. Two symplectic manifolds are birationally equivalent if they are related by a sequence of symplectic blow ups, symplectic blow downs and integral deformations. In this talk, I will explain a cohomological criterion of blowing down in the context of symplectic binational geometry in dimension six. This is based on a joint work with Tian-Jun Li and Yongbin Ruan.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221107T100000
DTEND:20221107T110000
DTSTAMP:20221106T150000Z
UID:ccd719e11ae7c9f87c7efbf700f4c2f8@cgp.ibs.re.kr
SUMMARY:Morita invariance of Categorical Enumerative Invariants
LOCATION:Online Streaming
DESCRIPTION:Speaker: Lino Jose Campos Amorim\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Caldararu-Costello-Tu defined Categorical Enumerative Invariants (CEI) as a set of invariants associated to a cyclic A-infinity category (with some extra conditions/data), that resemble the Gromov-Witten invariants in symplectic geometry. In this talk I will explain how one can define these invariants for Calabi-Yau A-infinity categories - a homotopy invariant version of cyclic - and then show the CEI are Morita invariant. This has applications to Mirror Symmetry and Algebraic Geometry.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221114T100000
DTEND:20221114T110000
DTSTAMP:20221113T150000Z
UID:3df5a303b1838969c9809350d0639669@cgp.ibs.re.kr
SUMMARY:Equivariant Homological Mirror Symmetry for $\mathbb{C}P^1$
LOCATION:Online Streaming
DESCRIPTION:Speaker: Masahiro Futaki\n\nEvent: Symplectic Monday Seminar\n\nAbstract: The mirror of an n-dimensional toric Fano manifold X is known to be $(C^*)^n$ equipped with a Laurent polynomial f and is called the Landau-Ginzburg model. The homological mirror symmetry for toric Fano manifold says that the Fukaya category of $X$ is equivalent to the category of matrix factorizations of $f$ (Cho, Hong and Lau 2019).Givental introduced the equivariant Landau-Ginzburg mirror $F$ by adding logarithmic terms to $f$.In this talk we formulate and show a version of equivariant homological mirror symmetry for $\mathbb{C}P^1$ by introducing equivariant Floer $A_\infty$ algebra for toric fibers.This is a joint work with Fumihiko Sanda (Gakushuin University) and is based on our preprint https://arxiv.org/abs/2112.14622 .
END:VEVENT
BEGIN:VEVENT
DTSTART:20221128T100000
DTEND:20221128T110000
DTSTAMP:20221127T150000Z
UID:ce5648d4a9858bf3dd58d359783b4dff@cgp.ibs.re.kr
SUMMARY:Abelian/Nonabelian correspondence and derived categories
LOCATION:Online Streaming
DESCRIPTION:Speaker: Dongwook Choa\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Abelian/Nonabelian correspondence is a relation between cohomology rings of GIT quotient(symplectic reduction) and its abelian version. I will shortly review what it is and the idea of its proof. Next, I will explain how to extend it to derived categories of coherent sheaves. One of the key ingredients is a grade restriction rules, which can be viewed as a derived version of Kirwan's map. This is a joint project with W. Yaoxiong and Z. Zhou.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221219T100000
DTEND:20221219T110000
DTSTAMP:20221218T150000Z
UID:55d0ad29e6f0aba99bfc668df4bf9c84@cgp.ibs.re.kr
SUMMARY:Symplectic duality for hypertoric varieties via Floer theory
LOCATION:Online Streaming
DESCRIPTION:Speaker: Xiao Zheng\n\nEvent: Symplectic Monday Seminar\n\nAbstract: To a hypertoric variety $X_{\alpha}$, where $\alpha$ denotes the Kähler parameter, and a choice of an equivariant parameter $\beta$, we associate an A-infinity algebra $B(X_{\alpha},\beta)$ and a dga $A(X_{\alpha},\beta)$, which are given by the Floer theory of the "attracting Lagrangian" determined by $\beta$ and its Maurer-Cartan dga. For a symplectic dual pair of hypertoric varieties $X_{\alpha}$ and $X^!_{\beta}$, we show that $B(X_{\alpha},\beta) (resp. A(X_{\alpha},\beta))$ is Koszul dual to $B(X^!_{\beta},\alpha) (resp. A(X^!_{\beta},\alpha))$. This can be thought of as an A-infinity analogue of the work of Braden-Licata-Proudfoot-Wesbter on the Koszul duality for hypertoric category $O$. This is based on a joint work of Lau and Ma.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221205T090000
DTEND:20221205T100000
DTSTAMP:20221204T150000Z
UID:94bf1df4cd84f9557210b54b18f5d73b@cgp.ibs.re.kr
SUMMARY:TBD
LOCATION:Creswick Campus of The University of Melbourne, Australia
DESCRIPTION:Speaker: TBD\n\nEvent: IBS-CGP and MATRIX workshop on Symplectic Topology\n\nAbstract:
END:VEVENT
BEGIN:VEVENT
DTSTART:20221018T160000
DTEND:20221018T180000
DTSTAMP:20221017T150000Z
UID:f39a9e7a90ff3fc8015595376137f129@cgp.ibs.re.kr
SUMMARY:A classification of 3+1D topological orders in bosonic systems
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Xiao-Gang Wen\n\nEvent: Seminar\n\nAbstract: I will present a classification of 3+1D topological orders in bosonic quantum systems in terms of a few simple classes of fusion 2-categories. This may correspond to a classification of 4D unitary fully extended topological quantum field theories (TQFT). Those TQFTs are given by the center of the simple fusion 2-categories.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221122T160000
DTEND:20221122T180000
DTSTAMP:20221121T150000Z
UID:97c20f0461d24281545aaabd83c1bcbf@cgp.ibs.re.kr
SUMMARY:Bethe/Gauge correspondence I - Introducing integrable models
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The integrable models are physic systems characterized by the existence of maximal number of conserved quantities. Such system has far fewer degree of freedom than their phase space dimensionality. Thus its evolution is restricted to sub-manifolds of its phase space. In the first part of the lecture I will introduce basic properties of the integrable model and give the example of the Toda lattice integrable model by Morikazu Toda (1967) describing a 1+1-dimensional crystal.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221123T160000
DTEND:20221123T170000
DTSTAMP:20221122T150000Z
UID:be09cc18380a1644087f164ddebe66ab@cgp.ibs.re.kr
SUMMARY:Bethe/Gauge correspondence II - Introducing supersymmetry
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The study of N=2 supersymmetric Yang-Mills theory in 4 dimensions has been a fruitful field for theoretical physicists. The existence of two sets of supersymmetry allows us to have better detail of understanding comparing to N=1 or non-supersymmetric systems. In this lecture I will introduce Seiberg and Witten's exact low energy solution of the N=2 supersymmetric system in 4 dimension. The Seiberg-Witten curve allows us to study the moduli space of the vacua. Here we will see the first hint of the Bethe/Gauge correspondence in the classical level. Relating the 4 dimensional super Yang-Mills system to the 2 dimensional Toda lattice integrable model.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221125T160000
DTEND:20221125T170000
DTSTAMP:20221124T150000Z
UID:9617d3b0f5f3d1c7e01f87eaba1bdf18@cgp.ibs.re.kr
SUMMARY:Bethe/Gauge correspondence III - From instanton partition function to Schrodinger equation
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: The Bethe/Gauge correspondence can be further extended to the quantum level thanks to the localization computation in the supersymmetric gauge theory subjected to the Omega-background. By placing the Yang-Mills theory on non-commutative geometry, the partition function and many BPs-observables can be computed exactly. In this talk I will demonstrate how the Yang-Mills theory are formulated on the non-commutative $R^4$. Finally establish the Bethe/Gauge correspondence in the quantum level by identifying the super Yang-Mills partition function as the wave function of the corresponding Toda lattice integrable model.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221215T170000
DTEND:20221215T180000
DTSTAMP:20221214T150000Z
UID:69cd367555332d25ce5b84914e26a18b@cgp.ibs.re.kr
SUMMARY:Some results and conjectures the rank of some knot homologies
LOCATION:Online Streaming
DESCRIPTION:Speaker: Marco Marengon\n\nEvent: CGP Seminar\n\nAbstract: Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology. Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer. Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots. This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221025T160000
DTEND:20221025T180000
DTSTAMP:20221024T150000Z
UID:f7ba6f6b8acdfd18620a07b6c3c856d0@cgp.ibs.re.kr
SUMMARY:On birationally solid Fano 3-fold hypersurfaces
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Fano 3-folds that are embedded as (quasismooth) hypersurfaces in weighted projective 4-spaces are classified and they form 130 families. Among them 95 families consist of Fano 3-fold weighted hypersurfaces of Fano index 1, and Cheltsov-Park proved that they are all birationally rigid. Recently, Abban-Cheltsov-Park showed that none of Fano 3-fold weighted hypersurfaces of Fano index at least 2 is birationally rigid. The aim of this talk is to explain birational properties of these Fano 3-fold weighted hypersurfaces of Fano index at least 2, and explain that some of them are birationally solid which is a notion weaker than birational rigidity.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230118T170000
DTEND:20230118T180000
DTSTAMP:20230117T150000Z
UID:b0bffaa1ba142d389dbc42889bea079a@cgp.ibs.re.kr
SUMMARY:Symmetry-Resolved Density of States
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hirosi Ooguri\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: It is well-known that the density of states of a unitary quantum field theory has a universal behavior at high energy. In two dimensions, it is known as the Cardy formula. When the theory has a global symmetry, it is interesting to find out how the Hilbert space is decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas regarding the decomposition of states at high energy. The formulae are applicable to any unitary quantum field theory in any spacetime dimensions. When the AdS/CFT correspondence applies, our formulae agree with the entropy formula for the Kerr and Reissner-Nordstrom black holes. We also settle some question on the Reissner-Nordstrom black hole.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221104T170000
DTEND:20221104T180000
DTSTAMP:20221103T150000Z
UID:fd6cee0f99891887bb118d630b17cbe6@cgp.ibs.re.kr
SUMMARY:Strings, knots and quivers
LOCATION:Online Streaming
DESCRIPTION:Speaker: Piotr Sułkowski\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In this talk I will review the knots-quivers correspondence and mention some recent developments in this regard. The knots-quivers correspondence is the statement that various invariants associated to a knot are encoded in the corresponding quiver. This statement follows from engineering both knots and quivers in related brane systems in string theory. Recent developements, which I will mention at least briefly, include understanding the structure of various quivers that correspond to the same knot, using topological recursion to determinequiver generating series and corresponding quiver A-polynomias, and finding a quiver representation of so-called Z-hat invariants.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221118T170000
DTEND:20221118T180000
DTSTAMP:20221117T150000Z
UID:b78aca6c9f4b79ef20928c9c39021762@cgp.ibs.re.kr
SUMMARY:Open r-spin theories with multiple boundary states
LOCATION:Online Streaming
DESCRIPTION:Speaker: Ran Tessler\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In his 92' work, Witten has defined the r-spin intersection theory. This theory have found an open counterpart, in genus 0, in a recent joint work with Buryak and Clader.In the closed and open setting there are (internal) marked points, which are allowed to carry any twist from the set 0,1,...,r-1, and in the open setting there are also boundary markings whose twist is restricted to be r-2.My talk will describe a new construction of genus=0 open r-spin theories, which allows different collections of boundary states, as well as the relations satisfied by the resulting intersection numbers. If time permits I will also say a few words on higher genus.Based on a joint work with Yizhen Zhao.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221219T140000
DTEND:20221219T160000
DTSTAMP:20221218T150000Z
UID:e85accd526bfbba188e48fd417b26d64@cgp.ibs.re.kr
SUMMARY:Conjugacy classes in gln over DVR
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Sungmun Cho\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, we will explain a new method of describing conjugacy classes of a regular semisimple element in gln defined over any ring of integers of a local field having characteristic 0 or >n.Using this, we will explain how to obtain a volume of a conjugacy class using smoothening of a certain scheme over DVR. As an application, we will provide a closed formula of such volume (called the orbital integral) for n=2,3 and a lower bound for a general n. We will also propose a conjecture of the second leading term of the volume for any n. This is a joint work with Yuchan Lee.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221222T160000
DTEND:20221222T180000
DTSTAMP:20221221T150000Z
UID:4da1ca13db380cb779b4cd96e9fd8f96@cgp.ibs.re.kr
SUMMARY:Morphism spaces between coisotropic A-branes
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Yu Tung Yau\n\nEvent: CGP Seminar\n\nAbstract: Seeking for a mathematical definition of morphism spaces between coisotropic A-branes has been a long-standing problem for understanding mirror symmetry. In 2009, a paper of Gukov-Witten showed that this problem is also closely related to deformation quantization and geometric quantization. In this talk, I shall explain my recent joint work with NaiChung Conan Leung that for a fixed prequantum line bundle L over a hyperKahler manifold X, there is a natural but hidden Sp(1)-symmetry intertwining a twistor family of Spin^c-Dirac operators on the spaces of L-valued (0, *)-forms on X. It leads to a proposed definition of the morphism space of a brane-conjugate brane system for a space-filling coisotropic A-brane on a symplectic manifold, and it establishes geometric quantization via brane quantization on a hyperKahler manifold.
END:VEVENT
BEGIN:VEVENT
DTSTART:20221229T160000
DTEND:20221229T180000
DTSTAMP:20221228T150000Z
UID:e66dc36695e01336a180c5c7f0512c5d@cgp.ibs.re.kr
SUMMARY:Negatively curved asymptotically harmonic manifolds with non-uniform lattices and related rigidity phenomena
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Jaelin Kim\n\nEvent: CGP Seminar\n\nAbstract: Asymptotically harmonic manifolds are first introduced by F. Ledrappier in the ergodic-theoretical context.We shall recall the importance of asymptotically harmonic manifolds with negative curvature from a dynamical viewpoint, with their relationship with Katok’s rigidity conjecture on Liouville measures.We also verify characterizations of asymptotically harmonic manifolds, which reveal their geometric, dynamical, and stochastic aspects.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230105T160000
DTEND:20230105T180000
DTSTAMP:20230104T150000Z
UID:f37eb3ad76b5f4810884fe289f4e5e9f@cgp.ibs.re.kr
SUMMARY:Deviation spectrum of Birkhoff integrals for locally Hamiltonian flows on compact surfaces
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Minsung Kim\n\nEvent: CGP Seminar\n\nAbstract: In this talk, we will introduce the deviation of Birkhoff integrals for locally Hamiltonian flows on compact surfaces and recent related results. In our work, we study the spectrum for deviations of Birkhoff integrals beyond the case where the observable vanishes at the singularities by improving the result of G. Forni (02'). New developments include a better understanding of the asymptotics at singularities and the appearance of new exponents in the deviation spectrum. This is joint work with Krzysztof Frączek.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230202T160000
DTEND:20230202T180000
DTSTAMP:20230201T150000Z
UID:bc1e95bcad787d7c785887572a6f131c@cgp.ibs.re.kr
SUMMARY:The Operad of Series Parallel posets and an identity of Ramanujan
LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium
DESCRIPTION:Speaker: Eric Rubiel Dolores Cuenca\n\nEvent: CGP Seminar\n\nAbstract: We introduce the operad of series parallel posets and study algebras over this operad. The main application of out theory is a new proof of several statements by Ramanujan.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230201T170000
DTEND:20230201T180000
DTSTAMP:20230131T150000Z
UID:f259c42fc182792f5476c0dba7c7a336@cgp.ibs.re.kr
SUMMARY:Castelnuovo Bound and Higher Genus Gromov-Witten Invariants of Quintic 3-fold
LOCATION:Online Streaming
DESCRIPTION:Speaker: Yongbin Ruan\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: One of most difficult problems in geometry and physics is to compute higher genus Gromov-Witten (GW) invariants of compact Calabi-Yau 3-folds such as quintic 3-folds. The effort to solve the problem leads to the inventions of several subjects such as mirror symmetry and FJRW theory. Almost twenty years ago, physicist Albrecht Klemm and his group shocked the community to produce explicit predications of higher genus GW invariants up to $g=51$! Their calculation is based on five mathematical conjectures, four BCOV conjectures from B-model and one A-model conjecture called Castelnuovo bound. Several years ago, a spectacular progress has been made to solve four BCOV conjectures. In this talk, I will report the solution of Castelnuovo bound conjecture. This is a joint work with Zhiyu Liu.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230419T170000
DTEND:20230419T180000
DTSTAMP:20230418T150000Z
UID:c521f650c13a2c026330a84f60f2e741@cgp.ibs.re.kr
SUMMARY:Orthosymplectic bow varieties
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hiraku Nakajima\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Bow varieties are introduced by Cherkis as the analog of ADHMN description of instantons on multi-Taub NUT spaces for unitary groups. They are closely related to quiver varieties and Coulomb branches of quiver gauge theories of affine type A. They are also useful to understand brane configurations that appeared in Hanany-Witten's work. In an on-going joint project with Finkelberg and Hanany, we introduce their variants, called orthosymplectic bow varieties. In this talk, I will give introduction to orthosymplectic bow varieties.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230322T170000
DTEND:20230322T180000
DTSTAMP:20230321T150000Z
UID:336931b9d2f0776e4a24527c7bc77c0a@cgp.ibs.re.kr
SUMMARY:Holography with End-of-the-World Branes and Quantum Entanglement
LOCATION:Online Streaming
DESCRIPTION:Speaker: Tadashi Takayanagi\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Holography relates quantum many-body systems to gravitational theories. Quantum entanglement plays a key role to explain how the spacetime geometries in gravity emerge from quantum systems. A new class of holography can be found by introducing so called end-of-the-world branes and has been actively studied recently. Such holographic models describe quantum systems with boundaries, such as boundary conformal field theories (BCFTs), where the boundary dynamics is described by gravitational degrees of freedom localized on the branes. Considerations of quantum entanglement in these setups help us to have deep insights on the black hole information problem. At the same time, they can also be used to analyze quantum information aspects of non-equilibrium processes. In this talk, I will explain these developments.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230224T160000
DTEND:20230224T180000
DTSTAMP:20230223T150000Z
UID:549555163ac9ad8dd92688848f12276a@cgp.ibs.re.kr
SUMMARY:ACC of plc thresholds
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We introduce potential log canonical threshold and prove that the set of those thresholds satisfies the ascending chain condition (ACC). We also study the relation with the existence of complements.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230215T170000
DTEND:20230215T180000
DTSTAMP:20230214T150000Z
UID:3985e1a91419aeba070d0c4fab6e41c5@cgp.ibs.re.kr
SUMMARY:Infra-red phases of class R theories
LOCATION:Online Streaming
DESCRIPTION:Speaker: Dongmin Gang\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Motivated by the physics of M5-branes in M-theory, there is a class of 3D gauge theories (called class R theories) labeled by 3-manifolds. After briefly reviewing the field theoretic construction, I will explain how to understand various infra-red (macroscopic) behavior of the 3D gauge theories from basic topological properties of 3-manifolds.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230308T170000
DTEND:20230308T180000
DTSTAMP:20230307T150000Z
UID:f16e0a42eb900ddedb7411179fe8a0c2@cgp.ibs.re.kr
SUMMARY:What can the working (pure) mathematician expect from deep learning?
LOCATION:Online Streaming
DESCRIPTION:Speaker: Geordie Williamson\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Deep learning (the training of deep neural nets) is a simple idea, which has had many extraordinary applications throughout industry and science over the last decade. In mathematics the impact has so-far been modest at best. I will discuss a few instances where it has proved useful, and led to interesting (pure) mathematics. I will also discuss what can be learned from these examples, and try to guess an answer to the question in the title. I will also reflect on my experience as a pure mathematician interacting with deep learning.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230314T160000
DTEND:20230314T180000
DTSTAMP:20230313T150000Z
UID:2305b513773cb3b998fd2667a1b8b6a9@cgp.ibs.re.kr
SUMMARY:Bounds of weighted complete intersections and their Hodge numbers
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Victor Przyjalkowski\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We observe recent results that give effective bounds on smooth Fano weighted complete intersections. We compute their Hodge levels --- numbers that show how narrow their Hodgediamonds they can have. Based on this we classify smooth Fano weighted complete intersections with small Hodge levels. It turns out that all of them have categorical nature.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230330T160000
DTEND:20230330T180000
DTSTAMP:20230329T150000Z
UID:6fb38f3d4ce608bc9d7f98c94f6bd0d7@cgp.ibs.re.kr
SUMMARY:SIMPLICIAL DECOMPOSITIONS OF WEINSTEIN SECTORS AND TANGLE CONTACT HOMOLOGY
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Johan Asplund\n\nEvent: CGP Seminar\n\nAbstract: In this talk we introduce simplicial decompositions and give a brief account for asurgery-type decomposition of Weinstein sectors that generalize the notion of Weinstein connectedsum. Simplicial decompositions are proven to correspond (in the homotopical sense) to certain sectorialcovers of Weinstein sectors as defined by Ganatra–Pardon–Shende. Our main result that theChekanov–Eliashberg dg-algebra (with or without loop space coefficients) satisfies a gluing formulawith respect to simplicial decompositions. As an application we define knot contact homology oftangles and obtain a gluing formula for knot contact homology of knots that are presented as theresult of gluing two tangles.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230425T090000
DTEND:20230425T101500
DTSTAMP:20230424T150000Z
UID:280477cf8cc9c37989aaff586a266853@cgp.ibs.re.kr
SUMMARY:Lecture Series I (Part 1) Mapping class groups of surfaces: subgroups and infinitesimal representations
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Gwénaël Massuyeau\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: By classical results of Dehn and Nielsen, the mapping class group $\mathcal{M}(\Sigma)$ of a surface $\Sigma$ can be studied through its action on the fundamental group $\pi_1(\Sigma)$. In the first talk, we will review all the necessary material on mapping class groups (including their generation by Dehn twists), and we will explain how the Dehn--Nielsen representation of $\mathcal{M}(\Sigma)$ can be expanded diagrammatically by considering the action of $\mathcal{M}(\Sigma)$ on the Malcev Lie algebra of $\pi_1(\Sigma)$. In the second talk, we will mention a few applications of this “infinitesimal” version of the Dehn--Nielsen representation for certain subgroups of $\mathcal{M}(\Sigma)$. In particular, we shall use it to reformulate and extend previous works of Dimca-Hain-Papadima, Morita-Sakasai-Suzuki and Nozaki-Sato-Suzuki on the abelianization of the “Johnson kernel” (which is the subgroup of $\mathcal{M}(\Sigma)$ generated by Dehn twists along separating curves). The latter part is joint work with Quentin Faes.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230425T154500
DTEND:20230425T164500
DTSTAMP:20230424T150000Z
UID:336180aa3a4ed3a0417d1a13d9e06e1c@cgp.ibs.re.kr
SUMMARY:Marked graph mosaics
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Seonmi Choi\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: Lomonaco and Kauffman introduced a knot mosaic system to define a quantum knot system. Kuriya and Shehab proved Lomonaco-Kauffman conjecture which means that knot mosaic type is a complete invariant of tame knots. The mosaic number of a knot K is the smallest integer n for which K can be represented on an n × n mosaic board. In this talk, we consider the notion of mosaic diagrams for surface-links using marked graph diagrams. We establish bounds, in some cases tight, on the mosaic numbers for the surface-links with ch-index up to 10. As an application, we use mosaic diagrams to enhance the kei counting invariant for unoriented surface-links as well as classical knots and links. This is joint work with Sam Nelson.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230427T154500
DTEND:20230427T164500
DTSTAMP:20230426T150000Z
UID:520c92c44b06f87b6ed12a4e7b0b1542@cgp.ibs.re.kr
SUMMARY:One stabilization is not enough for exotic contractible 4-manifolds
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Sungkyung Kang\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: We construct the first example of an exotic pair of contractible 4-manifolds which remain exotic after one stabilization.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230426T091500
DTEND:20230426T101500
DTSTAMP:20230425T150000Z
UID:88b0d77adb3e151fc783b0e3d4a651e1@cgp.ibs.re.kr
SUMMARY:Groups acting on the circle with invariant veering pairs
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Hongtaek Jung\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: T he fundamental groups of many 3-manifolds can act on a circle. Examples include closed orientable 3-manifolds with taut foliations, closed orientable 3-manifolds with pseudo-Anosov flows, hyperbolic 3-manifolds with quasi-geodesic flows and so on. A fascinating feature is that all of these actions leave some circle laminations invariant. In this talk, I will present the inverse problem, asking whether a given group is the fundamental group of a 3-manifold if it acts on a circle preserving circle laminations. T he answer to this problem very depends on properties of the invariant laminations. I will introduce veering pair of circle laminations, which is motivated by recent work of Schleimer and Segerman on veering triangulations, and show that a group acting on a circle with an invariant veering pair must be the fundamental group of an irreducible 3-orbifold. T his is joint work with Hyungryul Baik and KyeongRo Kim.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230427T141500
DTEND:20230427T151500
DTSTAMP:20230426T150000Z
UID:3f117f8bbb0d9557566caa7acb00b173@cgp.ibs.re.kr
SUMMARY:On homological representations for braid groups and mapping class groups
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Arthur Soulié\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: I will describe a general construction of homological representations for families of motion groups or mapping class groups, including the families of braid groups, surface braid groups and loop braid groups. This recovers the well-known constructions of Lawrence-Bigelow, and in this sense it unifies these constructions. I will also discuss indecomposability and irreducibility of these representations. The construction is moreover “global” in the sense that, for each dimension d, it is a functor on a category whose automorphism groups are all d-dimensional motion groups and mapping class groups, and which also carries a richer structure. Using this richer structure, I will discuss polynomiality of these families of representations, and use this to prove twisted homological stability for the braid groups with coefficients in any one of the Lawrence-Bigelow representations.All this represents a joint work with Martin Palmer.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230427T104500
DTEND:20230427T114500
DTSTAMP:20230426T150000Z
UID:66002c166240b7d562cb5919b195a18f@cgp.ibs.re.kr
SUMMARY:On a smoothing technique of topological surfaces in 4-manifolds
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Byeohri Kim\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: In this talk, I will talk about a new smoothing technique for topologically embedded surfaces or disks in smooth 4-manifolds that provides topological isotopies to smooth surfaces. This result is motivated from recent David Gabai's Light bulb theorem. As an application, we can get some results which leading us to "topological = smooth" in dimension 4 for isotopy classifications of certain disks and spheres. This is a joint work with J. C. Cha.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230509T160000
DTEND:20230509T180000
DTSTAMP:20230508T150000Z
UID:b791966a5726e3d253b0ac4a0421107a@cgp.ibs.re.kr
SUMMARY:Birational geometry of del Pezzo surfaces
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: A del Pezzo surface is a smooth projective surface with ample anticanonical divisor.Over an algebraically closed field, any surface like this is rational. However, without this assumption del Pezzo surfaces exhibit very interesting birational properties. I will survey some old and new results about birational geometry of del Pezzo surfaces over arbitrary fields, mostly focusing on Severi--Brauer surfaces, quadrics, and del Pezzo surfaces of degree 4.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230306T100000
DTEND:20230306T110000
DTSTAMP:20230305T150000Z
UID:71d22bd74604680d15e133596d5c6af2@cgp.ibs.re.kr
SUMMARY:Translated points and Contact dynamical systems
LOCATION:Online Streaming
DESCRIPTION:Speaker: Dylan Cant\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Contact dynamical systems can be defined as the 1-parameter families of diffeomorphisms which preserve a contact distribution. Such systems appear throughout mathematics, in particular geodesic flows in Riemannian geometry and linear Hamiltonian flows in classical mechanics. It was conjectured that these dynamical systems always had “translated points,” a generalization of the notion of fixed point. In my talk, I will give an overview of the history of translated points and I will present my recent work disproving the aforementioned conjecture, namely by describing the construction of a contact system without translated points.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230405T170000
DTEND:20230405T180000
DTSTAMP:20230404T150000Z
UID:b19ef6db850d4a10001524ead3e35037@cgp.ibs.re.kr
SUMMARY:What is a holomorphic quantum modular form?
LOCATION:Online Streaming
DESCRIPTION:Speaker: Stavros Garoufalidis\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Holomorphic quantum modular forms arose naturally from asymptotic questions of quantum invariants in dimension three. HQMFs, along with resurgence and p-adic analytic continuation are three known realizations of functions that appear in mathematical physics. I will give a historical introduction on the subject, drawn from many years of joint work with Don Zagier, and illustrated with examples of the simplest hyperbolic 3-manifolds.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230420T160000
DTEND:20230420T180000
DTSTAMP:20230419T150000Z
UID:f9e1ada3d33956cf0ffe0d4e5019208c@cgp.ibs.re.kr
SUMMARY:Operator algebras in AdS/CFT: bulk reconstruction, quantum extremal surfaces, and baby universe
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Monica Jinwoo Kang\n\nEvent: CGP Seminar\n\nAbstract: From the AdS/CFT correspondence, we have a holographic isometric map arising between the local operator algebras of the bulk theory and the boundary conformal field theory. I will explain how operator algebras can naturally be used for understanding spacetime theories in this physical context to unveil some structures of quantum gravity. In particular, I will focus on building the formalism on the bulk reconstruction from the boundary operators to the bulk operators and explain how quantum extremal surfaces aid in studying the relative entropy of the bulk and the boundary. I will further describe how we can understand the formulation in low-dimensions to describe the topology changes of the bulk.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230425T141500
DTEND:20230425T151500
DTSTAMP:20230424T150000Z
UID:5a1d57fbc16b9198f18fe2a4ff53396f@cgp.ibs.re.kr
SUMMARY:Homology cylinder, as generalization of both string link and mapping class group
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Minkyoung Song\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: The homology cobordism group of 3-dimensional homology cylinders can be considered as an enlargement of both the mapping class group of a surface and the concordance group of string links. In this talk, I introduce history and notion of homology cylinders and their homology cobordism group. Also, we consider invariants related to lower central series of a free group: Johnson homomorphisms and Morita homomorphisms of a mapping class group, Milnor invariants and Orr invariants of (string) links. The invariants give rise to filtrations. We extend those invariants and filtrations to homology cylinders and compare them. We get relations of the filtrations to automorphism groups of free nilpotent groups, and free Lie algebras.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230425T104500
DTEND:20230425T120000
DTSTAMP:20230424T150000Z
UID:29294ecf3f780d542e9df004af86e637@cgp.ibs.re.kr
SUMMARY:Lecture Series II (Part 1) On ribbon Yetter-Drinfeld modules and tangle invariants
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Yuka Kotorii\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: Reshetikhin and Turaev introduced the notion of ribbon Hopf algebra and showed that the category of finite-dimensional modules over a ribbon Hopf algebra has a ribbon category structure. Since the category of framed, oriented tangles is a free ribbon category generated by one object, a ribbon category yields a functor from the tangle category to the category of finite-dimensional vector spaces, and thus gives a functorial invariants of tangles. In this talk, we define notions of ribbon objects in a monoidal category. These constructions give ribbon categories from a monoidal category. We apply this construction to the braided monoidal category of Yetter-Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter-Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of framed tangles. This research is joint work with Kazuo Habiro.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230404T160000
DTEND:20230404T180000
DTSTAMP:20230403T150000Z
UID:9da0ea28efb549703db8a4f8da72d197@cgp.ibs.re.kr
SUMMARY:Flags on Fano 3-fold hypersurfaces
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Livia Campo\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The existence of Kaehler-Einstein metrics on Fano 3-folds can be determined by studying some positive numbers called stability thresholds. K-stability is ensured if appropriate bounds can be found for these thresholds. An effective way to verify such bounds is to construct flags of point-curve-surface inside the Fano 3-folds. This approach was initiated by Abban-Zhuang, and allows us to restrict the computation of bounds for stability thresholds only on flags. We employ this machinery to prove K-stability of terminal quasi-smooth Fano 3-fold hypersurfaces. Many of these varieties had been attacked by Kim-Okada-Won using log canonical thresholds. In this talk I will tackle the remaining Fano hypersurfaces via Abban-Zhuang Theory.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230426T141500
DTEND:20230426T151500
DTSTAMP:20230425T150000Z
UID:304feb5ce7027db790393795be28a693@cgp.ibs.re.kr
SUMMARY:On the rigidity of three-dimensional Polyhedra
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Seonhwa Kim\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: We demonstrate that a three-dimensional polyhedron can be uniquely determined by its dihedral angles and edge lengths, regardless of whether it is non-convex or self-intersecting. We achieve this under three plausible sufficient conditions: (1) the polyhedron is composed solely of convex faces, (2) there are no partially-flat vertices, and (3) any triple of vertices is not collinear. Our method is universally valid for Euclidean, spherical, and hyperbolic geometry. Notably, our approach is entirely different from the argument of the Cauchy rigidity theorem. We provide various counterexamples that arise when our conditions are violated, as well as several interesting corollaries, and pose further questions and conjectures.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230427T090000
DTEND:20230427T101500
DTSTAMP:20230426T150000Z
UID:1bd21b3a4b7ec4ab308f55c769ef530e@cgp.ibs.re.kr
SUMMARY:Lecture Series I (Part 2) Mapping class groups of surfaces: subgroups and infinitesimal representations
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Gwénaël Massuyeau\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: By classical results of Dehn and Nielsen, the mapping class group $\mathcal{M}(\Sigma)$ of a surface $\Sigma$ can be studied through its action on the fundamental group $\pi_1(\Sigma)$. In the first talk, we will review all the necessary material on mapping class groups (including their generation by Dehn twists), and we will explain how the Dehn--Nielsen representation of $\mathcal{M}(\Sigma)$ can be expanded diagrammatically by considering the action of $\mathcal{M}(\Sigma)$ on the Malcev Lie algebra of $\pi_1(\Sigma)$. In the second talk, we will mention a few applications of this “infinitesimal” version of the Dehn--Nielsen representation for certain subgroups of $\mathcal{M}(\Sigma)$. In particular, we shall use it to reformulate and extend previous works of Dimca-Hain-Papadima, Morita-Sakasai-Suzuki and Nozaki-Sato-Suzuki on the abelianization of the “Johnson kernel” (which is the subgroup of $\mathcal{M}(\Sigma)$ generated by Dehn twists along separating curves). The latter part is joint work with Quentin Faes.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230426T104500
DTEND:20230426T120000
DTSTAMP:20230425T150000Z
UID:4886920dd0e33a72af5a1c0b2f99ca0f@cgp.ibs.re.kr
SUMMARY:Lecture Series II (Part 2) On ribbon Yetter-Drinfeld modules and tangle invariants
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Yuka Kotorii\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: Reshetikhin and Turaev introduced the notion of ribbon Hopf algebra and showed that the category of finite-dimensional modules over a ribbon Hopf algebra has a ribbon category structure. Since the category of framed, oriented tangles is a free ribbon category generated by one object, a ribbon category yields a functor from the tangle category to the category of finite-dimensional vector spaces, and thus gives a functorial invariants of tangles. In this talk, we define notions of ribbon objects in a monoidal category. These constructions give ribbon categories from a monoidal category. We apply this construction to the braided monoidal category of Yetter-Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter-Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of framed tangles. This research is joint work with Kazuo Habiro.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230411T160000
DTEND:20230411T180000
DTSTAMP:20230410T150000Z
UID:50ac58eaede39759ad0ace8285d33eee@cgp.ibs.re.kr
SUMMARY:Fano manifolds with big tangent bundles
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Jeong-Seop Kim\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Mori proves that the projective spaces are the only projective manifolds with ample tangent bundles over the complex number field. Also, Campana and Peternell conjecture that the rational homogeneous spaces are the only Fano manifolds with nef tangent bundles, and the conjecture is proved for dimension up to 5. Recently, there have been some results on big tangent bundles. For example, toric manifolds, and some Fano twofolds or threefolds of higher degree have big tangent bundles. In this talk, I will review the progress, and explain a method to determine the bigness of a tangent bundle developed by Höring, Liu, and Shao. Then I will introduce a result on Fano threefold with Picard number 2. This talk is based on joint work with Hosung Kim and Yongnam Lee.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230512T160000
DTEND:20230512T180000
DTSTAMP:20230511T150000Z
UID:53c5e3420d31f6d464f320b5957e9b48@cgp.ibs.re.kr
SUMMARY:Rationality problem for conic bundles
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: I am going to discuss applications of Sarkisov program to the rationality problem of three-dimensional algebraic varieties having conic bundle structures. I will give a survey of the problem and present a few new results. The talk is based on the work in progress joint with V. Shokurov.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230426T154500
DTEND:20230426T164500
DTSTAMP:20230425T150000Z
UID:622f76fd408148c16acab974d927960e@cgp.ibs.re.kr
SUMMARY:Normal generators of mapping class groups
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Hyungryul Baik\n\nEvent: Mini-workshop on Low-dimensional Topology\n\nAbstract: We will discuss how to show a given mapping class is and is not a normal generator of the mapping class group, and then discuss related open and closed questions.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230829T140000
DTEND:20230829T160000
DTSTAMP:20230828T150000Z
UID:ba94cd0bc1da9bb964bf78cb2bbfbf5a@cgp.ibs.re.kr
SUMMARY:Frobenius splitting and wonderful compactifications Ⅰ
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Michel Brion\n\nEvent: Intensive Lecture Series\n\nAbstract: The talk will first give an introduction toFrobenius splitting, a notion of algebraic geometry inpositive characteristic. It will then present applicationsto the geometry of wonderful compactifications ofsemisimple groups, in arbitrary characteristic.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230830T140000
DTEND:20230830T160000
DTSTAMP:20230829T150000Z
UID:e73faf9e33b3ef423ade776b9424572c@cgp.ibs.re.kr
SUMMARY:Frobenius splitting and wonderful compactifications Ⅱ
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Michel Brion\n\nEvent: Intensive Lecture Series\n\nAbstract: The talk will first give an introduction toFrobenius splitting, a notion of algebraic geometry inpositive characteristic. It will then present applicationsto the geometry of wonderful compactifications ofsemisimple groups, in arbitrary characteristic.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230831T140000
DTEND:20230831T160000
DTSTAMP:20230830T150000Z
UID:fe944c1b1c54c8e4ca68d3920b141be0@cgp.ibs.re.kr
SUMMARY:Frobenius splitting and wonderful compactifications Ⅲ
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Michel Brion\n\nEvent: Intensive Lecture Series\n\nAbstract: The talk will first give an introduction toFrobenius splitting, a notion of algebraic geometry inpositive characteristic. It will then present applicationsto the geometry of wonderful compactifications ofsemisimple groups, in arbitrary characteristic.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230829T160000
DTEND:20230829T180000
DTSTAMP:20230828T150000Z
UID:1495ca1543e02b90342b281b25c8ce5b@cgp.ibs.re.kr
SUMMARY:Non-maximality of algebraic subgroups of Cremona groups
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Susanna Zimmermann\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: The Cremona group is the group of birational maps of a projective space. It is an ancient aim to classify finite subgroups of Cremona groups, or more generally, algebraic groups acting birationally and faithfully on projective spaces. The connected ones are classified in dimension 2 over any perfect field and in dimension 3 over algebraically closed fields of characteristic zero. The classification shows that they are always contained in a maximal connected algebraic subgroup. I explain in this talk that in dimension 5 and higher, there are algebraic subgroups that are not contained in any maximal algebraic subgroups.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230327T100000
DTEND:20230327T110000
DTSTAMP:20230326T150000Z
UID:72bc450f6b7a084c4efab0507397395f@cgp.ibs.re.kr
SUMMARY:Homological Mirror Symmetry of Degenerate Cusp Singularities and their Representations
LOCATION:Online Streaming
DESCRIPTION:Speaker: Kyungmin Rho\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Venue: Online Streaming + Math. Bldg. #404Burban-Drozd (2017) introduced the decorated quiver to represent Cohen-Macaulay modules over degenerate cusp singularities. We review their construction and give its algebraic geometric interpretation using degenerate vector bundles. For some degenerate cusps which have a Riemann surface as their mirror, we also describe how to represent Lagrangians of the surface on the corresponding decorated quiver.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230413T160000
DTEND:20230413T180000
DTSTAMP:20230412T150000Z
UID:0a0d9f08ac6f3190d96a2614f8cfbde4@cgp.ibs.re.kr
SUMMARY:Wrapped Fukaya category of plumbings of cotangent bundles of spheres
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Dogancan Karabas\n\nEvent: CGP Seminar\n\nAbstract: Ganatra-Pardon-Shende introduced a local-to-global way to compute the wrapped Fukaya category of Weinstein manifolds by taking the homotopy colimit of the wrapped Fukaya categories of their sectorial coverings. In the joint work with Sangjin Lee, we described a practical formula for the homotopy colimit of dg categories. As an application, I will explain our result describing the wrapped Fukaya category of plumbings (along any quiver) of cotangent bundles of spheres of any dimension as perfect modules over Ginzburg dg algebras (work in progress with Sangjin Lee).
END:VEVENT
BEGIN:VEVENT
DTSTART:20230503T170000
DTEND:20230503T180000
DTSTAMP:20230502T150000Z
UID:14776934359e66e535a245540ca1222d@cgp.ibs.re.kr
SUMMARY:Twisted Real quasi-elliptic cohomology
LOCATION:Online Streaming
DESCRIPTION:Speaker: Zhen Huan\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic cohomology theories. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. In this talk we construct twisted Real quasi-elliptic cohomology as the twisted KR-theory of loop groupoids. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we construct Real analogues of the string power operation of quasi-elliptic cohomology. We also explore the relation of the theory to the Tate curve. This is joint work with Matthew Spong and Matthew Young.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230405T140000
DTEND:20230405T160000
DTSTAMP:20230404T150000Z
UID:6794f7b211a554f92c94e7a6495912ce@cgp.ibs.re.kr
SUMMARY:Organizational Meeting
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: Organizational MeetingReading Seminar on Quantum Entanglemnt and related topics.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230412T140000
DTEND:20230412T160000
DTSTAMP:20230411T150000Z
UID:c7060bc1e0b4d5108bd98c8f1dedf269@cgp.ibs.re.kr
SUMMARY:Quantum Entanglement and related topics
LOCATION:CGP Delta
DESCRIPTION:Speaker: Hisayoshi Muraki\n\nEvent: Director's Seminar\n\nAbstract: This seminar will be a continuous series of talks on "Quantum Entanglement and related topics". Quantum entanglement is one of the most fundamental features of quantum mechanics. It is a physical phenomenon that performing a local measure may instantaneously affect the outcome of local measurements far away. The concept of entanglement occurs in various areas such as in quantum information theory, communication and quantum computing. A rich field of research concerns the understanding of the role of entanglement in many body systems. In that regard, the theory can be applied to the study of knots and links in 3 manifolds by the `replica trick'. In this seminar, we will aim at learning the basics of quantum entanglement theory, understanding their applications to related areas such as Chern-Simons theory, and black hole dynamics and searching for other possible mathematical applications.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230417T170000
DTEND:20230417T180000
DTSTAMP:20230416T150000Z
UID:35051c35683f9504bcd7ad272453e52c@cgp.ibs.re.kr
SUMMARY:A universal formula for the density of states with global symmetry
LOCATION:Math. Bldg. #402
DESCRIPTION:Speaker: Monica Jinwoo Kang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Venue: Online streaming + On-site(Math. Bldg. #402)/ It has long been the case that representation theory played an important role in understanding the spectrum of states in physics. I will describe how it can be used to describe some universal aspect of d-dimensional unitary conformal field theories with a global symmetry group, which can be a discrete group or a compact Lie group.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230424T100000
DTEND:20230424T110000
DTSTAMP:20230423T150000Z
UID:9b6c2c7862439cf0c3ca6e083f3a1015@cgp.ibs.re.kr
SUMMARY:Equivariant Structures in Symplectic Floer Homotopy
LOCATION:Online Streaming
DESCRIPTION:Speaker: Semon Rezchikov\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will discuss a construction of a genuine Z/kZ equivariant homotopy type associated to the k-th iterate of a Hamiltonian diffeomorphism. Making sense of this construction requires an extension of the Cohen-Jones-Segal construction of Floer homotopy types to the setting of virtually smooth flow categories, in which the morphism spaces (i.e. moduli spaces of flow lines) are no longer smooth manifolds with corners, but instead admit a compatible system of Kuranishi charts. This construction elucidates obstruction-bundle computations in equivariant Morse theory, and will be motivated by connections to noncommutative hodge theory and to string topology.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230523T160000
DTEND:20230523T180000
DTSTAMP:20230522T150000Z
UID:13e07e7905cc3d1af2bce794cde7d46a@cgp.ibs.re.kr
SUMMARY:Minimal rational curves on complete symmetric varieties
LOCATION:Math. Bldg. #404
DESCRIPTION:Speaker: Shinyoung Kim\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents, say VMRT. In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves. We relate these results to the restricted root system of the associated symmetric space. In particular, for certain Fano wonderful symmetric varieties, the VMRT has two connected components. Moreover, VMRT is Legandrian when restricted root system is not of type A. This is a joint work with M.Brion and N. Perrin.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230419T140000
DTEND:20230419T160000
DTSTAMP:20230418T150000Z
UID:c42220bcc178e0e2f0f170ced023ca4b@cgp.ibs.re.kr
SUMMARY:Quantum Entanglement and related topics
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: Director's Seminar\n\nAbstract: This seminar will be a continuous series of talks on "Quantum Entanglement and related topics". Quantum entanglement is one of the most fundamental features of quantum mechanics. It is a physical phenomenon that performing a local measure may instantaneously affect the outcome of local measurements far away. The concept of entanglement occurs in various areas such as in quantum information theory, communication and quantum computing. A rich field of research concerns the understanding of the role of entanglement in many body systems. In that regard, the theory can be applied to the study of knots and links in 3 manifolds by the `replica trick'. In this seminar, we will aim at learning the basics of quantum entanglement theory, understanding their applications to related areas such as Chern-Simons theory, and black hole dynamics and searching for other possible mathematical applications.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230515T100000
DTEND:20230515T110000
DTSTAMP:20230514T150000Z
UID:491facf49d8ce3f60deaf83c14156e57@cgp.ibs.re.kr
SUMMARY:Moduli of curves of genus 11, and prime Fano 3-folds of adjacent poristic genera, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Shigeru Mukai\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Let Kg ⊂ Mg be the locus of curves of genus g ≥ 2 which are embeddablein a K3 surface. Kg is of expected dimension min{3g − 3, g + 19} exceptfor g = 10, 12, and one less for g = 10, 12. This implies the unirulednessof M11 for g = 11 (Mori-M. 1983). If a curve C in K10 does not belongto the BN-subloci [2 × 6] or [3 × 4], then C is a (complete) linear sectionof the homogeneous contact variety of type G2.In the case of genus 12, the 30-dimensional K12 contains four subloci[Clebsch-L¨uroth], [2 × 7], [3 × 5] and [4 × 4], corresponding to four onenodal degenerations of prime Fano 3-folds V22. If a curve C in K12 belongto none of these loci, then C is the intersection of two anti-canonicalmembers of V22 in a unique way (the last linear section theorem).
END:VEVENT
BEGIN:VEVENT
DTSTART:20230515T150000
DTEND:20230515T160000
DTSTAMP:20230514T150000Z
UID:8f51e8b82ca1f6d49b8959cb4045cd26@cgp.ibs.re.kr
SUMMARY:Moduli of curves of genus 11, and prime Fano 3-folds of adjacent poristic genera, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Shigeru Mukai\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Let Kg ⊂ Mg be the locus of curves of genus g ≥ 2 which are embeddablein a K3 surface. Kg is of expected dimension min{3g − 3, g + 19} exceptfor g = 10, 12, and one less for g = 10, 12. This implies the unirulednessof M11 for g = 11 (Mori-M. 1983). If a curve C in K10 does not belongto the BN-subloci [2 × 6] or [3 × 4], then C is a (complete) linear sectionof the homogeneous contact variety of type G2.In the case of genus 12, the 30-dimensional K12 contains four subloci[Clebsch-L¨uroth], [2 × 7], [3 × 5] and [4 × 4], corresponding to four onenodal degenerations of prime Fano 3-folds V22. If a curve C in K12 belongto none of these loci, then C is the intersection of two anti-canonicalmembers of V22 in a unique way (the last linear section theorem).
END:VEVENT
BEGIN:VEVENT
DTSTART:20230515T112000
DTEND:20230515T122000
DTSTAMP:20230514T150000Z
UID:39cc63753894e880958bdca169302897@cgp.ibs.re.kr
SUMMARY:The Calabi problem for Fano threefolds, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Kento Fujita\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: There are 105 irreducible families of smooth Fano threefolds, which havebeen classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kaehler-Einstein metricor not. This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Suess and Nivedita Viswanathan
END:VEVENT
BEGIN:VEVENT
DTSTART:20230515T163000
DTEND:20230515T173000
DTSTAMP:20230514T150000Z
UID:06b15716e32b18e76435df43d262b936@cgp.ibs.re.kr
SUMMARY:The Calabi problem for Fano threefolds, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Kento Fujita\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: There are 105 irreducible families of smooth Fano threefolds, which havebeen classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kaehler-Einstein metricor not. This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Suess and Nivedita Viswanathan
END:VEVENT
BEGIN:VEVENT
DTSTART:20230516T100000
DTEND:20230516T110000
DTSTAMP:20230515T150000Z
UID:d270dcad6c29f6e6fc6bc91483f1909e@cgp.ibs.re.kr
SUMMARY:On the classification of singular Fano threefolds, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: I will give an overview of the current state of the problem of classificationof singular Fano threefolds.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230516T150000
DTEND:20230516T160000
DTSTAMP:20230515T150000Z
UID:fa4f79bd6963415737e775f13ef06ce1@cgp.ibs.re.kr
SUMMARY:On the classification of singular Fano threefolds, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: I will give an overview of the current state of the problem of classificationof singular Fano threefolds.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230516T112000
DTEND:20230516T122000
DTSTAMP:20230515T150000Z
UID:901f4a2251e05ea0e46bdc9449982581@cgp.ibs.re.kr
SUMMARY:Conic bundles, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Consider a conic bundle over a smooth incomplete curve C, i.e. a smoothsurface S with a proper surjective morphism to C such that the pushforward of the structure sheaf of S coincides with the structure sheaf ofC, and the anticanonical class of S is ample over C. If the base field isperfect, a conic bundle always extends to a conic bundle over a completionof C. I will tell about a necessary and sufficient condition for the existenceof such an extension in the case of an arbitrary base field. The talk is basedon a joint work in progress with V. Vologodsky.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230516T163000
DTEND:20230516T173000
DTSTAMP:20230515T150000Z
UID:e2bc2b7cd198c1249026bdbbffb28f40@cgp.ibs.re.kr
SUMMARY:Conic bundles, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Constantin Shramov\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Consider a conic bundle over a smooth incomplete curve C, i.e. a smoothsurface S with a proper surjective morphism to C such that the pushforward of the structure sheaf of S coincides with the structure sheaf ofC, and the anticanonical class of S is ample over C. If the base field isperfect, a conic bundle always extends to a conic bundle over a completionof C. I will tell about a necessary and sufficient condition for the existenceof such an extension in the case of an arbitrary base field. The talk is basedon a joint work in progress with V. Vologodsky.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230517T100000
DTEND:20230517T110000
DTSTAMP:20230516T150000Z
UID:802af40cfce6504055635ff03eb8a8ad@cgp.ibs.re.kr
SUMMARY:Symmetric tensors on the intersection of two quadrics and Lagrangian fibration, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Arnaud Beauville\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Let X be a n-dimensional (smooth) intersection of two quadrics, and letT∗X be its cotangent bundle. I will show that the algebra of symmetrictensors on X is a polynomial algebra in n variables. The correspondingmap T∗X → Cn is a Lagrangian fibration, which admits an explicit geometric description; its general fiber is an open subset of an abelian variety,again with a precise geometric description.This is joint work with A. Etesse, A. H¨oring, J. Liu, C. Voisin.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230518T100000
DTEND:20230518T110000
DTSTAMP:20230517T150000Z
UID:109f5e7e4d6367771a692211bb1b0830@cgp.ibs.re.kr
SUMMARY:Symmetric tensors on the intersection of two quadrics and Lagrangian fibration, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Arnaud Beauville\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: Let X be a n-dimensional (smooth) intersection of two quadrics, and letT∗X be its cotangent bundle. I will show that the algebra of symmetrictensors on X is a polynomial algebra in n variables. The correspondingmap T∗X → Cn is a Lagrangian fibration, which admits an explicit geometric description; its general fiber is an open subset of an abelian variety,again with a precise geometric description.This is joint work with A. Etesse, A. H¨oring, J. Liu, C. Voisin.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230517T112000
DTEND:20230517T122000
DTSTAMP:20230516T150000Z
UID:b7893062bf4d792408d527441e98d0de@cgp.ibs.re.kr
SUMMARY:Effective K-stability of spherical varieties, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Thibaut Delcroix\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: The complexity of the action of a connected complex reductive group G ona (normal) algebraic variety X is the minimal codimension of an orbit in Xof a Borel subgroup of G. As suggested by the name, low complexity groupactions are easier to undrstand, the flagship example being toric varieties(that is, varieties with a complexity zero action of a torus G = (C∗)n).The class of varieties with a complexity zero group action is actually muchlarger, and also known as the class of spherical varieties.K-stability, one of the main topic of the conference, is the algebraic counterpart to existence of canonical K¨ahler metrics underlying the Yau-TianDonaldson conjecture. I will explain how and when, for spherical varieties,K-stability conditions can effectively be computed. Applications to canonical K¨ahler metrics on projective and affine spherical varieties will also be discussed.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230518T112000
DTEND:20230518T122000
DTSTAMP:20230517T150000Z
UID:5ea392cf7414ca6bdc55e788682d072b@cgp.ibs.re.kr
SUMMARY:Effective K-stability of spherical varieties, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Thibaut Delcroix\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: The complexity of the action of a connected complex reductive group G ona (normal) algebraic variety X is the minimal codimension of an orbit in Xof a Borel subgroup of G. As suggested by the name, low complexity groupactions are easier to undrstand, the flagship example being toric varieties(that is, varieties with a complexity zero action of a torus G = (C∗)n).The class of varieties with a complexity zero group action is actually muchlarger, and also known as the class of spherical varieties.K-stability, one of the main topic of the conference, is the algebraic counterpart to existence of canonical K¨ahler metrics underlying the Yau-TianDonaldson conjecture. I will explain how and when, for spherical varieties,K-stability conditions can effectively be computed. Applications to canonical K¨ahler metrics on projective and affine spherical varieties will also bediscussed.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230518T150000
DTEND:20230518T160000
DTSTAMP:20230517T150000Z
UID:785d127130e28bdbaa9d8f2bca615f47@cgp.ibs.re.kr
SUMMARY:Counting surfaces in projective varieties, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: One of the oldest problems in algebraic geometry is to enumerate points,curves and surfaces in a given projective variety satisfying certain given2conditions. Point counting is handled by intersection theory. To countcurves or surfaces, we construct compactified moduli spaces of curves orsurfaces and apply intersection theory. As there are many ways to compactify, we have many ways to count them. In the first hour, I will reviewknown methods to virtually enumerate curves such as Seiberg-Witten,Gromov-Witten and Donaldson-Thomas invariants. In the second hour, Iwill talk about recent advances in surface counting in Calabi-Yau varieties.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230519T100000
DTEND:20230519T110000
DTSTAMP:20230518T150000Z
UID:bbd48aec432809efa9c1596278924d3b@cgp.ibs.re.kr
SUMMARY:Counting surfaces in projective varieties, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: One of the oldest problems in algebraic geometry is to enumerate points,curves and surfaces in a given projective variety satisfying certain given2conditions. Point counting is handled by intersection theory. To countcurves or surfaces, we construct compactified moduli spaces of curves orsurfaces and apply intersection theory. As there are many ways to compactify, we have many ways to count them. In the first hour, I will reviewknown methods to virtually enumerate curves such as Seiberg-Witten,Gromov-Witten and Donaldson-Thomas invariants. In the second hour, Iwill talk about recent advances in surface counting in Calabi-Yau varieties.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230518T163000
DTEND:20230518T173000
DTSTAMP:20230517T150000Z
UID:cb78cc034790e6f0c5880b4211c2ff98@cgp.ibs.re.kr
SUMMARY:Status of the classification and old and new constructions for surfaces of general type with pg=q=2, I
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Fabrizio Catanese\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: The classification of surfaces of general type with pg = q = 2 is an intriguing and open chapter of surface theory.For these surfaces, apart from the elementary cases where the Albaneseimage is a curve, respectively when K2 attains its minimal value 4, wehave examples with K2 = 5, 6, 7, 8 and with degree d of the Albanese mapin the set {2, 3, 4, 6}.A component of their moduli space is said to be of the main stream ifthe map associating to a surface S its Albanese surface A = Alb(S) hasimage of dimension 3 (hence the component dominates a component ofthe moduli space of Abelian surfaces).I shall illustrate the status of the classification, and I will first showPenegini’s examples of components not of the main stream, given by surfaces isogenous to a product (this is the only case where degree d = 6 isattained).I will then show very simple equations for some components of the mainstream, named CHPP, PP4, AC3 surfaces, the letters standing for thenames of several authors: Chen-Hacon, Penegini-Polizzi, Alessandro-Catanese(here K2 = 5, 6, 6, d = 3, 4, 3).I shall then describe joint work with Edoardo Sernesi, concerning thebranch curve of an Abelian surface with a polarization of type (1,3): thisenables to show the existence of the family AC3.I shall then describe how these components, in view of the Fourier Mukaitransform, can be characterized via some assumption on the Albanesemap.Time permitting, I shall explain why the existence of such surfaces withK2 = 9 is still open, in spite of some recent results
END:VEVENT
BEGIN:VEVENT
DTSTART:20230519T112000
DTEND:20230519T122000
DTSTAMP:20230518T150000Z
UID:a9bd726a69b276d9a00002a986a124fa@cgp.ibs.re.kr
SUMMARY:Status of the classification and old and new constructions for surfaces of general type with pg=q=2, II
LOCATION:IBS Science Culture Center Daejeon, Republic of Korea
DESCRIPTION:Speaker: Fabrizio Catanese\n\nEvent: Workshop on Moduli, K-stability, Fano varieties, and related topics\n\nAbstract: The classification of surfaces of general type with pg = q = 2 is an intriguing and open chapter of surface theory.For these surfaces, apart from the elementary cases where the Albaneseimage is a curve, respectively when K2 attains its minimal value 4, wehave examples with K2 = 5, 6, 7, 8 and with degree d of the Albanese mapin the set {2, 3, 4, 6}.A component of their moduli space is said to be of the main stream ifthe map associating to a surface S its Albanese surface A = Alb(S) hasimage of dimension 3 (hence the component dominates a component ofthe moduli space of Abelian surfaces).I shall illustrate the status of the classification, and I will first showPenegini’s examples of components not of the main stream, given by surfaces isogenous to a product (this is the only case where degree d = 6 isattained).I will then show very simple equations for some components of the mainstream, named CHPP, PP4, AC3 surfaces, the letters standing for thenames of several authors: Chen-Hacon, Penegini-Polizzi, Alessandro-Catanese(here K2 = 5, 6, 6, d = 3, 4, 3).I shall then describe joint work with Edoardo Sernesi, concerning thebranch curve of an Abelian surface with a polarization of type (1,3): thisenables to show the existence of the family AC3.I shall then describe how these components, in view of the Fourier Mukaitransform, can be characterized via some assumption on the Albanesemap.Time permitting, I shall explain why the existence of such surfaces withK2 = 9 is still open, in spite of some recent results
END:VEVENT
BEGIN:VEVENT
DTSTART:20230428T160000
DTEND:20230428T180000
DTSTAMP:20230427T150000Z
UID:a66a9d693321b058a4a7f83a7138835e@cgp.ibs.re.kr
SUMMARY:Quantum Entanglement and related topics
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Norton Lee\n\nEvent: Director's Seminar\n\nAbstract: This seminar will be a continuous series of talks on "Quantum Entanglement and related topics". Quantum entanglement is one of the most fundamental features of quantum mechanics. It is a physical phenomenon that performing a local measure may instantaneously affect the outcome of local measurements far away. The concept of entanglement occurs in various areas such as in quantum information theory, communication and quantum computing. A rich field of research concerns the understanding of the role of entanglement in many body systems. In that regard, the theory can be applied to the study of knots and links in 3 manifolds by the `replica trick'. In this seminar, we will aim at learning the basics of quantum entanglement theory, understanding their applications to related areas such as Chern-Simons theory, and black hole dynamics and searching for other possible mathematical applications.
END:VEVENT
BEGIN:VEVENT
DTSTART:19700101T100000
DTEND:19700101T110000
DTSTAMP:19700101T000000Z
UID:43600a1b8d022e1b19f3270196a3c509@cgp.ibs.re.kr
SUMMARY:Spectral Sequence for Relative Contact Homology via Winding along a Binding and Applications
LOCATION:Online Streaming
DESCRIPTION:Speaker: Dahye Cho\n\nEvent: Symplectic Monday Seminar\n\nAbstract: There is a spectral sequence converging to symplectic cohomology of an affine variety whose E1-page consists of symplectic cohomology of the complement of a hypersurface in the affine variety, via the filtration on the chain complex induced from the winding number of Hamiltonian orbits along the hypersurface, arXiv:2201.10669. We will talk about the contact (as well as S1-equivariant) version of the theorem and provide applications including the invariants of fibered knots and the invariants of isolated hypersurface singularities. The data of each page of the spectral sequence consist of the invariants. If time permits, we will talk about properties of the relative contact homology and relations to other Floer-theoretic invariants. This is work in progress.
Location: Online Streaming & POSTECH Math. Bldg. #404
END:VEVENT
BEGIN:VEVENT
DTSTART:20230517T170000
DTEND:20230517T180000
DTSTAMP:20230516T150000Z
UID:d4efdc22cea2e17f0b909c2ea1fc891a@cgp.ibs.re.kr
SUMMARY:On the statistics of indecomposable components in large tensor products of representations Lie algebras and quantum groups.
LOCATION:Online Streaming
DESCRIPTION:Speaker: Nicolai Reshetikhin\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Let $V$ is a finite dimensional representation of a simple Lie group. Characters, being evaluated on positive elements, define statistics on irreducible components of the tensor power $V^{\otimes N}$ for each $N=1,2,\dots$. In the talk I will explain how this distribution behave in the limit $N\to \infty$. If time permit, I will explain a similar problem for representations of quantum groups at roots of unity where certain characters define statistics on indecomposable components of large tensor products.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230627T160000
DTEND:20230627T180000
DTSTAMP:20230626T150000Z
UID:29af631ed7e9007df402929f8dbcefd7@cgp.ibs.re.kr
SUMMARY:Cylindrical ample divisors on Du Val del Pezzo surfaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: Masatomo Sawahara\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Polarized cylinders in normal projective varieties receive a lot of attention from the viewpoint ofconnecting unipotent group actions on affine algebraic varieties. Hence, we shall focus on the configuration of sets of cylindrical ample divisors on normal projective varieties. Cheltsov, Park and Won studied sets of cylindrical ample divisors on smooth del Pezzo surfaces. Hence, we shall consider cylindrical ample divisors on Du Val del Pezzo surfaces. In this talk, we will explain the following result: Letting S be a Du Val del Pezzo surface S of degree at least 3 such that Sing(S) ̸= ∅, then S contains an H-polar cylinder for every ample Q-divisor H on S. If time permits, we also discuss cylindrical ample divisors on Du Val del Pezzo surfaces of degree 2.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230517T140000
DTEND:20230517T160000
DTSTAMP:20230516T150000Z
UID:e9a70a0f60901e17a7eef8732c6dd9e6@cgp.ibs.re.kr
SUMMARY:Quantum Entanglement and related topics
LOCATION:CGP Main Hall
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: This seminar will be a continuous series of talks on "Quantum Entanglement and related topics". Quantum entanglement is one of the most fundamental features of quantum mechanics. It is a physical phenomenon that performing a local measure may instantaneously affect the outcome of local measurements far away. The concept of entanglement occurs in various areas such as in quantum information theory, communication and quantum computing. A rich field of research concerns the understanding of the role of entanglement in many body systems. In that regard, the theory can be applied to the study of knots and links in 3 manifolds by the `replica trick'. In this seminar, we will aim at learning the basics of quantum entanglement theory, understanding their applications to related areas such as Chern-Simons theory, and black hole dynamics and searching for other possible mathematical applications.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230613T160000
DTEND:20230613T180000
DTSTAMP:20230612T150000Z
UID:09c8c38703b862dfcae4e67c43861cde@cgp.ibs.re.kr
SUMMARY:Maximally non-factorial Fano varieties
LOCATION:CGP Delta
DESCRIPTION:Speaker: Igor Krylov\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We say that a nodal Fano variety X is maximally non-factorial if rk Cl(X) = rk Pic(X) + #Sing(X). This property implies nice behavior of cohomologies and derived category of X under deformation which presents interesting relations of different families of Fano varities. I will give examples of maximally non-factorial Fano varieties and explain relations between cubic threefold and a Fano varietiy of degree 8. Then I will give a framework for classification of maximally non-factorial Fano varieties via elementary Sarkisov links.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230711T160000
DTEND:20230711T180000
DTSTAMP:20230710T150000Z
UID:b198a47425e968456dcc526ce39bcffe@cgp.ibs.re.kr
SUMMARY:Exploring the cohomology of a regular semisimple Hessenberg variety
LOCATION:CGP Delta
DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Regular semisimple Hessenberg varieties provide a fascinating link between geometry, the representation theory of finite groups, and combinatorics. In this talk, we investigate a torus action on a regular semisimple Hessenberg variety and how this action relates to the symmetric group $\mathfrak{S}_n$-action on the cohomology of a regular semisimple Hessenberg variety of Lie type $A$. Understanding this connection is important for studying the Stanley-Stembridge Conjecture, which deals with chromatic symmetric functions. We will consider a geometric proof of the Stanley-Stembridge conjecture using this connection for specific cases. This talk is based on joint work with Soojin Cho and Jaehyun Hong.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230725T160000
DTEND:20230725T180000
DTSTAMP:20230724T150000Z
UID:8e376555cf47e844036bc52142f745ed@cgp.ibs.re.kr
SUMMARY:Asymptotic nonvanishing of syzygies of algebraic varieties
LOCATION:CGP Delta
DESCRIPTION:Speaker: Jinhyung Park\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: About ten years ago, Ein and Lazarsfeld proposed to study asymptotic behaviors of syzygies of smooth projective varieties as the positivity of the embedding line bundle grows. They showed the asymptotic nonvanishing theorem, which roughly says that almost all “asymptotic syzygies” of algebraic varieties are nonvanishing, and they conjectured that the remaining “asymptotic syzygies” are vanishing. This conjecture was recently verified by myself. This suggests that there is a surprisingly uniform asymptotic behavior of syzygies of algebraic varieties. In this talk, we give more precise nonvanishing results for asymptotic syzygies of algebraic varieties, and we discuss some open problems.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230726T140000
DTEND:20230726T160000
DTSTAMP:20230725T150000Z
UID:eac7a0ec8a1e6db006f620e558c020e5@cgp.ibs.re.kr
SUMMARY:Classical, quantum, and isomonodromic Seiberg-Witten geometry of A-type theories
LOCATION:CGP Delta
DESCRIPTION:Speaker: Nikita Nekrasov\n\nEvent: Mathematical Physics Seminar\n\nAbstract: We construct Lax operators and associated meromorphic connections for genus zero and one Hitchin systems using non-perturbative Dyson-Schwinger equations of four. dimensional supersymmetric A-type quiver gauge theories. based on the work in progress with Andrey Grekov, Igor Krichever, and with Saebyeok Jeong and Norton Lee.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230830T110000
DTEND:20230830T120000
DTSTAMP:20230829T150000Z
UID:c164d4ce49ece45447fc53dd2109d772@cgp.ibs.re.kr
SUMMARY:Automorphism groups of del Pezzo surfaces
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Aurore Boitrel\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Del Pezzo surfaces play a key role in the study of algebraic subgroups of the Cremona group of the plane.Over an algebraically closed field, it is classically known that a del Pezzo surface is either isomorphic to \mathbb{P}^{2} or to \mathbb{P}^{1} \times \mathbb{P}^{1} or to the blow-up of \mathbb{P}^{2} in 1 \leq r \leq 8 points in general position, and in this case, automorphisms of del Pezzo surfaces are well known and have been completely described (by I. Dolgachev and V. Iskovskikh in 2009 for instance). In particular, there is only one isomorphism class of del Pezzo surfaces of degree $5$ over \mathbf{k}=\overline{\mathbf{k}}. In this talk, we will focus on del Pezzo surfaces of degree $5$ defined over a perfect field. Over a perfect field \mathbf{k}, there are a lot of extra surfaces (as we can already see for non-trivial rational real forms of del Pezzo surfaces of large degree), and the classification as well as the description of the automorphism groups over \mathbf{k} is reduced to understanding the actions of the Galois group Gal(\overline{\mathbf{k}}/\mathbf{k}) on the graph of $(−1)$-curves. This is what we will explain in this talk.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230731T160000
DTEND:20230731T180000
DTSTAMP:20230730T150000Z
UID:a0eaf86ace59381a618e18f3f58f41a2@cgp.ibs.re.kr
SUMMARY:Family Floer theory, non-abelianization and Spectral Networks
LOCATION:CGP Delta
DESCRIPTION:Speaker: Yoon Jae Nho\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In this talk, we study the relationship between Gaiotto-Moore-Neitzke's non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\phi$ defined on a closed Riemann surface $C$, let $\tilde{C}$ be the complement of the poles of $\phi$. In the case where the spectral curve $\Sigma_{\phi}$ is exact with respect to the canonical Liouville form on $T^{\ast}\tilde{C}$, we show that an ``almost flat" $GL(1;\mathbb{C})$-local system $\mathcal{L}$ on $\Sigma_{\phi}$ defines a Floer cohomology local system $HF_t(\Sigma_{\phi},\mathcal{L};\mathbb{C})$ on $\tilde{C}$ for $0< t\leq 1$. Then we show that for small enough $t$, the non-abelianization of $\mathcal{L}$ is isomorphic to the family Floer cohomology local system $HF_t(\Sigma_{\phi},\mathcal{L};\mathbb{C})$.
For the first half of the talk, I'll review the theory of quadratic differentials, spectral networks and non-abelianization. For the second half of the talk, I'll discuss the main result and sketch what goes behind the proof of the main result.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230803T160000
DTEND:20230803T180000
DTSTAMP:20230802T150000Z
UID:a850aa6bfa622bbb95c078c7d0743eb4@cgp.ibs.re.kr
SUMMARY:Calabi–Yau structures on Rabinowitz Fukaya categories
LOCATION:CGP Delta
DESCRIPTION:Speaker: Jongmyeong Kim\n\nEvent: CGP Seminar\n\nAbstract: In this talk, I will first introduce the definition of the Rabinowitz Floer cohomology for a pair of Lagrangian submanifolds in a Liouville domain. Then I will explain how one can regard it as an analogue of the cohomology $H^*(\partial M)$ of the boundary $\partial M$ of a compact manifold $M$ with boundary. Finally, I will explain the Rabinowitz Floer cohomology has a duality which can be thought of as an analogue of the Poincaré duality for $H^*(\partial M)$. This is based on a joint work with Hanwool Bae and Wonbo Jeong.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230908T170000
DTEND:20230908T180000
DTSTAMP:20230907T150000Z
UID:01c8883fbca9c4e7cbdd27b642028cc4@cgp.ibs.re.kr
SUMMARY:Tropical Coamoeba, Calabi-Yau Mirror Symmetry and the Combinatorics of Dimers
LOCATION:CGP Delta
DESCRIPTION:Speaker: Rak-Kyeong Seong\n\nEvent: Mathematical Physics Seminar\n\nAbstract: The talk will give a brief introduction on Calabi-Yau mirror symmetry and coamoeba projections in tropical geometry. The talk will illustrate how changes in the complex structure moduli in the Calabi-Yau mirror affect the coamoeba projection for toric Calabi-Yau 3-folds. We will explore how such variations in the complex structure moduli generate geometric transitions and affect the underlying dimer - a bipartite periodic graph, which through its combinatorial properties encodes the geometry of the associated toric Calabi-Yau 3-fold. By making connections to supersymmetric gauge theories realized in string theory, we will show that these geometric transitions relate to gauge theory dualities which can be generalized across different spacetime dimensions using higher-dimensional toric Calabi-Yau.
END:VEVENT
BEGIN:VEVENT
DTSTART:20230911T160000
DTEND:20230911T180000
DTSTAMP:20230910T150000Z
UID:e3f620c271a4d099f1223834cf1558ca@cgp.ibs.re.kr
SUMMARY:Induced Morphisms of Moduli Spaces of Pseudoholomorphic Discs
LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium
DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Given a pseudoholomorphic map between two symplectic manifolds with almost-complex structures, there are natural induced maps from moduli spaces of pseudoholomorphic curves and discs in the source manifold to corresponding moduli spaces for the target manifold. However, little is understand in general about how these maps interact with the obstruction theory of the moduli spaces.In this talk, we look at beginning to develop a theory of morphisms of moduli spaces of pseudoholomorphic curves and discs with Lagrangian boundary conditions as Kuranishi spaces, using a modification of the procedure of Fukaya-Oh-Ohta-Ono.As an example, we consider the total space of the line bundles $\mathscr{O}(-n)$ and $\mathscr{O}$ on $\mathbb{P}^1$ as toric K\" ahler manifolds, and we construct isomorphic Kuranishi structures on the moduli space of holomorphic discs in $\mathscr{O}(-n)$ on $\mathbb{P}^1$ with boundary on a moment map fiber Lagrangian $L$ and on a moduli space of holomorphic discs subject to appropriate tangency conditions in $\mathscr{O}$. We then deform this latter Kuranishi space and use this deformation to define a Lagrangian potential for $L$ in $\mathscr{O}(-n)$, and hence a superpotential for $\mathscr{O}(-n)$. With some conjectural assumptions regarding scattering diagrams in $\mathbb{P}^1\times \mathbb{P}$, this superpotential can then be calculated tropically analogously to a bulk-deformed potential of a Lagrangian in $\mathbb{P}^1\times \mathbb{P}^1$.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231005T160000
DTEND:20231005T180000
DTSTAMP:20231004T150000Z
UID:6ba081e5cd9279b9bc0a84283fe24073@cgp.ibs.re.kr
SUMMARY:Symmetry vs. Transversality for the moduli space of bordered stable maps
LOCATION:CGP Delta
DESCRIPTION:Speaker: Kenji Fukaya\n\nEvent: CGP Seminar\n\nAbstract:
After certain review I will report the present status of the project :
1: Prove generating criterion of Fukaya category in the compact case (AFOOO)
2: Use moduli space of bordered stable maps of arbitrary genus to obtain a solution of Master equation of IBL infinity structure.
There is a strong international research effort in the area of quantum information science. Here, the concepts of quantum coherence, superposition and entanglement of quantum states are exploited. These concepts were originally shown with photons as well as atoms and ions in vacuum traps. Over the past two decades, many advances at studying such quantum coherence in solid-state and molecular architectures have evolved [1]. In this talk we will focus on quantum-coherent experiments in Scanning Tunneling Microscopy (STM). STM enables the study of surfaces with atomic-scale spatial resolution and offers the ability to study individual atoms and molecules on surfaces. Here at Ewha, we have one of the world’s best facilities for such studies. STM can also be used to move atoms with atomic-scale precision, which enables us to build engineered nanostructures where each atom is in the exactly correct place. In order to study qubits with STM, we recently learned how to combine STM with electron spin resonance [2,3]. Spin resonance gives us the means to quantum-coherently control an individual atomic or molecular spin on a surface. Using short pulses of microwave radiation further enables us to perform qubit rotations and learn about the quantum coherence times of our spins [4]. Finally, we will finish with unpublished results on multi-qubit operations with spins on surfaces.
1. Andreas J. Heinrich, William D. Oliver, Lieven M. K. Vandersypen, Arzhang Ardavan, Roberta Sessoli, Daniel Loss, Ania Bleszynski Jayich, Joaquin Fernandez-Rossier, Arne Laucht, Andrea Morello, “Quantum-coherent nanoscience”, Nature Nanotechnology, 16, 1318-1329 (2021).
2. Susanne Baumann, William Paul, Taeyoung Choi, Christopher P. Lutz, Arzhang Ardavan, Andreas J. Heinrich, “Electron Paramagnetic Resonance of Individual Atoms on a Surface”, Science 350, 417 (2015).
3. Yi Chen, Yujeong Bae, Andreas Heinrich, “Harnessing the Quantum Behavior of Spins on Surfaces”, Advanced Materials 2022, 2107534 (2022).
4. Kai Yang, William Paul, Soo-Hyon Phark, Philip Willke, Yujeong Bae, Taeyoung Choi, Taner Esat, Arzhang Ardavan, Andreas J. Heinrich, and Christopher P. Lutz, “Coherent spin manipulation of individual atoms on a surface”, Science 366, 509 (2019).
Support from Institute for Basic Science (IBS-R027-D1) is gratefully acknowledged. END:VEVENT BEGIN:VEVENT DTSTART:20231020T150000 DTEND:20231020T170000 DTSTAMP:20231019T150000Z UID:7bae8368951b3497467db8bb4804a474@cgp.ibs.re.kr SUMMARY:[IBS-CGP&POSTECH-Math Colloquium] Applications of automorphic forms LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sug Woo Shin\n\nEvent: Seminar\n\nAbstract: Modular forms, and more generally automorphic forms, have a wide array of applications in number theory, representation theory, topology, combinatorics, mathematical physics, and more. While I don't have a full explanation for the ubiquity of automorphic forms, I will showcase some of these applications and try to address why automorphic forms appear in them as well as I can. END:VEVENT BEGIN:VEVENT DTSTART:20231025T140000 DTEND:20231025T153000 DTSTAMP:20231024T150000Z UID:e9736ddd614dffd446584a4cbe45970e@cgp.ibs.re.kr SUMMARY:Diagram genus, generators and applications LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Alexander Stoimenov\n\nEvent: CGP Seminar\n\nAbstract: The goal is to report on some long-term work on certain combinatorial properties of knot/link diagrams of given canonical genus. These turned out to have various ramifications and applications, including (1) enumeration of alternating knots by genus, (2) words in formal alphabets (Wicks forms), (3) graph embedding problems on surfaces, (4) markings and the $sl_N$ graph polynomial, (5) hyperbolic volume of polyhedra, graphs and links. I will try to explain (at least as far as time allows) some interrelations between these topics. END:VEVENT BEGIN:VEVENT DTSTART:20231106T170000 DTEND:20231106T180000 DTSTAMP:20231105T150000Z UID:a2534b4ba6f717ec08b095ef49a29cf1@cgp.ibs.re.kr SUMMARY:Floer cohomology of compositions of Lagrangian Dehn twists LOCATION:Online Streaming DESCRIPTION:Speaker: Weiwei Wu\n\nEvent: Symplectic Monday Seminar\n\nAbstract: There is a conjecture due to Paul Seidel, that asserts the composition of a sequence of Lagrangian Dehn twists can be computed as a mapping cone between the Floer chain complex of the identity, as well as a cube complex formed by the Hochschild complex of a directed subcategory with spherical objects. We give two proofs of this conjecture, one is purely algebraic, and the other relies on clean surgery and should be of independent interest. This result was previously announced by Sikimeti M'au and Tim Perutz, but either approach we present in this talk is different from their solution. This is partly an upcoming work of Shuo Zhang, and partly a joint work in progress with Cheuk-Yu Mak and Shuo Zhang.
Pre-registration is required by November 5 on https://cgp.ibs.re.kr.
END:VEVENT BEGIN:VEVENT DTSTART:20231113T160000 DTEND:20231113T180000 DTSTAMP:20231112T150000Z UID:5fd1aba59952966000472aae24f9e7b8@cgp.ibs.re.kr SUMMARY:Toric vector bundles, non-abelianization and spectral networks LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Spectral networks and non-abelianization were introduced by Gaiotto-Moore-Neitzke and they have many applications in mathematics and physics. In a recent work by Nho, he proved that the non-abelianization of a twisted-flat local system over the spectral curve of a meromorphic quadratic differential is actually given by the family Floer construction. Based on the SYZ philosophy, it is then natural to ask how holomorphic vector bundles arise from spectral networks and non-abelianization. In this talk, I will demonstrate how to construct toric vector bundles on toric surfaces via spectral networks and non-abelianization. END:VEVENT BEGIN:VEVENT DTSTART:20231123T160000 DTEND:20231123T180000 DTSTAMP:20231122T150000Z UID:367d71ba98a950504284a07d0f2d75ee@cgp.ibs.re.kr SUMMARY:Unimodular random rooted manifolds LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jaelin Kim\n\nEvent: CGP Seminar\n\nAbstract: In geometry and topology, a limit of spaces is useful to understand a stability of properties, and invariants. In this talk, as a statistical version of the Smooth Gromov-Hausdorff limit, we consider unimodular random rooted manifolds. It was first introduced by M. Abért and I. Biringer, which is a generalization of unimodular random rooted graphs and the Benjamini-Schramm convergence in the space of rooted graphs with bounded degree. We shall present a characterization using the desingularization of the space of rooted Riemannian manifolds into a Riemannian foliated space, compactness theorem, and an application for locally symmetric cases. And then we discuss our on-going project with M. Abért on measures of maximal entropy for the geodesic flow on a unimodular random rooted manifold. END:VEVENT BEGIN:VEVENT DTSTART:20231122T160000 DTEND:20231122T180000 DTSTAMP:20231121T150000Z UID:6974f5b593abb46121800562b72dec72@cgp.ibs.re.kr SUMMARY:Automorphism groups of affine varieties with at most one $\mathbb{G}_a$-action LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Alexander Perepechko\n\nEvent: Algebraic Geometry Seminar\n\nAbstract:
Given an affine algebraic variety $X$ over an algebraically closed field $\mathbb{K}$, we study the structure of the neutral component $\mathrm{Aut}^\circ(X)$ depending on the number of non-equivalent actions of the additive group of the field $\mathbb{G}_a=\mathbb{G}_a(\mathbb{K})$ on $X$. We conjectured jointly with M.Zaidenberg and A.Regeta that
- if $X$ admits no $\mathbb{G}_a$-actions (i.e., is rigid ), then $\mathrm{Aut}^\circ(X)$ is an algebraic torus;
- if $X$ admits one $\mathbb{G}_a$-action up to equivalence (i.e., is semirigid ), then $\mathrm{Aut}^\circ(X)\cong T\times U$, where $T$ is an algebraic torus and $U$ is an abelian unipotent group;
- if $X$ admits at least two $\mathbb{G}_a$-actions up to equivalence, then $\mathrm{Aut}^\circ(X)$ is not a union of algebraic subgroups.
The first two conjectures were confirmed for normal algebraic surfaces in [4] and [1] respectively using birational transformations of minimal completions of $X$ with a normal crossing boundary divisor. The third one was confirmed in [2] for arbitrary affine varieties in the stronger form: under the conjecture assumption there is a pair of $\mathbb{G}_a$-actions $H_1,H_2\subset\mathrm{Aut}^\circ(X)$ such that $\langle H_1,H_2\rangle$ is not a union of algebraic subgroups.The first and second conjectures remain open in arbitrary dimension, yet in [2] and [3] we proved that the subgroup of $\mathrm{Aut}^\circ(X)$ generated by its algebraic subgroups indeed equals $T\times U$ for a rigid or semirigid variety $X$.We will discuss these results and methods used in their proofs.
$keywords$ affine variety, automorphism group, ind-group, nested group
References
[1] A. Perepechko, S. Kovalenko, M. Zaidenberg. On automorphism groups of affine surfaces,
ASPM 75 (2017), Algebraic Varieties and Automorphism Groups, pp. 207-286.
[2] Perepechko, A., Regeta, A. When is the automorphism group of an affine variety nested? ,
Trans. Groups (2022), DOI:10.1007/s00031-022-09711-1.
[3] Perepechko, A., Regeta, A. Automorphism groups of affine varieties without non-algebraic elements , preprint, arXiv:2203.08950.
[4] A. Perepechko, M. Zaidenberg. Automorphism groups of rigid affine surfaces: the identity component , preprint, arXiv:2208.09738.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231109T160000
DTEND:20231109T180000
DTSTAMP:20231108T150000Z
UID:2b846a734a3eef2555ae27137c17048e@cgp.ibs.re.kr
SUMMARY:Diophantine approximation in the view point of homogenous dynamics and its S-arithmetic generalization
LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium
DESCRIPTION:Speaker: Jiyoung Han\n\nEvent: CGP Seminar\n\nAbstract: Diophantine approximation is one of the areas of number theory meeting homogeneous dynamics, which studies approximation problems of irrational numbers by rationals. In this talk, through so-called Khintchine—Groshev theorem, we will recall the machinery to connect the rational-approximation problems to the homogeneous dynamics and how the mixing property of the geodesic flow helps to prove the theorem, sticking to the SL(2,R)-case. And we will discuss about quantification problems of the Khintchine—Groshev theorem. If time permits, we will see how one can generalize Diophantine approximation to the S-arithmetic setting.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231206T160000
DTEND:20231206T180000
DTSTAMP:20231205T150000Z
UID:09adf045dddbe55e0697278079cd42db@cgp.ibs.re.kr
SUMMARY:DM stacks from surfaces and local Calabi-Yau 3-folds
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Sung Woo Nam\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: DM stacks are usually introduced in the context of moduli theory. They can also be constructed in a bottom-up way. In this talk, we will discuss the construction of smooth, separated DM stacks using varieties with at worst quotient singularities. As a byproduct, we will see constructions of local Calabi-Yau 3-folds containing some simple normal crossing surfaces, which show up in high-energy physics. If time permits, I will describe an extension of local Gromov-Witten and Gopakumar-Vafa theory to such singular surfaces. Such theories will be an extension of the local mirror symmetry of local del Pezzo surfaces.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231027T130000
DTEND:20231027T140000
DTSTAMP:20231026T150000Z
UID:01186f387252533af5e367696e79d573@cgp.ibs.re.kr
SUMMARY:Reading seminar on stacks 5: Descent
LOCATION:CGP Delta
DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: Reading Seminar\n\nAbstract:
END:VEVENT
BEGIN:VEVENT
DTSTART:20231110T130000
DTEND:20231110T140000
DTSTAMP:20231109T150000Z
UID:3343c98009a2c062f5412c39afdd9b94@cgp.ibs.re.kr
SUMMARY:Reading seminar on stacks 6: Descent on algebraic spaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: Taeyeoup Kang\n\nEvent: Reading Seminar\n\nAbstract:
END:VEVENT
BEGIN:VEVENT
DTSTART:20231117T130000
DTEND:20231117T140000
DTSTAMP:20231116T150000Z
UID:4445677afcf7191784edcb0042ca866c@cgp.ibs.re.kr
SUMMARY:Sheaves and cohomology on algebraic spaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: Igor Krylov\n\nEvent: Reading Seminar\n\nAbstract: Reading seminar on algebraic stacks
END:VEVENT
BEGIN:VEVENT
DTSTART:20231124T130000
DTEND:20231124T140000
DTSTAMP:20231123T150000Z
UID:6a24af4a80264fb50310ba998cc90f55@cgp.ibs.re.kr
SUMMARY:Points and topology of algebraic spaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: Dasol Jeong\n\nEvent: Reading Seminar\n\nAbstract: Reading seminar on algebraic stacks
END:VEVENT
BEGIN:VEVENT
DTSTART:20231201T130000
DTEND:20231201T140000
DTSTAMP:20231130T150000Z
UID:f34035f6855d7e6a8e83ae07d4cab053@cgp.ibs.re.kr
SUMMARY:Proper and projective morphisms of algebraic spaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: \n\nEvent: Reading Seminar\n\nAbstract: Reading seminar on algebraic stacks
END:VEVENT
BEGIN:VEVENT
DTSTART:20231208T130000
DTEND:20231208T140000
DTSTAMP:20231207T150000Z
UID:d3a92e44599f93452953b5d570c41530@cgp.ibs.re.kr
SUMMARY:Integral algebraic spaces
LOCATION:CGP Delta
DESCRIPTION:Speaker: Yuchan Lee\n\nEvent: Reading Seminar\n\nAbstract: Reading seminar on algebraic stacks
END:VEVENT
BEGIN:VEVENT
DTSTART:20231127T100000
DTEND:20231127T105000
DTSTAMP:20231126T150000Z
UID:f6125df84694c6923251415213b322c3@cgp.ibs.re.kr
SUMMARY:Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: Both statistical phase space (SPS) and kinetic theory phase space (KTPS), which is the cotangent bundle of the probability space on SPS, carry canonical symplectic structures. Starting from this first principle, we provide a canonical derivation of thermodynamic phase space (TPS) of nonequilibrium thermodynamics as a contact manifold in two steps. First, regarding the collective observation of observables in SPS as a moment map defined on KTPS, we apply the Marsden-Weinstein reduction and obtain a mesoscopic phase space in between KTPS and TPS as a (infinite dimensional) symplectic fibration. Then we show that the reduced relative information entropy defines a generating function that covariantly constructs a thermodynamic equilibrium as a Legendrian submanifold. This Legendrian submanifold is not necessarily graph-like. We interpret the Maxwell construction of equal-area law as the procedure of finding a continuous, not necessarily differentiable, thermodynamic potential and explain the associated phase transition by identifying the procedure with that of finding a graph selector in symplecto-contact geometry and in the Aubry-Mather theory of dynamical system. (This talk is based on the joint work with Jin-wook Lim.)
END:VEVENT
BEGIN:VEVENT
DTSTART:20231127T111000
DTEND:20231127T120000
DTSTAMP:20231126T150000Z
UID:b50e875d21fcaf40f1243309790e0c59@cgp.ibs.re.kr
SUMMARY:Contact Hamiltonians for thermodynamic systems with and without metastable states
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Shin-itiro Goto \n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: Contact geometry provides an appropriate language for describing someequilibrium thermodynamic systems. Thus, one natural question iswhether or not this language can also describe nonequilibrium systems.In this talk we attempt to answer this question by showing the validity ofcontact geometric descriptions of nonequilibrium statistical systems.To this end, we pay attention to two Ising systems.As a first system, consider a system that exhibitsa phase transition with metastable states at equilibrium.We then show that a relaxation process is described bya contact Hamiltonian vector field on a contact manifold.As a second system, consider a system that has no spin-spin interactions.We then show that there is consistency between a contact Hamiltonian vectorfield for a relaxation process and its kinetic theory constructed from the master equation.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231127T133000
DTEND:20231127T142000
DTSTAMP:20231126T150000Z
UID:01213b9fcf97aeb047ba784df662cdf0@cgp.ibs.re.kr
SUMMARY:Brownian motions and thermodynamic formalisms in negative curvature
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Jaelin Kim\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: On a Riemannian manifold, the Laplace-Beltrami operator and the Brownian motion, as the diffusion process generated by the Laplace-Beltrami operator, have been studied in various aspects, e.g. geometry, probability theory, and ergodic theory. In this talk, we present statistical properties of Brownian motions on manifolds of finite volume with pinched negative curvature: a Law of large numbers and a central limit theorem. Using the thermodynamic formalisms for geodesic flow in negative curvature, their relationship with the ergodic theory of geodesic flow will be explained.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231128T100000
DTEND:20231128T105000
DTSTAMP:20231127T150000Z
UID:6c0ee5138a8545ba930eb140160ba15a@cgp.ibs.re.kr
SUMMARY:Uniqueness criteria for the Vlasov equation and application to semiclassical mean-field limits
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Laurent Lafleche\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: I will present some uniqueness criteria for the Vlasov–Poisson system, emerging as corollaries of stability estimates in strong or weak topologies, and show how they serve as a guideline to understand the limit from many-body quantum mechanics to the Hartree–Fock equation and the Vlasov equation with singular potentials. The different topologies allow to treat different classes of quantum states and potentials, and lead to different rates of convergence.
END:VEVENT
BEGIN:VEVENT
DTSTART:20231128T133000
DTEND:20231128T142000
DTSTAMP:20231127T150000Z
UID:0fdcbace2d0de838b326fa41f37d87d8@cgp.ibs.re.kr
SUMMARY:Aspects in the Analysis of the Hartree–Fock–Bogoliubov Equations for Bosons
LOCATION:IBS POSTECH Campus Bldg. #301
DESCRIPTION:Speaker: Jacky Chong\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: The dynamics of a Bose–Einstein condensate in an interacting Bose gas can be modeled bya system of coupled nonlinear dispersive equations of the Hartree–Fock–Bogoliubov (HFB)type. In this talk, we focus on some aspects of the analysis of the nonlinear system. In particular, we consider the HFB system with the interaction potential $V_N (x−y) = N^{3β}$ $v(N^β (x−y))$for $0 < β < 1$ and its solutions. These solutions have initial conditions that have finite energyand satisfy a smallness condition on the ‘pair correlation’ part, but are otherwise generalfunctions in some suitable Sobolev spaces. We study its dynamical formation of correlationstructures and obtain global-in-time dispersive estimates on the solutions. The estimates areexpected to improve the Fock space error bounds for the mean-field approximation of thequantum many-body dynamics
END:VEVENT
BEGIN:VEVENT
DTSTART:20231128T111000
DTEND:20231128T120000
DTSTAMP:20231127T150000Z
UID:82496d25c4c878b72ea4010db0318fd5@cgp.ibs.re.kr
SUMMARY:Nonequilibrium Thermodynamics: Stopping-time FTs and energy-driven drug synergy (Online)
LOCATION:Online Streaming
DESCRIPTION:Speaker: Hao Ge\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: I will discuss two different stories about nonequilibrium thermodynamics. One is theoretical. We investigated the thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems and second-law-like thermodynamic inequalities. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with insights into the fundamental principles governing nonequilibrium systems. The other is applicable. To understand the mechanism of noise-induced synergy in reactivating latent HIV, we developed a four-gene-state model with Tat transcription/translation and found that drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of the HIV promoter. The inhibition effect of transcription activators is actually a phenomenon of energy dissipation in the nonequilibrium gene transition system.
ID: 889 7390 7685
PW: IBSCGP
END:VEVENT BEGIN:VEVENT DTSTART:20231128T144000 DTEND:20231128T153000 DTSTAMP:20231127T150000Z UID:3a699031bf033420f35455f64c93112b@cgp.ibs.re.kr SUMMARY:Complex Balancing and Detailed Balancing of Biochemical Interacting Systems LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jinsu Kim\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: When biochemical species interact in a spatially well-mixed system, a set of ordinary differential equations can be employed to model the macroscopic behavior (e.g., concentration) of the species. However, when the inherent randomness in molecular interactions significantly influences system dynamics, a microscopic behavior (e.g., copy numbers) of the species can be represented by a continuous-time Markov chain in a jump-by-jump fashion, serving as a stochastic counterpart to the system. END:VEVENT BEGIN:VEVENT DTSTART:20231129T100000 DTEND:20231129T105000 DTSTAMP:20231128T150000Z UID:3e56331ef38bbcad47ac474e1fe736fc@cgp.ibs.re.kr SUMMARY:Universality of log-correlated fields LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kyeongsik Nam\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: Log-correlation naturally appears in various objects such as random matrices, random discrete geometries and Riemann zeta function. In this talk, I will give an overview on the theory of log-correlated fields. END:VEVENT BEGIN:VEVENT DTSTART:20231129T111000 DTEND:20231129T120000 DTSTAMP:20231128T150000Z UID:49255365dca8779fdf97578b7636eab1@cgp.ibs.re.kr SUMMARY:Universality and non-universality of the free energy in spherical spin glass models LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Ji Oon Lee\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: Spherical spin glass models are variants of the Sherrington-Kirkpatrick model of spin glass, where the spin variables are uniformly distributed on a hypersphere. Some of these models exhibit universal behavior in their free energies, meaning that properties such as limits and limiting fluctuations are independent of the details of their Hamiltonians. On the other hand, non-universal behaviors can also be observed in the free energies of certain other models. In this talk, I will outline a general approach for analyzing the free energy in spherical spin glass models and discuss several distinct phase transition phenomena. END:VEVENT BEGIN:VEVENT DTSTART:20231130T100000 DTEND:20231130T105000 DTSTAMP:20231129T150000Z UID:348c863b2356fd29f62a319c38dfd35a@cgp.ibs.re.kr SUMMARY:Kinetic PDE approach to H-theorem LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Chanwoo Kim\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20231130T111000 DTEND:20231130T120000 DTSTAMP:20231129T150000Z UID:d0638071567dba33633374222646658f@cgp.ibs.re.kr SUMMARY:Kinetic Models for Semiflexible Polymers in a Half-plane LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jin Woo Jang\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: In this talk, we introduce a derivation of a kinetic equation for semi-flexible polymers. The equation describes the limiting behavior of a N-segment discrete chain via the continuum-limit. In the half-plane, we also present a formal derivation of the trapping boundary condition by assuming the energy-minimizing transition of a segment at the boundary. Then we will briefly introduce the proof of global well-posedness, long-time asymptotic behavior, hypoellipticity, and the Hölder regularity of solutions near the boundary. END:VEVENT BEGIN:VEVENT DTSTART:20231130T133000 DTEND:20231130T142000 DTSTAMP:20231129T150000Z UID:9b69d003727fa3f9dd90913ba52ebf4c@cgp.ibs.re.kr SUMMARY:Instantaneous everywhere-blowup of parabolic SPDEs LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Davar Khoshnevisan \n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: We consider the following stochastic heat equation $\partial_t u(t\,,x) = \tfrac12\partial^2_x u(t\,,x) + b(u(t\,,x)) + \sigma(u(t\,,x))\dot{W}(t\,,x),$ defined for $(t\,,x)\in(0\,,\infty)\times\mathbb{R}$, where $\dot{W}$ denotes space-time white noise. The function $\sigma$ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function $b$ is assumed to be positive, locally Lipschitzand nondecreasing. We prove that the Osgood condition $\int_1^\infty {\rm d}y/b(y)<\infty$ implies that the solution almost surely blows up everywhere and instantaneously. In other words, the Osgood condition ensures that $P\{u(t\,,x)=\infty\text{ for all $t>0$ and $x\in\mathbb{R}$}\}=1$. The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities, and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincar\’e inequalities that were developed by Le Chen, D. Khoshnevisan, David Nualart, and Fei Pu (2021, 2022).This is based on joint work with Mohammud Foondun and Eulalia Nualart. END:VEVENT BEGIN:VEVENT DTSTART:20231130T144000 DTEND:20231130T153000 DTSTAMP:20231129T150000Z UID:0e292014c9633aac78fac073ac32651e@cgp.ibs.re.kr SUMMARY:Interface motion and its fluctuation in Glauber-Kawasaki dynamics LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tadahisa Funaki\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: We consider Glauber-Kawasaki dynamics (i.e., interacting random walks with creation and annihilation of particles) of non-gradient type and derive a direction-dependent curvature flow under a hydrodynamic scaling limit. This extends a series of our recent results obtained under the gradient condition, deriving mean-curvature flow or Huygens' principle. We also discuss its fluctuation in a simpler situation. Partly joint work with Hyunjoon Park. END:VEVENT BEGIN:VEVENT DTSTART:20231201T100000 DTEND:20231201T105000 DTSTAMP:20231130T150000Z UID:6b9bc5a5a0a5323838a815aa9dedae1d@cgp.ibs.re.kr SUMMARY:A mean-field limit of the particle swarmalator model LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jinwook Jung\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: In this talk, we present a mean-field limit of the particle swarmalator model introduced in [O'Keeffe et al, Nat. Commun., '17] with singular communication weights. For a mean-field limit, we employ a probabilisticapproach for the propagation of molecular chaos and suitable cut-offs in singular terms, which results in the validation of the mean-field limit. We also provide a local-in-time well-posedness of strong and weak solutions to the derived kinetic swarmalatorequation. END:VEVENT BEGIN:VEVENT DTSTART:20231201T111000 DTEND:20231201T120000 DTSTAMP:20231130T150000Z UID:13a9f319f691bb98de96cda5752404fa@cgp.ibs.re.kr SUMMARY:Mean-field limits: from particle descriptions to macroscopic equations LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Young-Pil Choi\n\nEvent: Workshop in Kinetic theory, thermodynamics and contact topology\n\nAbstract: In this talk, we discuss a rigorous derivation of pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. We crucially make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions. END:VEVENT BEGIN:VEVENT DTSTART:20231117T150000 DTEND:20231117T170000 DTSTAMP:20231116T150000Z UID:ead194372eb956a16c2e7c7ec299931f@cgp.ibs.re.kr SUMMARY:[IBS-CGP&POSTECH-Math Colloquium] Low Dimensional Topology and Algebraic Geometry LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Seminar\n\nAbstract: Recently there have been increasing interactions between low dimensional topology and algebraic geometry. In this talk, I will discuss some of these interactions focusing on links and Milnor fibers of hypersurface singularities. The last part of this talk is based on joint works (some in progress) with Anatoly Libgober and Nikolai Saveliev. END:VEVENT BEGIN:VEVENT DTSTART:20231204T100000 DTEND:20231204T110000 DTSTAMP:20231203T150000Z UID:b9192acf64d068448f11bc695a17e472@cgp.ibs.re.kr SUMMARY:Augmentation Varieties and Disk Potential LOCATION:Online Streaming DESCRIPTION:Speaker: Soham Chanda\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology(LCH) for Rizell-Golovko's lifted Legendrians by counting treed disks. Our formalism of LCH allows us to obtain augmentations from certain non-exact fillings. We prove a conjecture of Rizell-Golovko relating the augmentation variety assoiciated to the LCH of a lifted Legendrian and the disk potential of the base Lagrangian. As an application, we show that lifts of monotone Lagrangian tori in projective spaces with different disk-potentials, e.g. as constructed by Vianna, produce non-isotopic Legendrian tori in contact spheres. The above work is a joint project with Blakey, Sun and Woodward. END:VEVENT BEGIN:VEVENT DTSTART:20231218T160000 DTEND:20231218T180000 DTSTAMP:20231217T150000Z UID:15e3d9a312fc44266f78d9f44ba727c9@cgp.ibs.re.kr SUMMARY:Monopole Floer homology and holomorphic curves LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yi-Jen Lee\n\nEvent: Symplectic Monday Seminar\n\nAbstract: I will give a survey on the relations between different versions of Seiberg-Witten Floer homologies with various Gromov-type Floer homologies such as the embedded contact homology and the periodic Floer homology. END:VEVENT BEGIN:VEVENT DTSTART:19700101T130000 DTEND:19700101T140000 DTSTAMP:19700101T000000Z UID:bc84524bdb47d2c0527c5d69cd2d337a@cgp.ibs.re.kr SUMMARY:Proper and projective morphisms of algebraic spaces LOCATION:CGP Delta DESCRIPTION:Speaker: Taeyeoup Kang\n\nEvent: Reading Seminar\n\nAbstract: Proper and projective morphisms of algebraic spaces END:VEVENT BEGIN:VEVENT DTSTART:20231206T153000 DTEND:20231206T160000 DTSTAMP:20231205T150000Z UID:d29a469b1be44a35457e69d1f6148d7d@cgp.ibs.re.kr SUMMARY:Reading seminar on symplectic and birational geometry LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Director's Seminar\n\nAbstract: TBD END:VEVENT BEGIN:VEVENT DTSTART:20240105T170000 DTEND:20240105T180000 DTSTAMP:20240104T150000Z UID:d0b1cd9c4464f70e92f415b96eb9fb43@cgp.ibs.re.kr SUMMARY:Algebraic engineering and (q,t)-deformed integrable hierarchies LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jean-Emile Bourgine\n\nEvent: Mathematical Physics Seminar\n\nAbstract: I will present a deformation of the 2d Toda hierarchyinspired by a correspondence with (refined) topological strings. It isderived by enhancing the underlying $gl(\infty)$ symmetry algebra tothe quantum toroidal gl(1) algebra. The difference-differentialequations of the deformed hierarchy are obtained from the expansion of(q,t)-bilinear identities, and two equations refining the 2d Todaequation are found in this way. I will also present an interestingclass solutions built from the R-matrix of the toroidal algebra. END:VEVENT BEGIN:VEVENT DTSTART:20240103T160000 DTEND:20240103T180000 DTSTAMP:20240102T150000Z UID:8b732acfc37c1de568ffd6a2e34c8ea5@cgp.ibs.re.kr SUMMARY:Floer theory for the variation operator of an isolated singularity LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongwook Choa\n\nEvent: Seminar\n\nAbstract: The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define a new Floer cohomology, called monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the Seifert form. I will also explain the algorithm of finding exceptional collection of a certain curve singularity using A’Campo’s divide construction. If time permits, I will discuss an A-infinity extension of this Floer cohomology and the action of two-associahedra. END:VEVENT BEGIN:VEVENT DTSTART:20231213T103000 DTEND:20231213T114500 DTSTAMP:20231212T150000Z UID:3d4566941c5b99dcf4cb898396475efb@cgp.ibs.re.kr SUMMARY:Hyperbolic knot theory (Part 2) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jessica S. Purcell\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: It has been known since work of Thurston over fifty years ago that many knots (in an appropriate sense, “most” knots) have a complement that admit a hyperbolic structure. This structure is known to be unique up to isometry. Thus, hyperbolic geometry is a complete knot invariant. However, knots are classically presented by a diagram: a graph with over-under crossing information. It remains difficult to extract hyperbolic geometric information from the diagram of a knot, even if the knot is known to be hyperbolic. There have been many tools developed that give insight into hyperbolic geometry; these tools can be particularly effective for special classes of knots. In these talks, I will give background on hyperbolic geometry and present some of the techniques that have been leading to new results in knot theory. These will include triangulations and gluing equations, geometric deformation and Dehn filling, and tools used to bound hyperbolic volumes of knot complements. I will also point to a few open conjectures along the way. END:VEVENT BEGIN:VEVENT DTSTART:20231215T090000 DTEND:20231215T101500 DTSTAMP:20231214T150000Z UID:e5a386b425c2a4474b4557b7b00438f0@cgp.ibs.re.kr SUMMARY:Hyperbolic knot theory (Part 3) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jessica S. Purcell\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: It has been known since work of Thurston over fifty years ago that many knots (in an appropriate sense, “most” knots) have a complement that admit a hyperbolic structure. This structure is known to be unique up to isometry. Thus, hyperbolic geometry is a complete knot invariant. However, knots are classically presented by a diagram: a graph with over-under crossing information. It re-mains difficult to extract hyperbolic geometric information from the diagram of a knot, even if the knot is known to be hyperbolic. There have been many tools developed that give insight into hyper-bolic geometry; these tools can be particularly effective for special classes of knots. In these talks, I will give background on hyperbolic geometry and present some of the techniques that have been leading to new results in knot theory. These will include triangulations and gluing equations, geo-metric deformation and Dehn filling, and tools used to bound hyperbolic volumes of knot comple-ments. I will also point to a few open conjectures along the way. END:VEVENT BEGIN:VEVENT DTSTART:20231214T140000 DTEND:20231214T151500 DTSTAMP:20231213T150000Z UID:229ead94a9645e03db3082a8e5bc4674@cgp.ibs.re.kr SUMMARY:Braids and mapping class groups (Part 2) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tara Brendle\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: The mapping class group MCG(S) of a surface S is the group of symmetries of S, that is, the group of self-homeomorphisms of S up to isotopy; braid groups are the special case where the surface S is a punctured disk. MCG(S) acts naturally on the first homology group of S, giving rise to a represen-tation MCG(S) → Sp(2g,Z). The Torelli group of the surface S is the kernel of this representation, and is often described as the “nonlinear” or “mysterious” part of the mapping class group. A basic question about any group is: what is its abelianization, and what does that tell us about the group? In 1978, Birman-Craggs discovered the first abelian quotients of the Torelli group, giving a family of maps to Z/2 via the Rokhlin invariant of 4-manifolds. A few years later, Dennis Johnson discovered a new abelian quotient of the Torelli group onto a free abelian group. He further showed that this map, now known as the Johnson homomorphism, together with the Birman-Craggs maps, are suffi-cient to calculate the abelianization of the Torelli group.In these talks, we will explain both “pieces” of the abelianization: we will describe the Birman-Craggs maps and also give two ways to define the Johnson homomorphism, one in terms of certain 3-manifolds and one that is more algebraic in flavor. We will also briefly survey more recent work of Masatoshi Sato and of Tudur Lewis on the abelianization of a closely related group, the level 2 congruence subgroup of MCG(S), and describe how this sheds new light on the work of Johnson and Birman-Craggs. Finally, we will describe aspects of Johnson theory in the context of braid groups. END:VEVENT BEGIN:VEVENT DTSTART:20231215T103000 DTEND:20231215T114500 DTSTAMP:20231214T150000Z UID:7d9ae44678e46e80c0a3d0e7e4aba0f7@cgp.ibs.re.kr SUMMARY:Braids and mapping class groups (Part 3) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tara Brendle\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: The mapping class group MCG(S) of a surface S is the group of symmetries of S, that is, the group of self-homeomorphisms of S up to isotopy; braid groups are the special case where the surface S is a punctured disk. MCG(S) acts naturally on the first homology group of S, giving rise to a represen-tation MCG(S) → Sp(2g,Z). The Torelli group of the surface S is the kernel of this representation, and is often described as the “nonlinear” or “mysterious” part of the mapping class group. A basic question about any group is: what is its abelianization, and what does that tell us about the group? In 1978, Birman-Craggs discovered the first abelian quotients of the Torelli group, giving a family of maps to Z/2 via the Rokhlin invariant of 4-manifolds. A few years later, Dennis Johnson discovered a new abelian quotient of the Torelli group onto a free abelian group. He further showed that this map, now known as the Johnson homomorphism, together with the Birman-Craggs maps, are suffi-cient to calculate the abelianization of the Torelli group.In these talks, we will explain both “pieces” of the abelianization: we will describe the Birman-Craggs maps and also give two ways to define the Johnson homomorphism, one in terms of certain 3-manifolds and one that is more algebraic in flavor. We will also briefly survey more recent work of Masatoshi Sato and of Tudur Lewis on the abelianization of a closely related group, the level 2 congruence subgroup of MCG(S), and describe how this sheds new light on the work of Johnson and Birman-Craggs. Finally, we will describe aspects of Johnson theory in the context of braid groups. END:VEVENT BEGIN:VEVENT DTSTART:20231212T140000 DTEND:20231212T151500 DTSTAMP:20231211T150000Z UID:e4cf1d2ae522dc6c65b4fe323c988d41@cgp.ibs.re.kr SUMMARY:Algebraic Knot Theory (Part 2) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Zsuzsanna Dancso\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: The notion of formality originates in the early rational homotopy theory of the 70's, and it has be-come a powerful notion in many other fields including group theory and Lie theory. In knot theo-ry formality isomorphisms provide powerful invariants, studied under the synonymous names universal finite type/ Vassiliev invariants, universal quantum invariants or homomorphic ex-pansions. The first prototype for a such an invariant is the Kontsevich integral: this was one of the results which won Kontsevich the Fields medal in 1998.In this mini course we formalise (ha!) a method - a recipe, if you will - for constructing and studying formality isomorphisms for classes of knotted objects: most prominently knotted objects which can be finitely presented as a kind of algebraic structure. A prime example is the braid group, which has a famous finite presentation, the Artin presentation; other examples abound, from tangles viewed as a planar algebra to virtual/welded tangles viewed as a circuit algebra, tensor category or PROP, and even knotted graphs with their own strange and unique operations.We'll investigate a range of examples of structure-preserving formality isomorphisms from the easy (welded braids) through the hard (knots, welded foams), to the impossible (tangles). We'll see how these invariants provide deep connections to various branches of algebra, again from simple (expo-nential maps) to complex (tensor categories, Drinfeld associators, Lie Theory, Kashiwara-Vergne and Duflo theory). Finally, we'll learn to use these connections to import tools and theorems between from topology to algebra and vice versa, and explore areas where this could be further exploited. END:VEVENT BEGIN:VEVENT DTSTART:20231214T090000 DTEND:20231214T101500 DTSTAMP:20231213T150000Z UID:7b18b3395943c5c3c05a32e094d765b4@cgp.ibs.re.kr SUMMARY:Algebraic Knot Theory (Part 3) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Zsuzsanna Dancso\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: The notion of formality originates in the early rational homotopy theory of the 70's, and it has be-come a powerful notion in many other fields including group theory and Lie theory. In knot theo-ry formality isomorphisms provide powerful invariants, studied under the synonymous names universal finite type/ Vassiliev invariants, universal quantum invariants or homomorphic ex-pansions. The first prototype for a such an invariant is the Kontsevich integral: this was one of the results which won Kontsevich the Fields medal in 1998.In this mini course we formalise (ha!) a method - a recipe, if you will - for constructing and studying formality isomorphisms for classes of knotted objects: most prominently knotted objects which can be finitely presented as a kind of algebraic structure. A prime example is the braid group, which has a famous finite presentation, the Artin presentation; other examples abound, from tangles viewed as a planar algebra to virtual/welded tangles viewed as a circuit algebra, tensor category or PROP, and even knotted graphs with their own strange and unique operations.We'll investigate a range of examples of structure-preserving formality isomorphisms from the easy (welded braids) through the hard (knots, welded foams), to the impossible (tangles). We'll see how these invariants provide deep connections to various branches of algebra, again from simple (expo-nential maps) to complex (tensor categories, Drinfeld associators, Lie Theory, Kashiwara-Vergne and Duflo theory). Finally, we'll learn to use these connections to import tools and theorems between from topology to algebra and vice versa, and explore areas where this could be further exploited. END:VEVENT BEGIN:VEVENT DTSTART:20231212T103000 DTEND:20231212T114500 DTSTAMP:20231211T150000Z UID:5ffe25e4affe5ec4e312fc811b268839@cgp.ibs.re.kr SUMMARY:Volume conjecture of knots (Part 2) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jun Murakami\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: In this series of talks, I would like to explain the volume conjecture, which gives a bridge between quantum invariants and geometric structures of knots. In 1980's, V. Jones discovered the Jones polynomial of knots. This invariant relates to the quantum group and generalized by various ways. In 1990's, R. Kashaev invented quantum invariants and observed that certain limit of his in-variants converges to the hyperbolic volume of the knot complement. Kashaev's invariants turned out to be specializations of the colored Jonespolynomial, and his observation led to the volume conjecture which predicts the relation between the colored Jones polynomial and the volume of the knot complement. I first introduce quantum invariants of knots and its relation to quantum groups. Then explain the volume conjecture. For some simple knots, proof is given and the idea of the proof is ex-plained. Even though the volume conjecture is not solved yet for general case, the relation be-tween colored Jones invariants and the hyperbolic structure of knot complements is known. This relation is a good clue that the conjecture actually holds. Some generalizations and applications of the volume conjecture are also explained. END:VEVENT BEGIN:VEVENT DTSTART:20231214T103000 DTEND:20231214T114500 DTSTAMP:20231213T150000Z UID:a0b4e859a110f8f26a1038f745345fb7@cgp.ibs.re.kr SUMMARY:Volume conjecture of knots (Part 3) LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jun Murakami\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: In this series of talks, I would like to explain the volume conjecture, which gives a bridge between quantum invariants and geometric structures of knots. In 1980's, V. Jones discovered the Jones polynomial of knots. This invariant relates to the quantum group and generalized by various ways. In 1990's, R. Kashaev invented quantum invariants and observed that certain limit of his in-variants converges to the hyperbolic volume of the knot complement. Kashaev's invariants turned out to be specializations of the colored Jonespolynomial, and his observation led to the volume conjecture which predicts the relation between the colored Jones polynomial and the volume of the knot complement. I first introduce quantum invariants of knots and its relation to quantum groups. Then explain the volume conjecture. For some simple knots, proof is given and the idea of the proof is ex-plained. Even though the volume conjecture is not solved yet for general case, the relation be-tween colored Jones invariants and the hyperbolic structure of knot complements is known. This relation is a good clue that the conjecture actually holds. Some generalizations and applications of the volume conjecture are also explained. END:VEVENT BEGIN:VEVENT DTSTART:20231211T115000 DTEND:20231211T122500 DTSTAMP:20231210T150000Z UID:5955ddd78f1e2816b195d9e8de49ab96@cgp.ibs.re.kr SUMMARY:Hyperbolic Dehn filling, volume, and transcendentality LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sunul Oh\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Let $M$ be a 1-cusped hyperbolic 3-manifold. In this talk, we discuss experimental results concern-ing the behavior of the number $N_M(v)$ of Dehn fillings of $M$ with a given volume $v$. We also give necessary conditions for Dehn fillings that share the same complex volume or exhibit conjugate complex volume differences. Additionally, we show the transcendentality of the Neumann-Zagier volume formula, proving that the growth of $N_M$ is slower than any power of its filling coefficient. END:VEVENT BEGIN:VEVENT DTSTART:20231211T140000 DTEND:20231211T143500 DTSTAMP:20231210T150000Z UID:a45b6f5d6d9fd8695a4cac64e9d00069@cgp.ibs.re.kr SUMMARY:Quasi-isometry classification of graph-2-braid groups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Byung Hee An\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: For a compact (weakly) special square complex, the intersection complex which is a certain com-plex-of-group decomposition structure of its fundamental group is a well-defined invariant under quasi-isometry. In this talk, we use this invariant to classify quasi-isometry types of 2-braid groups of circumference 1 graphs. As an application, we also classify quasi-isometry types of 4-braid groups of trees. END:VEVENT BEGIN:VEVENT DTSTART:20231211T143500 DTEND:20231211T151000 DTSTAMP:20231210T150000Z UID:3bcd074fa7a254d7e9f5221fdada56be@cgp.ibs.re.kr SUMMARY:Some generalizations of racks and invariants of Legendrian knots LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Naoki Kimura\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Racks and quandles are algebraic systems which bring knot invariants. In this talk, we introduce al-gebraic systems called a bi-Legendrian rack and a 4-Legendrian rack, both of which are racks equipped with additional structures. We explain these algebraic systems provide invariants of Leg-endrian knots. END:VEVENT BEGIN:VEVENT DTSTART:20231211T153000 DTEND:20231211T160500 DTSTAMP:20231210T150000Z UID:0c5e77851e8ba90a9315e7db10513065@cgp.ibs.re.kr SUMMARY:An invertible non-semisimple TQFT varying over the character stack LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Patrick Kinnear\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: In this talk I will describe the construction of an invertible sheaf of vector spaces (i.e. a line bundle) on the G-character stack of a 3-manifold, which is the moduli stack of G-local systems for a fixed reductive group G. In fact, this is just one part of a TQFT which has a nice invertibility property rela-tive to G-gauge theory, constructed from the representations of the quantum group at a root of unity. At the level of surfaces we obtain an invertible sheaf of categories over the character stack, which is expected to relate to a sheaf of algebras whose global sections are the skein algebra of the sur-face. Invertibility of the sheaf of categories should relate to an invertibility property of the skein al-gebra called being Azumaya. I will explain how this TQFT is expected to relate to other root-of-unity invariants such as those constructed by Akutsu-Deguchi-Ohtsuki and Costantino-Geer-Patureau-Mirand. END:VEVENT BEGIN:VEVENT DTSTART:20231212T115000 DTEND:20231212T122500 DTSTAMP:20231211T150000Z UID:02ee1ec6d8e6c41b7c81c2eca47e1e10@cgp.ibs.re.kr SUMMARY:Satellites and Lorenz knots LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Thiago de Paiva Souza\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Morton conjectured that every Lorenz knot that is a satellite is a cable on a Lorenz knot. In this talk, we construct infinitely many families of Lorenz knots that are satellites but not cables, giving coun-terexamples to this conjecture. END:VEVENT BEGIN:VEVENT DTSTART:20231212T153000 DTEND:20231212T160500 DTSTAMP:20231211T150000Z UID:f8c63ef5f7e63250ab4149219ade3ca0@cgp.ibs.re.kr SUMMARY:Burau representation, stabilization and exchange moves of braids LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Alexander Stoimenov\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: We discuss how the Burau representation can be used to obstruct to reducibility and exchangeability of braids. We determine the exact location of Burau eigenvalues of reducible and exchangeable braids (for suitable parameter). We apply this to show non-conjugate irreducible representatives of many knots. END:VEVENT BEGIN:VEVENT DTSTART:20231212T160500 DTEND:20231212T164000 DTSTAMP:20231211T150000Z UID:87bcba5c1101e8026da902ed8b411e5b@cgp.ibs.re.kr SUMMARY:Epimorphisms between genus two handlebody-knot groups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Yuko Ozawa\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: For two genus $g$ handlebody-knots $H_{1}$ and $H_{2}$, we denote by $H_{1}\geq H_{2}$ if there exists an epimorphism from the (handlebody-)knot group of $H_{1}$ onto the one of $H_{2}$. In the case of $g=1$ (knot case), this ``$\geq$" is a partial order for prime knots and has been determined up to 11 crossings. In this talk, we consider the case of $g=2$ and exhibit a lot of ordered pairs of irreducible handlebody-knots in the table up to 6 crossings. END:VEVENT BEGIN:VEVENT DTSTART:20231212T170000 DTEND:20231212T173500 DTSTAMP:20231211T150000Z UID:11b51dbfb07f1c63dde7e6d3279f2234@cgp.ibs.re.kr SUMMARY:Alexander polynomial of twisted torus knots LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Adnan\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Twisted torus knots are a generalization of torus knots obtained by introducing additional full twists to adjacent strands of torus knots. In this talk, we present an explicit formula for the Alexander pol-ynomial of twisted torus knots. We use a presentation of the knot group of twisted torus knots and Fox’s free differential calculus. We further explore the applications of our computations, including a determination of the genus for certain families of twisted torus knots. This is joint work with Kyungbae Park. END:VEVENT BEGIN:VEVENT DTSTART:20231213T115000 DTEND:20231213T122500 DTSTAMP:20231212T150000Z UID:d50e857513ceb9492212367cbfaf1a0c@cgp.ibs.re.kr SUMMARY:Modular links: Bunch algorithm and upper volume bounds LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Connie On Yu Hui\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: In the 1970s, Williams developed an algorithm that has been used to construct and study modular links in the Lorenz template. We introduce the bunch algorithm to provide more insights into the geometry of modular links and Lorenz links. Using the machinery developed for the bunch algorithm, we provide the first upper volume bound that is independent of word exponents and quadratic in the braid index of the Lorenz link component for all modular link complements. We find families of modular knot complements with upper volume bounds that are linear in the braid index. A classifi-cation of modular link complements based on the relative magnitudes of word exponents is also presented. END:VEVENT BEGIN:VEVENT DTSTART:20231214T115000 DTEND:20231214T122500 DTSTAMP:20231213T150000Z UID:2033e21f5e1654b1e7fa1b190fe2d104@cgp.ibs.re.kr SUMMARY:“Link-homotopy" of spatial graphs LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Yuka Kotorii\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: A link-homotopy of links is an equivalence relation on links generated by ambient isotopies and self-crossing changes, defined by Milnor. The self-crossing change is a crossing change between the same components. A spatial graph is an embedding of an abstract graph in $S^3$. A component-homotopy is a link-homotopy for spatial graphs, defined by Fleming. In this talk, we give a Markov type theorem for component-homotopy classes of spatial graphs, by using Habegger-Lin’s idea for link-homotopy classes of string links. This research is joint work with Atsuhiko Mizusawa. END:VEVENT BEGIN:VEVENT DTSTART:20231214T153000 DTEND:20231214T160500 DTSTAMP:20231213T150000Z UID:d98b93e71c46debf92c55e6bdba9cfd4@cgp.ibs.re.kr SUMMARY:Automorphisms of fine curve graphs for nonorientale surfaces LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Erika Kuno\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consist-ing of the actual essential simple closed curves on the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine curve graph of a closed orientable surface is isomorphic to the homeomorphism group of the surface. We generalized their result to closed nonorientable surfaces $N$ of genus $g \geq 4$. This is a joint work with Mitsuaki Kimura. END:VEVENT BEGIN:VEVENT DTSTART:20231214T160500 DTEND:20231214T164000 DTSTAMP:20231213T150000Z UID:ff0a4704eefaa5d318dcf127141372dc@cgp.ibs.re.kr SUMMARY:Strong quasipositivity and arc index LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Gyo Taek Jin\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: We present a viewpoint on Euler characteristic 0 braided surfaces as grid diagrams. This leads to some results regarding estimates of Thurston-Bennequin invariants of knots, strong quasipositivity of Whitehead doubles, jump numbers of slice-torus invariants, and arc and braid index. END:VEVENT BEGIN:VEVENT DTSTART:20231214T170000 DTEND:20231214T173500 DTSTAMP:20231213T150000Z UID:aa9c1081c196ccc4a128961ced4ead51@cgp.ibs.re.kr SUMMARY:Twisted Virtual Braids and Twisted links LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Komal Negi\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Twisted knot theory introduced by M. Bourgoin is a generalization of knot theory. It leads us to the notion of twisted virtual braids. In this talk we show theorems for twisted links corresponding to the Alexander theorem and the Markov theorem in knot theory. We also provide a group presentation and a reduced group presentation of the twisted virtual braid group. END:VEVENT BEGIN:VEVENT DTSTART:20231215T115000 DTEND:20231215T122500 DTSTAMP:20231214T150000Z UID:cf2ab7adc444f0ed9990cdd787b5a57c@cgp.ibs.re.kr SUMMARY:Twisted Alexander Vanishing order LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Masaaki Suzuki\n\nEvent: Winter School on Low-dimensional Topology and Related Topics\n\nAbstract: Suppose that there exists a surjective homomorphism of a knot group onto a finite group. The com-position with the regular representation of the finite group provides the twisted Alexander polyno-mial of the knot. We focus on the order of the smallest finite group so that the corresponding twist-ed Alexander polynomial is zero, which we call TAV order (Twisted Alexander Vanishing order). In this talk, we see some examples and properties of TAV order. END:VEVENT BEGIN:VEVENT DTSTART:20240219T161500 DTEND:20240219T180000 DTSTAMP:20240218T150000Z UID:1c4af14e112d92e828e4708b0be107f8@cgp.ibs.re.kr SUMMARY:Intersection theory on derived stacks I LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Adeel A. Khan\n\nEvent: Intensive Lecture Series\n\nAbstract: Equivariant and stacky extensions of algebraic cycle theories have been the subject of important work of Gillet, Vistoli, Totaro, Edidin-Graham, Kresch, and others dating back to at least 1984. In this lecture series we will revisit this subject from the perspective of Voevodsky’s motivic cohomology and its recently developed extension to algebraic stacks. Using this language we will be able to not only recover but go beyond the classical results. Moreover, we will explain how to incorporate derived algebraic geometry into the picture in order to get virtual extensions of intersection theory (such as the virtual fundamental class and virtual localization formulas). The general theory will be illustrated using the example of the moduli stack of stable maps and applications to quantum cohomology and quantum K-theory. END:VEVENT BEGIN:VEVENT DTSTART:20240221T161500 DTEND:20240221T180000 DTSTAMP:20240220T150000Z UID:7ce2f48cf9ac866111408723de7a6e91@cgp.ibs.re.kr SUMMARY:Intersection theory on derived stacks II LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Adeel A. Khan\n\nEvent: Intensive Lecture Series\n\nAbstract: Equivariant and stacky extensions of algebraic cycle theories have been the subject of important work of Gillet, Vistoli, Totaro, Edidin-Graham, Kresch, and others dating back to at least 1984. In this lecture series we will revisit this subject from the perspective of Voevodsky’s motivic cohomology and its recently developed extension to algebraic stacks. Using this language we will be able to not only recover but go beyond the classical results. Moreover, we will explain how to incorporate derived algebraic geometry into the picture in order to get virtual extensions of intersection theory (such as the virtual fundamental class and virtual localization formulas). The general theory will be illustrated using the example of the moduli stack of stable maps and applications to quantum cohomology and quantum K-theory. END:VEVENT BEGIN:VEVENT DTSTART:20240222T161500 DTEND:20240222T180000 DTSTAMP:20240221T150000Z UID:1f3fa23db8023af717cc37623a8f4a10@cgp.ibs.re.kr SUMMARY:Intersection theory on derived stacks III LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Adeel A. Khan\n\nEvent: Intensive Lecture Series\n\nAbstract: Equivariant and stacky extensions of algebraic cycle theories have been the subject of important work of Gillet, Vistoli, Totaro, Edidin-Graham, Kresch, and others dating back to at least 1984. In this lecture series we will revisit this subject from the perspective of Voevodsky’s motivic cohomology and its recently developed extension to algebraic stacks. Using this language we will be able to not only recover but go beyond the classical results. Moreover, we will explain how to incorporate derived algebraic geometry into the picture in order to get virtual extensions of intersection theory (such as the virtual fundamental class and virtual localization formulas). The general theory will be illustrated using the example of the moduli stack of stable maps and applications to quantum cohomology and quantum K-theory. END:VEVENT BEGIN:VEVENT DTSTART:20240131T170000 DTEND:20240131T180000 DTSTAMP:20240130T150000Z UID:72d31e449adbe0f38e6c844e66f44d9e@cgp.ibs.re.kr SUMMARY:Mapping the Phase Space of Supersymmetric Gauge Theories using Explainable Machine Learning LOCATION:Online Streaming DESCRIPTION:Speaker: Rak-Kyeong Seong\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: A large class of 4d N=1 supersymmetric gauge theories that are worldvolume theories of D3-branes probing toric Calabi-Yau 3-folds exhibit toric phases that are IR equivalent under Seiberg duality. These theories are realized in terms of a Type IIB brane configuration characterized by a bipartite graph on a 2-torus known as a brane tiling or dimer model. This graph originates from the coamoeba projection of the mirror curve associated to the toric Calabi-Yau 3-fold. When the complex structure moduli of the mirror Calabi-Yau 3-fold are varied, the coamoeba and corresponding brane tilings change their shape, giving rise to different toric phases related by Seiberg duality. In this work, we show how explainable machine learning techniques can be introduced in order to systematically identify the relationship between choices of complex structure moduli and specific toric phases of 4d N=1 supersymmetric gauge theories. We show that machine learning techniques enable us to explicitly map the phase space of 4d N=1 supersymmetric gauge theories corresponding to a given toric Calabi-Yau 3-fold. Please register for Zoom link here by January 29. END:VEVENT BEGIN:VEVENT DTSTART:20240214T170000 DTEND:20240214T180000 DTSTAMP:20240213T150000Z UID:238277f4106c04e54539a154079d2428@cgp.ibs.re.kr SUMMARY:Geometry from categorical enumerative invariants LOCATION:Online Streaming DESCRIPTION:Speaker: Junwu Tu\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Let M be a miniversal moduli space of pairs consisting of a smooth projective Calabi-Yau 3-fold together with a volume form. Based on Witten’s interpretation of background independence of string theory, Costello conjectured that the generating function of categorical enumerative invariants (CEI) is a projectively flat section of certain Fock bundle over M. In this talk we discuss Costello’s conjecture, which naturally leads to the construction of a canonical quantization of M in the sense of Kontsevich-Soibelman.Please register for Zoom link here by February 12. END:VEVENT BEGIN:VEVENT DTSTART:20240228T170000 DTEND:20240228T180000 DTSTAMP:20240227T150000Z UID:626853c27f6920b74d4f2d5a3b02ad9e@cgp.ibs.re.kr SUMMARY:KP integrability through the $x-y$ swap relation LOCATION:Online Streaming DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: I will discuss a universal relation sometimes called the $x-y$ swap relation, which plays a prominent role in the theory of topological recursion. In particular, the $x-y$ swap relation is very natural for the KP integrability and can be described by certain integral transforms. As an application, I prove a recent conjecture that relates some particular instances of topological recursion to the Mironov-Morozov-Semenoff matrix integrals and derive explicit formulas for the multipoint functions in some enumerative geometry problems. This talk is based on a joint work with Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, and Sergey Shadrin. END:VEVENT BEGIN:VEVENT DTSTART:20240313T170000 DTEND:20240313T180000 DTSTAMP:20240312T150000Z UID:82fd090240fc982ee57981ad69475921@cgp.ibs.re.kr SUMMARY:Dimers, clusters, and mirrors LOCATION:Online Streaming DESCRIPTION:Speaker: Kazushi Ueda\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Dimer models were originally introduced as statistical mechanical models of diatomic molecules in the 1930s, and developed into a substantial field at the intersection of physics and mathematics. In this talk, I will discuss aspects of dimer models related to symplectic topology (Lefschetz fibrations, Fukaya categories, ..) and representation theory (quivers with potentials, Calabi-Yau algebras, ...) with a view toward mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20240327T170000 DTEND:20240327T180000 DTSTAMP:20240326T150000Z UID:a4d60ad15507c0834215a97b38d34686@cgp.ibs.re.kr SUMMARY:Three dimensional mirror symmetry and degenerations of Riemann surface LOCATION:Online Streaming DESCRIPTION:Speaker: Dan Xie\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: I will discuss how to use the classification of degenerations of Riemann surface to find mirror pairs of 3d N=4 superconformal field theory. Please register for Zoom link here by March 25. END:VEVENT BEGIN:VEVENT DTSTART:20240319T161500 DTEND:20240319T174500 DTSTAMP:20240318T150000Z UID:92904d590569f77e24469b13f9af113d@cgp.ibs.re.kr SUMMARY:Deformations of weighted homogeneous surface singularities LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Every isolated singularity has the semi-universal deformation. Therefore, we have to study the base of the deformation and it has many components.A convenient description of the components is a P-resolution, a certain partial resolution of the singularity. János Kollár conjectured that every irreducible component of the deformation of a rational surface singularity corresponds to a P-resolution.Recently, we prove that the conjecture holds for almost weighted homogeneous surface singularities.To prove the conjecture, we use the deformation theory of sandwiched singularities and explicit minimal model program for 3-folds.I will explain the background of the conjecture and an overview of the proof, as well as related topics and my future research plan. This is a joint work with Dongsoo Shin. END:VEVENT BEGIN:VEVENT DTSTART:20240326T161500 DTEND:20240326T174500 DTSTAMP:20240325T150000Z UID:c9f469127035ca8ee70886ad7f9145b3@cgp.ibs.re.kr SUMMARY:Castelnuovo Curves LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Gerriet Martens\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: We call a smooth irreducible projective curve a Castelnuovo curve if it admits a birational map into the projective space of dimension r such that the image curve has degree at least 2r+1 and, then, the maximum possible geometric genus (which one can calculate by a classical formula due to G. Castelnuovo 1893). It is well known that a Castelnuovo curve must lie on a Hirzebruch surface, i.e. on a rational ruled surface. In this talk we are concerned with the converse: to what extent are smooth curves on Hirzebruch surfaces Castelnuovo curves? We will show that the answer is, in a sense: almost always. END:VEVENT BEGIN:VEVENT DTSTART:20240423T161500 DTEND:20240423T171500 DTSTAMP:20240422T150000Z UID:1111b95cfc1560029160363dcf7e1adc@cgp.ibs.re.kr SUMMARY:Adjoint Asymptotic Multiplier Ideal Sheaves LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, we define and study a triple called a potential triple which consists of a pair $(X,\Delta)$ and a polarizing pseudoeffective divisor $D$. To such a triple, we define a so-called potential multiplier ideal sheaf which gives a simultaneous generalization of the multiplier ideal sheaf and asymptotic multiplier ideal sheaf. We give a description of the closed subset defined by potential multiplier ideal sheaf in terms of the minimal model program. We also characterize the case where potential multiplier ideal sheaf is trivial. Lastly, we also prove a Nadel type vanishing theorem of cohomology for potential multiplier ideal sheaf. We further present applications of the theory of potential triples. This is a joint work with S.Jang and D.Kim. END:VEVENT BEGIN:VEVENT DTSTART:20240423T173000 DTEND:20240423T183000 DTSTAMP:20240422T150000Z UID:7e55036c4c52ec66cc0a21348bd0bd0b@cgp.ibs.re.kr SUMMARY:Anticanonical minimal models and Zariski decomposition LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sungwook Jang\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Abstract : If there exists a $(K_{X}+\Delta)$-minimal model, then $K_{X}+\Delta$ admits a birational Zariski decomposition. Birkar and Hu conversely showed that if a pair $(X,\Delta)$ is lc and $K_{X}+\Delta$ admits a birational Zariski decomposition, then $(X,\Delta)$ has a minimal model. Analogously, we can prove that if a pair $(X,\Delta)$ is pklt and $-(K_{X}+\Delta)$ admits a birational Zariski decomposition, then $(X,\Delta)$ has an anticanonical minimal model. Furthermore, we can show that the existence of $-(K_{X}+\Delta)$-minimal model for movable divisor $-(K_{X}+\Delta)$ implies the existence of $-(K_{X}+\Delta)$-minimal model for arbitrary pseudoeffective divisor $-(K_{X}+\Delta)$. END:VEVENT BEGIN:VEVENT DTSTART:20240308T150000 DTEND:20240308T170000 DTSTAMP:20240307T150000Z UID:9fba1b2a221b6ef8bdc7c8cc33cc6996@cgp.ibs.re.kr SUMMARY:[IBS CGP-POSTECH Math Colloquium] Enumerative geometry of curves and surfaces LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: Seminar\n\nAbstract: Enumerative geometry is the study of questions like “How many geometric figures of fixed topological type satisfy certain given conditions?” It is one of the oldest subjects in mathematics dating back to Apollonius, 22 centuries ago. In 1900, Hilbert included the Schubert calculus, enumerative geometry of linear subspaces, as the fifteenth in his famous list of 23 problems for the coming century. About 30 years ago, enumerative geometry of curves was revolutionized by conjectures generated by string theory, many of which are now firmly established mathematical theorems. By a technical breakthrough only a few years ago, we now have a modern surface counting theory. In this colloquium, I’d like to convey some of the key ideas in classical and modern enumerative geometry. END:VEVENT BEGIN:VEVENT DTSTART:20240314T161500 DTEND:20240314T181500 DTSTAMP:20240313T150000Z UID:ddda4ec00441fde6245f66e97577c63d@cgp.ibs.re.kr SUMMARY:Enumerative Geometry and Algebraic cycles LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Ramesh Sreekantan\n\nEvent: CGP Seminar\n\nAbstract: It is well known that there is a line through 2 points in the plane, a conic through 5 points and nodal cubics through 8 points. In general there are rational curves of degree d through 3d-1 points in a plane. We will show how the existence of these rational curves is related to the construction of motivic cycles in families of K3 surfaces and Abelian surfaces.
We will discuss two applications. First, we show how the rational curves can be used to obtain equations of curves whose Jacobians have real multiplication generalizing a classical result of Humbert. Second, we show that the motivic cycles can be used to obtain algebraicity results for values of higher Green's functions at CM points, along the lines of a conjecture of Gross and Zagier, now a theorem of Li. END:VEVENT BEGIN:VEVENT DTSTART:20240321T161500 DTEND:20240321T181500 DTSTAMP:20240320T150000Z UID:50e4bcc545084caad6161c6082ec75e5@cgp.ibs.re.kr SUMMARY:Joint ergodicity of piecewise monotone maps LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Younghwan Son\n\nEvent: CGP Seminar\n\nAbstract: Ergodic properties of piecewise monotone maps on the unit interval are widely studied for both ergodic theory and number theory. Times b-maps and Gauss map, for example, are utilized in the study of b-expansions and continued fraction expansion. In this talk, we will discuss multiple ergodic averages of piecewise monotone maps, especially the phenomenon of joint ergodicity. This is joint work with Vitaly Bergelson. END:VEVENT BEGIN:VEVENT DTSTART:20240425T161500 DTEND:20240425T171500 DTSTAMP:20240424T150000Z UID:ee28a2c0dd6b9ed52da6452526f39712@cgp.ibs.re.kr SUMMARY:[IBS-CGP Colloquium] The Movement of Carbon Atoms in Metals LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Rodney Ruoff\n\nEvent: CGP Seminar\n\nAbstract:
Scientists are keenly interested in how carbon, a fundamental element of many materials, moves within metals. Specific types of carbon atoms, known as isotopes, behave differently due to their varying mass. These variations are crucial for researchers, particularly in the study of advanced materials like graphene and diamond.Traditionally, the heavier carbon isotope, $^{13}$C, is more expensive and challenging to separate. Our innovative approach seeks to make this process more cost-effective. By guiding isotopes through metals, we can potentially enrich $^{13}$C efficiently.We've observed that in metals like nickel and cobalt, carbon atoms move from point to point – though not always as predicted. For instance, cobalt sometimes favors the movement of the heavier $^{13}$C isotope, contrary to our expectations.To understand this phenomenon, we use Monte Carlo modeling, akin to a strategic game that forecasts the atom's pathways. Advancements such as machine learning could refine these predictions.We also propose a novel challenge: Could we bypass simulations by using the metal's structure as a guide to predict the distribution of carbon isotopes? It's an intriguing puzzle that invites further exploration and innovative problem-solving techniques. END:VEVENT BEGIN:VEVENT DTSTART:20240322T150000 DTEND:20240322T170000 DTSTAMP:20240321T150000Z UID:bcbc27b1bb0b18f2aa63a3f5e1abef61@cgp.ibs.re.kr SUMMARY:[IBS CGP-POSTECH Math Colloquium]Group theoretic understanding of manifold diffeomorphism groups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sang-hyun Kim\n\nEvent: Seminar\n\nAbstract: Given a smooth manifold M equipped with a geometric or analytic structure $\Omega$, the collection of $\Omega$--preserving diffeomorphisms of M naturally form a group denoted as $Diff^r(M,\Omega)$. These groups often exhibit strong rigidity phenomena, even when treated purely as algebraic objects. In this talk, I will focus on two aspects of these groups along this line. (1) The isomorphism types of finitely generated subgroups. (2) The set of true first-order group--theoretical sentences. This talk is based on joint works with Thomas Koberda (UVa) and with Javier de la Nuez-Gonzalez (KIAS). END:VEVENT BEGIN:VEVENT DTSTART:20240424T170000 DTEND:20240424T180000 DTSTAMP:20240423T150000Z UID:0bb22b2e2b84249ef416e4b0f33ec144@cgp.ibs.re.kr SUMMARY:Equivariant Lagrangian correspondences and applications LOCATION:Online Streaming DESCRIPTION:Speaker: Nai Chung Conan Leung\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: I will explain equivariant Lagrangian correspondence tri-module structures and their applications to equivariant Floertheory and a conjecture of Teleman. This is a joint work with Siu-Cheong Louis Lau and Yan- Lung Leon Li.Please register for Zoom link here by April 22. END:VEVENT BEGIN:VEVENT DTSTART:02040404T170000 DTEND:02040404T180000 DTSTAMP:02040403T153208Z UID:274c72a870095b653079bfc9c25b4945@cgp.ibs.re.kr SUMMARY:Cluster algebras and Poisson geometry LOCATION:Nowhere DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: \n\nAbstract: Cluster algebras are commutative rings with distinguished sets of gen-erators characterized by a remarkable combinatorial structure. Discovered by S. Fomin and A. Zelevinsky in the early 2000s, these algebraic struc-tures have found applications across diverse mathematical fields, including integrable systems, total positivity, Teichm¨uller theory, Poisson geometry, knot theory and mathematical physics.Fomin and Zelevinsky conjectured that numerous varieties in Lie the-ory are equipped with a cluster structure. Early examples include dou-ble Bruhat cells, Grassmannians and simple complex algebraic groups. M. Gekhtman, M. Shapiro and A. Vainshtein observed that cluster al-gebras in these examples are compatible with certain Poisson brackets. Specifically, for any given cluster (x1, x2, . . . , xn), there exist constants ωij such that {xi, xj } = ωij xixj . This observation led to a program aim-ing to construct cluster algebras by addressing the inverse problem: given a Poisson bracket in the coordinate ring of an algebraic variety and a col-lection of regular functions (x1, . . . , xn) satisfying {xi, xj } = ωij xixj , does there exist a compatible cluster algebra? The research initiative led to the formulation of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class, there exists a compatible cluster structure. END:VEVENT BEGIN:VEVENT DTSTART:02040404T170000 DTEND:02040404T180000 DTSTAMP:02040403T153208Z UID:7d18738b1045659c923a0a1edeba86a1@cgp.ibs.re.kr SUMMARY:Cluster algebras and Poisson geometry LOCATION:Nowhere DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: \n\nAbstract: Cluster algebras are commutative rings with distinguished sets of gen-erators characterized by a remarkable combinatorial structure. Discovered by S. Fomin and A. Zelevinsky in the early 2000s, these algebraic struc-tures have found applications across diverse mathematical fields, including integrable systems, total positivity, Teichm¨uller theory, Poisson geometry, knot theory and mathematical physics.Fomin and Zelevinsky conjectured that numerous varieties in Lie the-ory are equipped with a cluster structure. Early examples include dou-ble Bruhat cells, Grassmannians and simple complex algebraic groups. M. Gekhtman, M. Shapiro and A. Vainshtein observed that cluster al-gebras in these examples are compatible with certain Poisson brackets. Specifically, for any given cluster (x1, x2, . . . , xn), there exist constants ωij such that {xi, xj } = ωij xixj . This observation led to a program aim-ing to construct cluster algebras by addressing the inverse problem: given a Poisson bracket in the coordinate ring of an algebraic variety and a col-lection of regular functions (x1, . . . , xn) satisfying {xi, xj } = ωij xixj , does there exist a compatible cluster algebra? The research initiative led to the formulation of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class, there exists a compatible cluster structure. END:VEVENT BEGIN:VEVENT DTSTART:20240401T171500 DTEND:20240401T181500 DTSTAMP:20240331T150000Z UID:d8a1398763455598a66eb72f3b3267b3@cgp.ibs.re.kr SUMMARY:Cluster algebras and Poisson geometry I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Cluster algebras are commutative rings with distinguished sets of generators characterized by a remarkable combinatorial structure. Discovered by S. Fomin and A. Zelevinsky in the early 2000s, these algebraic structures have found applications across diverse mathematical fields, including integrable systems, total positivity, Teichmüller theory, Poisson geometry, knot theory and mathematical physics. Fomin and Zelevinsky conjectured that numerous varieties in Lie theory are equipped with a cluster structure. Early examples include double Bruhat cells, Grassmannians and simple complex algebraic groups. M. Gekhtman, M. Shapiro and A. Vainshtein observed that cluster algebras in these examples are compatible with certain Poisson brackets. Specifically, for any given cluster (x1, x2, . . . , xn), there exist constants ωij such that {xi, xj} = ωijxixj . This observation led to a program aiming to construct cluster algebras by addressing the inverse problem: given a Poisson bracket in the coordinate ring of an algebraic variety and a collection of regular functions (x1, . . . , xn) satisfying {xi, xj} = ωijxixj , does there exist a compatible cluster algebra? The research initiative led to the formulation of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class, there exists a compatible cluster structure. The outline for this lecture series is as follows: 1) Motivation for cluster algebras from total positivity theory;2) Main definitions and properties of cluster algebras of geometric type;3) Construction of cluster algebras using Poisson geometry;4) Overview of the theory of Poisson-Lie groups and the Belavin-Drinfeld classification of factorizable quasi-triangular Poisson brackets;5) Discussion on the current status of the GSV conjecture, results from the latest papers (arXiv:2312.04859, 2308.16701), novel techniques,more examples and the current research. END:VEVENT BEGIN:VEVENT DTSTART:20240403T171500 DTEND:20240403T181500 DTSTAMP:20240402T150000Z UID:eff44c8c5b846133116c95aa9d4229db@cgp.ibs.re.kr SUMMARY:Cluster algebras and Poisson geometry II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Cluster algebras are commutative rings with distinguished sets of generators characterized by a remarkable combinatorial structure. Discovered by S. Fomin and A. Zelevinsky in the early 2000s, these algebraic structures have found applications across diverse mathematical fields, including integrable systems, total positivity, Teichmüller theory, Poisson geometry, knot theory and mathematical physics. Fomin and Zelevinsky conjectured that numerous varieties in Lie theory are equipped with a cluster structure. Early examples include double Bruhat cells, Grassmannians and simple complex algebraic groups. M. Gekhtman, M. Shapiro and A. Vainshtein observed that cluster algebras in these examples are compatible with certain Poisson brackets. Specifically, for any given cluster (x1, x2, . . . , xn), there exist constants ωij such that {xi, xj} = ωijxixj . This observation led to a program aiming to construct cluster algebras by addressing the inverse problem: given a Poisson bracket in the coordinate ring of an algebraic variety and a collection of regular functions (x1, . . . , xn) satisfying {xi, xj} = ωijxixj , does there exist a compatible cluster algebra? The research initiative led to the formulation of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class, there exists a compatible cluster structure. The outline for this lecture series is as follows: 1) Motivation for cluster algebras from total positivity theory;2) Main definitions and properties of cluster algebras of geometric type;3) Construction of cluster algebras using Poisson geometry;4) Overview of the theory of Poisson-Lie groups and the Belavin-Drinfeld classification of factorizable quasi-triangular Poisson brackets;5) Discussion on the current status of the GSV conjecture, results from the latest papers (arXiv:2312.04859, 2308.16701), novel techniques,more examples and the current research. END:VEVENT BEGIN:VEVENT DTSTART:20240404T171500 DTEND:20240404T181500 DTSTAMP:20240403T150000Z UID:10c18f8ea3ed2426f4e46ccac18ab8a0@cgp.ibs.re.kr SUMMARY:Cluster algebras and Poisson geometry III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Dmytro Voloshyn\n\nEvent: IBS-CGP Post-doc lecture series\n\nAbstract: Cluster algebras are commutative rings with distinguished sets of generators characterized by a remarkable combinatorial structure. Discovered by S. Fomin and A. Zelevinsky in the early 2000s, these algebraic structures have found applications across diverse mathematical fields, including integrable systems, total positivity, Teichmüller theory, Poisson geometry, knot theory and mathematical physics. Fomin and Zelevinsky conjectured that numerous varieties in Lie theory are equipped with a cluster structure. Early examples include double Bruhat cells, Grassmannians and simple complex algebraic groups. M. Gekhtman, M. Shapiro and A. Vainshtein observed that cluster algebras in these examples are compatible with certain Poisson brackets. Specifically, for any given cluster (x1, x2, . . . , xn), there exist constants ωij such that {xi, xj} = ωijxixj . This observation led to a program aiming to construct cluster algebras by addressing the inverse problem: given a Poisson bracket in the coordinate ring of an algebraic variety and a collection of regular functions (x1, . . . , xn) satisfying {xi, xj} = ωijxixj , does there exist a compatible cluster algebra? The research initiative led to the formulation of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class, there exists a compatible cluster structure. The outline for this lecture series is as follows: 1) Motivation for cluster algebras from total positivity theory;2) Main definitions and properties of cluster algebras of geometric type;3) Construction of cluster algebras using Poisson geometry;4) Overview of the theory of Poisson-Lie groups and the Belavin-Drinfeld classification of factorizable quasi-triangular Poisson brackets;5) Discussion on the current status of the GSV conjecture, results from the latest papers (arXiv:2312.04859, 2308.16701), novel techniques,more examples and the current research. END:VEVENT BEGIN:VEVENT DTSTART:20240618T130000 DTEND:20240618T150000 DTSTAMP:20240617T150000Z UID:ddbd3a37ead61b8a0a7166e44c3dba92@cgp.ibs.re.kr SUMMARY:On the ideals and syzygies of some Gaussian Graphical Models in Statistics LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kangjin HAN\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: In this talk, we consider some polynomial equations which define Gaussian Graphical models in algebraic statistics. First, we briefly review background materials and some preliminaries on this topic. Next, we regard a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle graph and explain how to prove it. We also report a result on higher linear syzygies of any model coming from block graphs. The former work was done jointly with A. Conner and M. Michalek and the latter with J. Choe. END:VEVENT BEGIN:VEVENT DTSTART:20240521T161500 DTEND:20240521T181500 DTSTAMP:20240520T150000Z UID:f218aac4fc8f4da8cefbecf730e2fd10@cgp.ibs.re.kr SUMMARY:Automorphisms and deformations of regular semisimple Hessenberg varieties LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Donggun Lee\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Hessenberg varieties are subvarieties in flag varieties which have interesting nontrivial symmetric group actions on their cohomology. In this talk, we discuss automorphisms and deformations of Hessenberg varieties when they are hypersurfaces in flag varieties. Especially in type A, we provide a complete classification, along with an interpretation in terms of moduli of pointed rational curves, and describe the moduli stack of regular semisimple Hessenberg varieties. This is a joint work in progress with P. Brosnan, L. Escobar, J. Hong, E. Lee, A. Mellit and E. Sommers. END:VEVENT BEGIN:VEVENT DTSTART:20240329T101500 DTEND:20240329T120000 DTSTAMP:20240328T150000Z UID:a1cc073c27c9697bc462294f480875c0@cgp.ibs.re.kr SUMMARY:Reading seminar on quantum entanglement and related topics; Contact geometry and black hole thermodynamics LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Reading Seminar\n\nAbstract: I will explain the contact geometric formulation of black hole theormodynamics following the paper by Ahosh. Ghosh and Chandrasekhar Bhamidipati (arXiv:19019.11506v4). Along the way, I will also review basic black hole thermodynamics. END:VEVENT BEGIN:VEVENT DTSTART:20240405T101500 DTEND:20240405T120000 DTSTAMP:20240404T150000Z UID:ab78bc3ef07618f30bf7df55366f736d@cgp.ibs.re.kr SUMMARY:Reading seminar on quantum entanglement and related topics; Contact geometry and black hole thermodynamics LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Reading Seminar\n\nAbstract: We will discuss the energy conditions on the energy-momentum tensors, and examine various exact solutions (space-times) of Einstein's equation and their properties. END:VEVENT BEGIN:VEVENT DTSTART:20240412T101500 DTEND:20240412T120000 DTSTAMP:20240411T150000Z UID:78f247006a6905cd32e92848631aad7b@cgp.ibs.re.kr SUMMARY:Reading seminar on quantum entanglement and related topics; Contact geometry and black hole thermodynamics LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Reading Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20240426T101500 DTEND:20240426T120000 DTSTAMP:20240425T150000Z UID:343eba6a7109563dc3d2abca8872559f@cgp.ibs.re.kr SUMMARY:Reading seminar on black hole information paradox LOCATION:CGP Delta DESCRIPTION:Speaker: Jorge Valcarcel\n\nEvent: Reading Seminar\n\nAbstract: Black hole information paradox is a thought experiment that points out an apparent conflict between two of the most remarkable theories in Physics: quantum field theory and general relativity. In this talk, I will give a pedagogical introduction to quantum field theory in curved space-time and its fundamental role in the apparent loss of information in black holes. END:VEVENT BEGIN:VEVENT DTSTART:20240503T101500 DTEND:20240503T120000 DTSTAMP:20240502T150000Z UID:52f1817de3496de3072f11c1a44aa42e@cgp.ibs.re.kr SUMMARY:Reading seminar on quantum entanglement and related topics; Contact geometry and black hole thermodynamics LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Reading Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20240628T101500 DTEND:20240628T120000 DTSTAMP:20240627T150000Z UID:7f8e1c5f57af9150759caf4822a68d60@cgp.ibs.re.kr SUMMARY:Contact geometry and black hole thermodynamics of AdS spacetimes LOCATION:CGP Delta DESCRIPTION:Speaker: Yong-Geun Oh\n\nEvent: Reading Seminar\n\nAbstract: Continuation of the last talk : We will continue the lecture on the contact geometric interpretation of black hole thermodynamics of AdS spacetimes. END:VEVENT BEGIN:VEVENT DTSTART:20240522T170000 DTEND:20240522T180000 DTSTAMP:20240521T150000Z UID:7819e2fafe9d0e9de561df162da55a1e@cgp.ibs.re.kr SUMMARY:Tetrahedron and 3D reflection equations in integrable systems and quantum cluster algebras LOCATION:Online Streaming DESCRIPTION:Speaker: Atsuo Kuniba\n\nEvent: Eastern Hemisphere Colloquium on Geometry and Physics (EHCGP) : Biweekly\n\nAbstract: Tetrahedron and three-dimensional (3D) reflection equations are generalizations of the Yang-Baxter and 2D reflection equations into 3D systems. By now, a number of interesting solutions have been constructed which are connected to the representation theory of quantized coordinate rings, quantum cluster algebras and so forth. In this talk I will briefly review the subject and present a new solution associated with the Fock-Goncharov quiver as a main example.(Joint work with Rei Inoue, Xiaoyue Sun, Yuji Terashima and Junya Yagi)Please register for Zoom link here by May 20. END:VEVENT BEGIN:VEVENT DTSTART:20240430T161500 DTEND:20240430T181500 DTSTAMP:20240429T150000Z UID:117d98fe22ffe9d41110a2d1c225d572@cgp.ibs.re.kr SUMMARY:Curvature of Direct Images and Infinitesimal Deformations LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Luca Rizzi\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Let $f\colon X\to B$ be a proper holomorphic fibration of relative dimension $n$ between two non-singular, compact K\"ahler manifolds. We show some key properties of the curvature of the direct images of sheaves of relative differential forms $R^if_*\Omega_{X/B}^{n-i}$ and of their twists by suitable line bundles $R^if_*(\Omega_{X/B}^{n-i}\otimes L)$. In particular, the curvature of the direct image of the relative dualizing sheaf $f_*\omega_{X/B}$ is strictly related to questions concerning the infinitesimal deformations of the fibers of $f$ and the cup product with the associated Kodaira-Spencer class.As a generalization, we show how these ideas can be used to relate curvature of suitable vector bundles and deformations of semistable maps with fixed target. END:VEVENT BEGIN:VEVENT DTSTART:20240502T161500 DTEND:20240502T181500 DTSTAMP:20240501T150000Z UID:777da65cfe4ef5a9271ceb4877d53cee@cgp.ibs.re.kr SUMMARY:Classification of neighbourhoods around leaves of a singular foliation LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Simon-Raphael Fischer\n\nEvent: CGP Seminar\n\nAbstract: This talk is about my recent work with Camille Laurent-Gengoux. I will present our results aboutclassifying singular foliations admitting a given leaf and a given transverse model; a transverse model is a singular foliation admitting a fixed point as a leaf. Such a classification is motivated by the fact that every foliation induces a singular foliation in the fibres of a normal bundle, the transverse (singular) foliation, and these transverse foliations at each point in the given leaf are canonically isomorphic, giving rise to a Lie algebra bundle whose characteristic Lie algebra defines the transverse model. Those isomorphisms are given by the parallel transport of a canonical connection associated to every singular foliation.The idea of this talk is to recover a singular foliation given the transverse model, and we will see that in a local neighbourhood around the fixed leaf every foliation admitting the given transverse model is in aone-to-one correspondence to a certain (possibly infinite-dimensional) principal bundle. END:VEVENT BEGIN:VEVENT DTSTART:20240429T161500 DTEND:20240429T181500 DTSTAMP:20240428T150000Z UID:b33be5ade984892945696e72bad51315@cgp.ibs.re.kr SUMMARY:Symplectic approach to Milnor fibers of surface singularities LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Symplectic Monday Seminar\n\nAbstract: (This seminar also serves as a schedule coordination for future plan for the seminar : Symplectic geometry and birational geometry)
For a surface singularity, the link of the singularity and the general fiber of its smoothing have the natural 3-dimensional contact and 4-dimensional symplectic structure respectively.
I am trying to study two related topics on the Milnor fibers.
One topic is the comparision between the Milnor fibers(as the general fiber of a smoothing) and the sympelctif fillings(as a 4 dimensional sympelctic manifolds that the boundary is the link of the singularity).
Symplectic fillings can often be derived from Milnor fibers, though there are also many cases where this is not possible. I will give brief overview of this topic. This topic was in the disccusion with Hakho Choi, Heesang Park, Jongil Park and Dongsoo Shin.
The other topic is the Mirror symmetry of the object. I am a novice for this topic. Therefore, I will give my research aim and want to make plan for reading related papers. END:VEVENT BEGIN:VEVENT DTSTART:20240516T161500 DTEND:20240516T181500 DTSTAMP:20240515T150000Z UID:60acc735cd25861582b28be8c4d4e44e@cgp.ibs.re.kr SUMMARY:Polyhedral parametrization of canonical bases LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Gleb Koshevoi\n\nEvent: CGP Seminar\n\nAbstract: Parametrizations of the canonical bases, string basis and theta basis, can be obtained by the tropicalization of the Berenstein-Kazhdan decoration function and the Gross-Hacking-Keel-Kontsevich potential respectively. For a classical Lie algebra and a reduced decomposition $\mathbf i$, the decorated graphs are constructed algorithmically, vertices of such graphs are labeled by monomials which constitute the set of monomials of the Berenstein-Kazhdan potential. Due to this algorithm we obtain a characterization of $\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our algorithm uses multiplication and summations only, its complexity is linear in time of writing the monomials of the potential. For SL_n, there is an algorithm due to Gleizer and Postnikov which gets all monomials of the Berenstein-Kazhdan potential using combinatorics of wiring diagrams. For this case, our algorithm uses simpler combinatorics and is faster than the Gleizer-Postnikov algorithm. For computing Gross-Hacking-Keel-Kontsevich potential there is an algorithm using cluster mutations due to Genz, Schumann and me, which is polynomial in time but it uses divisions of polynomials of several variables.The talk is based on joint works with Yuki Kanakubo and Toshiki Nakashima and with Volker Genz and Bea Schumann. END:VEVENT BEGIN:VEVENT DTSTART:20240926T141500 DTEND:20240926T154500 DTSTAMP:20240925T150000Z UID:ef0bb757004746e6a577b0925bce199c@cgp.ibs.re.kr SUMMARY:K-stability of Fano 3-fold hypersurfaces of index 1 LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Takuzo Okada\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: My talk is on the 95 families of quasismooth Fano 3-fold weighted hypersurfaces of index 1. It is conjectured that any such Fano 3-fold is K-stable. This conjecture is verified for 84 families due to the previous works by Cheltsov, Cheltsov-Park-Won, Fujita, Kim-Okada-Won and Sano-Tasin. I will explain the very recent result: we complete the proof of K-stability of the remaining 11 families and the conjecture is fully verified. This is a joint work with Livia Campo. END:VEVENT BEGIN:VEVENT DTSTART:20240528T160000 DTEND:20240528T173000 DTSTAMP:20240527T150000Z UID:5b854f15f51ae78da336226335831afb@cgp.ibs.re.kr SUMMARY:POSTECH Many-Body Physics Study Group LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: TBA\n\nEvent: Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20240603T093000 DTEND:20240603T103000 DTSTAMP:20240602T150000Z UID:1a776d527d6f22ed925c5f87aa32817b@cgp.ibs.re.kr SUMMARY:Skein valued open curve counts I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Counting open holomorphic curves with Maslov zero Lagrangian boundary condition in Calabi-Yau threefolds by the values of their boundaries in the HOMFLYPT skein module of the Lagrangian removes wall-crossing and leads to deformation invariant counts. We will describe this construction and discuss its applications. For example, we use the theory to give a mathematical proof of the Ooguri-Vafa conjecture giving an enumerative geometric meaning to all colored HOMFLYPT polynomials of knots and links in the three sphere. We will also show how in non-compact cases, curves at infinity lead to rather simple skein valued recursion relations that control the more complicated curve counts in the bulk, for example we give three simple polynomials in the skein of the torus that determine all colored HOMFLYPT polynomials of the Hopf link. END:VEVENT BEGIN:VEVENT DTSTART:20240604T093000 DTEND:20240604T103000 DTSTAMP:20240603T150000Z UID:9693de707a60aecb1c66541fd6c6cf86@cgp.ibs.re.kr SUMMARY:Skein valued open curve counts II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Counting open holomorphic curves with Maslov zero Lagrangian boundary condition in Calabi-Yau threefolds by the values of their boundaries in the HOMFLYPT skein module of the Lagrangian removes wall-crossing and leads to deformation invariant counts. We will describe this construction and discuss its applications. For example, we use the theory to give a mathematical proof of the Ooguri-Vafa conjecture giving an enumerative geometric meaning to all colored HOMFLYPT polynomials of knots and links in the three sphere. We will also show how in non-compact cases, curves at infinity lead to rather simple skein valued recursion relations that control the more complicated curve counts in the bulk, for example we give three simple polynomials in the skein of the torus that determine all colored HOMFLYPT polynomials of the Hopf link. END:VEVENT BEGIN:VEVENT DTSTART:20240605T110000 DTEND:20240605T120000 DTSTAMP:20240604T150000Z UID:810f2513de7b923e9f51764ed472d4b1@cgp.ibs.re.kr SUMMARY:Skein valued open curve counts III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Counting open holomorphic curves with Maslov zero Lagrangian boundary condition in Calabi-Yau threefolds by the values of their boundaries in the HOMFLYPT skein module of the Lagrangian removes wall-crossing and leads to deformation invariant counts. We will describe this construction and discuss its applications. For example, we use the theory to give a mathematical proof of the Ooguri-Vafa conjecture giving an enumerative geometric meaning to all colored HOMFLYPT polynomials of knots and links in the three sphere. We will also show how in non-compact cases, curves at infinity lead to rather simple skein valued recursion relations that control the more complicated curve counts in the bulk, for example we give three simple polynomials in the skein of the torus that determine all colored HOMFLYPT polynomials of the Hopf link. END:VEVENT BEGIN:VEVENT DTSTART:20240605T153000 DTEND:20240605T163000 DTSTAMP:20240604T150000Z UID:34c3f06844dfac8d1c62037e04fc6b0c@cgp.ibs.re.kr SUMMARY:Skein valued open curve counts IV LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tobias Ekholm\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Counting open holomorphic curves with Maslov zero Lagrangian boundary condition in Calabi-Yau threefolds by the values of their boundaries in the HOMFLYPT skein module of the Lagrangian removes wall-crossing and leads to deformation invariant counts. We will describe this construction and discuss its applications. For example, we use the theory to give a mathematical proof of the Ooguri-Vafa conjecture giving an enumerative geometric meaning to all colored HOMFLYPT polynomials of knots and links in the three sphere. We will also show how in non-compact cases, curves at infinity lead to rather simple skein valued recursion relations that control the more complicated curve counts in the bulk, for example we give three simple polynomials in the skein of the torus that determine all colored HOMFLYPT polynomials of the Hopf link. END:VEVENT BEGIN:VEVENT DTSTART:20240603T110000 DTEND:20240603T120000 DTSTAMP:20240602T150000Z UID:3c9b24e78a00c98fe42a6ecc32f84471@cgp.ibs.re.kr SUMMARY:Floer cohomology for contact isotopies of ideal boundaries LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Dylan Cant\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: I will present recent work concerning the Floer cohomology associated to a contact isotopy of the ideal boundary of a convex-at-infinity symplectic manifold. This framework is a flexible tool for studying contact isotopies, and the technical background is based on well-established analytical results in Floer theory. Applications to Shelukhin's Hofer geometry on the contactomorphism group, orderability of the contactomorphism group, and contact non-squeezing will be discussed. END:VEVENT BEGIN:VEVENT DTSTART:20240603T140000 DTEND:20240603T150000 DTSTAMP:20240602T150000Z UID:0fd4d756f9c292d3dd3c85e22eeb873b@cgp.ibs.re.kr SUMMARY:Heegaard Floer theory, new perspectives and applications I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Ian Zemke\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: The goal of these lectures is to describe some applications of Heegaard Floer theory. In the first lecture, we will give an introduction to the basics of Ozsváth and Szabó's Heegaard Floer homology and knot Floer homology. In the second lecture, we will describe functorial aspects of Heegaard Floer theory, focusing on the knot and link theories. We will describe some applications of the TQFT, such as obstructions to ribbon concordances. The the third lecture, we will describe applications of Heegaard Floer theory to the homology cobordism group and the knot concordance group, focusing on the involutive refinement of Hendricks and Manolescu. In the fourth lecture, we will describe the link Floer homology of algebraic links. END:VEVENT BEGIN:VEVENT DTSTART:20240604T153000 DTEND:20240604T163000 DTSTAMP:20240603T150000Z UID:2d051796c5229dd71285bb113ca0d41f@cgp.ibs.re.kr SUMMARY:Heegaard Floer theory, new perspectives and applications II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Ian Zemke\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: The goal of these lectures is to describe some applications of Heegaard Floer theory. In the first lecture, we will give an introduction to the basics of Ozsváth and Szabó's Heegaard Floer homology and knot Floer homology. In the second lecture, we will describe functorial aspects of Heegaard Floer theory, focusing on the knot and link theories. We will describe some applications of the TQFT, such as obstructions to ribbon concordances. The the third lecture, we will describe applications of Heegaard Floer theory to the homology cobordism group and the knot concordance group, focusing on the involutive refinement of Hendricks and Manolescu. In the fourth lecture, we will describe the link Floer homology of algebraic links. END:VEVENT BEGIN:VEVENT DTSTART:20240605T093000 DTEND:20240605T103000 DTSTAMP:20240604T150000Z UID:0cf840c536a5b10e30b365a0372735b9@cgp.ibs.re.kr SUMMARY:Heegaard Floer theory, new perspectives and applications III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Ian Zemke\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: The goal of these lectures is to describe some applications of Heegaard Floer theory. In the first lecture, we will give an introduction to the basics of Ozsváth and Szabó's Heegaard Floer homology and knot Floer homology. In the second lecture, we will describe functorial aspects of Heegaard Floer theory, focusing on the knot and link theories. We will describe some applications of the TQFT, such as obstructions to ribbon concordances. The the third lecture, we will describe applications of Heegaard Floer theory to the homology cobordism group and the knot concordance group, focusing on the involutive refinement of Hendricks and Manolescu. In the fourth lecture, we will describe the link Floer homology of algebraic links. END:VEVENT BEGIN:VEVENT DTSTART:20240607T093000 DTEND:20240607T103000 DTSTAMP:20240606T150000Z UID:9e843149d621692a5f0e97bb4992902d@cgp.ibs.re.kr SUMMARY:Heegaard Floer theory, new perspectives and applications IV LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Ian Zemke\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: The goal of these lectures is to describe some applications of Heegaard Floer theory. In the first lecture, we will give an introduction to the basics of Ozsváth and Szabó's Heegaard Floer homology and knot Floer homology. In the second lecture, we will describe functorial aspects of Heegaard Floer theory, focusing on the knot and link theories. We will describe some applications of the TQFT, such as obstructions to ribbon concordances. The the third lecture, we will describe applications of Heegaard Floer theory to the homology cobordism group and the knot concordance group, focusing on the involutive refinement of Hendricks and Manolescu. In the fourth lecture, we will describe the link Floer homology of algebraic links. END:VEVENT BEGIN:VEVENT DTSTART:20240604T140000 DTEND:20240604T150000 DTSTAMP:20240603T150000Z UID:885448ab19e452092e1309751c74fe51@cgp.ibs.re.kr SUMMARY:Symplectic annular Khovanov homology and knot symmetry LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Kristen Hendricks\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Khovanov homology is a combinatorially-defined invariant which has proved to contain a wealth of geometric information. In 2006 Seidel and Smith introduced a candidate Lagrangian Floer analog of the theory, which has been shown by Abouzaid and Smith to be isomorphic to the original theory over fields of characteristic zero. The relationship between the theories is still unknown over other fields. In 2010 Seidel and Smith showed there is a spectral sequence relating the symplectic Khovanov homology of a two-periodic knot to the symplectic Khovanov homology of its quotient; in contrast, in 2018 Stoffregen and Zhang used the Khovanov homotopy type to show that there is a spectral sequence from the combinatorial Khovanov homology of a two-periodic knot to the annular Khovanov homology of its quotient. (An alternate proof of this result was subsequently given by Borodzik, Politarczyk, and Silvero.) These results necessarily use coefficients in the field of two elements. This inspired investigations of Mak and Seidel into an annular version of symplectic Khovanov homology, which they defined over characteristic zero. In this talk we introduce a new, conceptually straightforward, formulation of symplectic annular Khovanov homology, defined over any field. Using this theory, we show how to recover the Stoffregen-Zhang spectral sequence on the symplectic side. We further give an analog of recent results of Lipshitz and Sarkar for the Khovanov homology of strongly invertible knots. This is work in progress with Cheuk Yu Mak and Sriram Raghunath. END:VEVENT BEGIN:VEVENT DTSTART:20240605T140000 DTEND:20240605T150000 DTSTAMP:20240604T150000Z UID:fe68eef5efc6f541a994e5cc22a7a101@cgp.ibs.re.kr SUMMARY:Relating d-invariants and signatures for 2-component links LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jonathan Hanselman\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: For an n-component link L in S^3, we consider the Heegaard Floer d-invariants associated with the 2^{n-1} spin structures on the double branched cover of L. When L is a knot and the double branched cover is an L-space, Lin-Ruberman-Saveliev showed that the d-invariant is -1/4 times the signature. We show that an analogous statement holds for 2-component links when the double branched cover is a graph manifold. The result by Lin-Ruberman-Saveliev in fact shows the same relationship holds in this case if we sum over the two spin structures; it remains to relate the difference between the two spin structures for each invariant. To do this we relate both the difference in d-invariants and the difference in signatures to a new invariant for plumbing trees of the appropriate form defined using bordered Floer homology. The new invariant relies on the immersed curve formulation of bordered Floer invariants; it exploits a symmetry of the immersed curves representing bordered Floer homology and measures the deviation of a distinguished curve from a straight line. By analyzing how plumbing tree operations affect immersed curves we can prove the desired relationship inductively for all appropriate plumbing trees. END:VEVENT BEGIN:VEVENT DTSTART:20240607T140000 DTEND:20240607T150000 DTSTAMP:20240606T150000Z UID:60848903a82f1cd825047b5dcfacee4b@cgp.ibs.re.kr SUMMARY:Plumbed 3-Manifolds, BPS Spectra and Machine Learning LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Rak-Kyeong Seong\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: We study a family of plumbed 3-manifolds corresponding to 3-dimensional N=2 strongly coupled supersymmetric theories. In particular, we explore the statistical properties of BPS q-series, which are BPS indices associated with the 3d N=2 theory and can be considered as invariants of the plumbed 3-manifolds. By using explainable machine learning techniques, we discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q, implying that the q-series capture most of the information about the quantum system with the first few terms in their expansion. END:VEVENT BEGIN:VEVENT DTSTART:20240607T153000 DTEND:20240607T163000 DTSTAMP:20240606T150000Z UID:5dea4737f6224eed47e9cc35d001895c@cgp.ibs.re.kr SUMMARY:Legendrian contact instanton cohomology and its spectral invariants on the one-jet bundle LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seung-ook Yu\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Pseudoholomorphic curves on symplectization have been used to study contact topology and dynamics. The analysis of contact instantons, which is developed by Oh, directly studies contact topology and dynamics without symplectization, in contrast to pseudoholomorphic curves on symplectization. In this talk, we apply this theory to the case of one-jet bundles and associate the Legendrian contact instanton cohomology $HI^*(J^1B, H; R)$ to each Legendrian submanifold $R$ contact isotopic to the zero section of the one-jet bundle. Then we give a Floer theoretic construction of Legendrian spectral invariants and establish their basic properties. This talk is a joint work with Yong-Geun Oh. END:VEVENT BEGIN:VEVENT DTSTART:20240610T093000 DTEND:20240610T103000 DTSTAMP:20240609T150000Z UID:77a841382c71cac60f8fda672fb17e72@cgp.ibs.re.kr SUMMARY:Topological and smooth disks in 4-manifolds I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jae Choon Cha\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In dimension 4, the works of Freedman and Donaldson led us to the striking discovery that the smooth category behaves very differently from the topological category, compared to other dimensions. Since then, studying “topological $\ne$ smooth” has been a very successful direction in various contexts in dimension 4, using modern smooth techniques. The difference is essentially from the non-smoothability of certain topological disks in 4-manifolds. On the other hand, little was understood, if any, about when smooth and topological cases are similar in dimension 4. We will discuss some backgrounds and recent progress on the difference and similarity of topological and smooth disks and their isotopy in 4-manifolds, including new “topological = smooth” results for disks admitting algebraic dual spheres in the boundary. END:VEVENT BEGIN:VEVENT DTSTART:20240611T153000 DTEND:20240611T163000 DTSTAMP:20240610T150000Z UID:48645c150660f04536f8fee62b3192b3@cgp.ibs.re.kr SUMMARY:Topological and smooth disks in 4-manifolds II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jae Choon Cha\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In dimension 4, the works of Freedman and Donaldson led us to the striking discovery that the smooth category behaves very differently from the topological category, compared to other dimensions. Since then, studying “topological $\ne$ smooth” has been a very successful direction in various contexts in dimension 4, using modern smooth techniques. The difference is essentially from the non-smoothability of certain topological disks in 4-manifolds. On the other hand, little was understood, if any, about when smooth and topological cases are similar in dimension 4. We will discuss some backgrounds and recent progress on the difference and similarity of topological and smooth disks and their isotopy in 4-manifolds, including new “topological = smooth” results for disks admitting algebraic dual spheres in the boundary. END:VEVENT BEGIN:VEVENT DTSTART:20240613T093000 DTEND:20240613T103000 DTSTAMP:20240612T150000Z UID:1703dd38b7fab490ffab9fe027658a78@cgp.ibs.re.kr SUMMARY:Topological and smooth disks in 4-manifolds III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jae Choon Cha\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In dimension 4, the works of Freedman and Donaldson led us to the striking discovery that the smooth category behaves very differently from the topological category, compared to other dimensions. Since then, studying “topological $\ne$ smooth” has been a very successful direction in various contexts in dimension 4, using modern smooth techniques. The difference is essentially from the non-smoothability of certain topological disks in 4-manifolds. On the other hand, little was understood, if any, about when smooth and topological cases are similar in dimension 4. We will discuss some backgrounds and recent progress on the difference and similarity of topological and smooth disks and their isotopy in 4-manifolds, including new “topological = smooth” results for disks admitting algebraic dual spheres in the boundary. END:VEVENT BEGIN:VEVENT DTSTART:20240610T110000 DTEND:20240610T120000 DTSTAMP:20240609T150000Z UID:778af03252db7b91b135eeb5ee446304@cgp.ibs.re.kr SUMMARY:Relative Calabi-Yau structures on wrapped Fukaya categories LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hanwool Bae\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Rabinowitz Floer homology, introduced by Cieliebak and Frauenfelder, is a Floer homology associated to a symplectic manifold with contact boundary. In the open-string setting, Rabinowitz Floer homology can be associated to a pair of Lagrangian submanifolds with Legendrian boundary. Rabinowitz Fukaya category is a categorification of Rabinowitz Floer homology of Lagrangian submanifolds. By its construction, there is a natural A_infinity functor from wrapped Fukaya category to Rabinowitz Fukaya category.
In this talk, I will introduce the notion of relative (graded) proper Calabi-Yau structure on an A_infinity functor between (graded) proper A_infinity categories, which was introduced by Brav-Dyckerhoff. Then I will explain that under the assumption that the wrapped Fukaya category of a Liouville domain is graded proper, the natural functor from the wrapped Fukaya category to the Rabinowitz Fukaya category is relative graded proper Calabi-Yau. END:VEVENT BEGIN:VEVENT DTSTART:20240610T140000 DTEND:20240610T150000 DTSTAMP:20240609T150000Z UID:27e128cf2c4d51b1eb5f976ed58eefc3@cgp.ibs.re.kr SUMMARY:Legendrian links, Lagrangian fillings, and cluster structures LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Youngjin Bae\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: We will discuss Legendrian links of finite and affine type, and then argue that there are at least as many Lagrangian fillings as seeds in the corresponding cluster structure. The main ingredients are N-graphs developed by Casals-Zaslow, and cluster structures by Fomin-Zelevinsky. This is a joint work with Eunjeong Lee, and Byung Hee An. END:VEVENT BEGIN:VEVENT DTSTART:20240611T093000 DTEND:20240611T103000 DTSTAMP:20240610T150000Z UID:4d939bc3296aa0ccaa3de8abd4f7f452@cgp.ibs.re.kr SUMMARY:Invariant splitting principles for the Lipshitz-Ozsváth-Thurston correspondence LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sungkyung Kang\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: We prove that the Lipshitz-Ozsváth-Thurston correspondence between extended type D structures of knot complements and F[U,V]/(UV) knot Floer complexes can be arranged so that involution-invariant splittings of knot Floer chain complexes correspond to bordered involution-invariant splittings of bordered Floer homology of knot complements. For patterns satisfying the satellite extension property, which include cabling patterns, this provides a novel way to compute the involutive knot Floer homology of satellites from that of their companions. END:VEVENT BEGIN:VEVENT DTSTART:20240614T110000 DTEND:20240614T120000 DTSTAMP:20240613T150000Z UID:e5121e2ab88eb6989c16c0b6c79dd3c3@cgp.ibs.re.kr SUMMARY:Minimal periodic orbits on 3D convex hypersurfaces LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jungsoo Kang\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In 1998, Hofer, Wysocki, and Zehnder asked whether a minimal periodic orbit on a convex hypersurface in R^4 bounds a global surface of section of disk type (or equivalently, is unknotted and has self-linking number -1). In this talk, I will give a proof answering this question positively. This is joint work with Alberto Abbondandolo and Oliver Edtmair. END:VEVENT BEGIN:VEVENT DTSTART:20240611T140000 DTEND:20240611T150000 DTSTAMP:20240610T150000Z UID:6595466c63e81329462019454f9e5742@cgp.ibs.re.kr SUMMARY:Computational symplectic topology and RTBP LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Otto van Koert\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In this joint work with Chankyu Joung, I discuss how a computer can be used to prove theorems in symplectic topology. I will focus on application of symplectic topology to the classical three-body problem, and discuss how how to prove properties and existence of periodic orbits, including some Floer theoretical information. END:VEVENT BEGIN:VEVENT DTSTART:20240612T093000 DTEND:20240612T103000 DTSTAMP:20240611T150000Z UID:1ba9e54cea4385443b48e3da1024875a@cgp.ibs.re.kr SUMMARY:Exotic boundary Dehn twists on 4-manifolds LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jianfeng Lin\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: Given a 4-manifold X bounded by a Seifert manifold, one can use the circle action on the boundary to define a diffeomorphism on X, called the boundary Dehn twist. Such boundary Dehn twist naturally arises as monodromy of Milnor fibrations. In this talk, we will discuss a proof (using monopole Floer homology) that some of these Dehn twists represents "exotic" elements of infinite order in the mapping class group. This talk is based on a joint work in progress with Hokuto Konno, Anubhav Mukherjee and Juan Munoz-Echaniz. END:VEVENT BEGIN:VEVENT DTSTART:20240612T110000 DTEND:20240612T120000 DTSTAMP:20240611T150000Z UID:d9586fde010ec114d4287e448cec1908@cgp.ibs.re.kr SUMMARY:Calegari spheres and doubles of Casson-Gordon balls are standard LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Min Hoon Kim\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In 2009, Danny Calegari constructed an infinite family of smooth homotopy 4-balls from free group automorphisms. In this talk, I will prove that smooth homotopy 4-spheres constructed by Calegari are diffeomorphic to the standard 4-sphere. As a corollary, I will also prove that the doubles of Casson-Gordon homotopy 4-balls from fibered, ribbon knots in the 3-sphere are diffeomorphic to the 4-sphere. END:VEVENT BEGIN:VEVENT DTSTART:20240613T140000 DTEND:20240613T150000 DTSTAMP:20240612T150000Z UID:2d1dc9ac40279776aa74be1e82f69b7f@cgp.ibs.re.kr SUMMARY:Symplectic automorphisms with simple asymptotic behavior LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sangjin Lee\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: As the title implies, our focus is on symplectic automorphisms exhibiting simple asymptotic behaviors—that is, symplectic automorphisms $\phi$ for which $\phi^n$ behaves simply as $n \to \pm \infty$.
During the first half of the presentation, we will discuss the motivation behind studying asymptotic behaviors. In the latter portion, we will present our recent results, which involve constructing symplectic automorphisms with simple asymptotic behaviors from both geometric and Fukaya category perspectives. END:VEVENT BEGIN:VEVENT DTSTART:20240613T153000 DTEND:20240613T163000 DTSTAMP:20240612T150000Z UID:6ef388bad29e91cae5060bd7b0ba6ff5@cgp.ibs.re.kr SUMMARY:Non-squeezing of Legendrians and open subsets in prequantization bundles LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Georgios Dimitroglou Rizell\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: We use a version of Rabinowitz-Floer homology for Legendrians defined using Symplectic Field Theory, and its quantitative invariance, to show that Legendrian lifts of Bohr—Sommerfeld Lagrangians satisfy a non-squeezing property. Consequences includes classical contact non-squeezing for preimages of symplectic balls and cubes under the prequantization-bundle projection. This is joint work with M. Sullivan. END:VEVENT BEGIN:VEVENT DTSTART:20240614T093000 DTEND:20240614T103000 DTSTAMP:20240613T150000Z UID:8a2e46932db816b4c8d7448a1bac3b5b@cgp.ibs.re.kr SUMMARY:Unboundedness from Hamiltonian deformations and symplectic squeezings LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jun Zhang\n\nEvent: 2024 MATRIX-IBSCGP Workshop on Symplectic and Low-dimensional Topology\n\nAbstract: In this talk, we will establish several separate constructions in symplectic geometry that result in various unboundedness phenomena. The objects in these constructions range from Hamiltonian diffeomorphisms, Lagrangian submanifolds, and Liouville domains. Here, unboundedness means diverging under a certain metric or no restrictions on geometry. More explicitly two key results: one, we prove that the orbit space of a Lagrangian fiber in some cotangent bundles contains a large family of Hamiltonian deformations that diverges under the Floer-theoretic spectral metric; two, we prove that any bounded Liouville domain in the cotangent bundle of a torus, in any dimension, can symplectically be squeezed into a fixed Liouville domain as a trivial bundle over this torus with the fiber being an irrationally tilted cylinder. This talk is based on joint work with Qi Feng. END:VEVENT BEGIN:VEVENT DTSTART:20240528T100000 DTEND:20240528T120000 DTSTAMP:20240527T150000Z UID:48edbec660f570275ad947d637582b4a@cgp.ibs.re.kr SUMMARY:2024 IBS Risk Assessment LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: IBS Safety Department\n\nEvent: Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20240529T161500 DTEND:20240529T181500 DTSTAMP:20240528T150000Z UID:8fc7190d07fcb5fdc1d89cddec490f79@cgp.ibs.re.kr SUMMARY:Some topological properties of Milnor fibers of sandwiched singularities LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: (continuation of the previous semianr)I will introduce the result of de Jong and van Straten about an approach to topological properties to Milnor fibers of sandwiched singularities.It contains descriptions of homology, intersection form and fundamental group of Milnor fibers of sandwiched singularities. END:VEVENT BEGIN:VEVENT DTSTART:20240618T161500 DTEND:20240618T173000 DTSTAMP:20240617T150000Z UID:eb5ab9decf93ab2a25c532742898f68b@cgp.ibs.re.kr SUMMARY:Central derivative values of Rankin-Selberg L-functions as periods and metaplectic Fourier coefficients LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Jeanine Van Order\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Motivated by the conjectures of Birch-Swinnerton-Dyer and Bloch-Kato, I will explain how we expect andsometimes know that the central derivative values of certain Rankin-Selberg L-functions can be realized as both periods and as Fourier coefficients of certain metaplectic forms. This is based partly on ongoing joint work with Spencer Bloch. END:VEVENT BEGIN:VEVENT DTSTART:20240708T161500 DTEND:20240708T181500 DTSTAMP:20240707T150000Z UID:90f8e7972dcbdb62209bd20433af8744@cgp.ibs.re.kr SUMMARY:Family Floer Program and a Mathematical Formulation of the SYZ Conjecture LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yuan Hang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Given a graded or special Lagrangian fibration, we propose that the dual torus fibration, for a precise formulation of the SYZ conjecture, must be a non-Archimedean version of torus fibration over the Novikov field.This proposal is based on a toy model of the SYZ conjecture between the complex logarithm map and the non-Archimedean tropicalization map, both viewed as torus fibrations over Euclidean space with the trivial integral affine structure. A canonical globalization of this toy model, preserving the integral affine structure, is achieved based on Fukaya-Oh-Ohta-Ono’s Lagrangian Floer theory, some novel ud-homotopy theory of A-infinity structures, and non-archimedean geometry.To further justify it, we discuss applications in Lagrangian Floer theory using the non-Archimedean structure and suggest a geometric version of unobstructedness that enriches the concept of bounding cochains. We also present explicit examples of SYZ duality that exactly align with physics predictions and Mark Gross's topological mirror symmetry. A key new feature is the inclusion of both Lagrangian and non-Archimedean singular fibers on the two sides. END:VEVENT BEGIN:VEVENT DTSTART:20240711T161500 DTEND:20240711T181500 DTSTAMP:20240710T150000Z UID:8c9879e0223ecb71c60b99527668ff69@cgp.ibs.re.kr SUMMARY:Finding isomorphic quantum field theories LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Monica Jinwoo Kang\n\nEvent: CGP Seminar\n\nAbstract: When do two different looking quantum field theories describe the same physics? This is essentially asking when the quantum field theories are isomorphic. In the case of topological quantum field theories, there is sometimes a way to determine them via topological invariants. For a superconformal field theory, what would be the minimal set of “invariants” to determine when they are isomorphic? I will discuss some approaches to this question in the context of a particular infinite class of superconformal field theories that admit Hitchin systems. Isomorphic pairs of such theories must have the same operator contents, such as Schur index and Hall-Littlewood index. Such theories can also be described using curve configurations and this will shine light on finding pairs of isomorphic superconformal field theories, which a priori look like distinct theories. In turn, this result provides a conjecture when two theories will necessarily have the same Schur index and Hall-Littlewood index. If time permitting, I will explain how this result further sheds light on the 3d (symplectic) duality. END:VEVENT BEGIN:VEVENT DTSTART:20240715T161500 DTEND:20240715T181500 DTSTAMP:20240714T150000Z UID:bb6ea4e3c4ac6acd34c36832b11017fb@cgp.ibs.re.kr SUMMARY:Operator algebras in holographic spacetime LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Monica Jinwoo Kang\n\nEvent: Symplectic Monday Seminar\n\nAbstract: Any physical theory is described with operators as its physical content and the local operators of a theory form an operator algebra. Unlike quantum fields, the algebra of local operators is an invariant notion of a quantum field theory that contains causal commutativity. Employing operator algebra as an invariant of quantum field theory, I will present a novel formalism, capturing how the algebra of local operators of quantum field theory encodes information about spacetime regions, which I apply to investigate both quantum field theory and quantum gravity. My formalism is particularly essential on understanding these theories, as they necessarily have infinite-dimensional Hilbert spaces. The particularly beneficial setting is in the context of holography, which enables lower dimensional boundary field theory to describe the emergent bulk gravity theory. This implies that quantum information in the bulk gravity is encoded redundantly in the boundary field theory, and hence the emergent bulk can be described by its quantum error correcting structure. I will present in my algebraic framework bulk reconstruction and relative entropy conservation, capture its quantum error correcting structure arising in the context of holographic spacetime, and discuss its significance. If time permitting, motivated by a recent conjecture of Bousso et. al. on the bulk AdS description of boundary cocycle flow, I will characterize (approximate) complementary recovery in terms of (approximate) intertwining of bulk and boundary cocycle derivatives. This suggests that from algebraic perspective, the kink transform is precisely the bulk cocycle flow, which provides the bulk geometry via geometric modular action and the notion of time. END:VEVENT BEGIN:VEVENT DTSTART:20240724T101500 DTEND:20240724T111500 DTSTAMP:20240723T150000Z UID:66c50689e053c825ce21499ef80fc632@cgp.ibs.re.kr SUMMARY:1. F-bundles and blowups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tony Yue Yu\n\nEvent: Intensive Lecture Series\n\nAbstract: I will discuss the basic ideas and properties of F-bundles and non-commutative Hodge structures, as well as applications to classical rationality problems in birational geometry. Joint work with Katzarkov, Kontsevich and Pantev. END:VEVENT BEGIN:VEVENT DTSTART:20240725T101500 DTEND:20240725T111500 DTSTAMP:20240724T150000Z UID:663b4703c97be47ede12222adaf666f7@cgp.ibs.re.kr SUMMARY:2. F-bundles and blowups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tony Yue Yu\n\nEvent: Intensive Lecture Series\n\nAbstract: I will discuss the basic ideas and properties of F-bundles and non-commutative Hodge structures, as well as applications to classical rationality problems in birational geometry. Joint work with Katzarkov, Kontsevich and Pantev. END:VEVENT BEGIN:VEVENT DTSTART:20240726T101500 DTEND:20240726T111500 DTSTAMP:20240725T150000Z UID:e2fccde35d9cfa65e632a1caeafcefe3@cgp.ibs.re.kr SUMMARY:3. F-bundles and blowups LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Tony Yue Yu\n\nEvent: Intensive Lecture Series\n\nAbstract: I will discuss the basic ideas and properties of F-bundles and non-commutative Hodge structures, as well as applications to classical rationality problems in birational geometry. Joint work with Katzarkov, Kontsevich and Pantev. END:VEVENT BEGIN:VEVENT DTSTART:20240725T161500 DTEND:20240725T181500 DTSTAMP:20240724T150000Z UID:31711b15281b7636f969f414af07f6c4@cgp.ibs.re.kr SUMMARY:Recent advances in the Langlands program LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: SugWoo Shin\n\nEvent: CGP Seminar\n\nAbstract: In this expository talk I will start by reviewing some pre-history (such as quadratic reciprocity) and early developments in the Langlands program. Then I will progress towards recent advances, highlighting certain ideas (but unfortunately skipping many others due to time constraints); one of them is Weil’s Rosetta Stone, which enriches and cross-pollinates different aspects of the Langlands program. END:VEVENT BEGIN:VEVENT DTSTART:20240621T100000 DTEND:20240621T120000 DTSTAMP:20240620T150000Z UID:95a0ffa34f5558f3bcacfe89cc225d2e@cgp.ibs.re.kr SUMMARY:2024 IBS Risk Assessment LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: IBS Safety Department\n\nEvent: Seminar\n\nAbstract: END:VEVENT BEGIN:VEVENT DTSTART:20240820T140000 DTEND:20240820T160000 DTSTAMP:20240819T150000Z UID:93079223e00a9ef26835317cbddce727@cgp.ibs.re.kr SUMMARY:An introductory course on mixed Hodge modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: This course gives an introduction to Morihiko Saito's theory of mixed Hodge modules. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. The main goal of this course is to understand how D-modules come into the theory and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry. The course goes as follows:Lecture 1: D-modules and perverse sheavesLecture 2: The classical Hodge theory and variations of Hodge structuresLecture 3: Hodge modulesLecture 4: Two important theorems END:VEVENT BEGIN:VEVENT DTSTART:20240820T163000 DTEND:20240820T173000 DTSTAMP:20240819T150000Z UID:975ca4f4478a9f3b824d681910a94d64@cgp.ibs.re.kr SUMMARY:On the resulting models of anti-MMP. LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: In this talk, we give some updates on a theory on a potential triples and anti-MMP. We study how to run the -(K_X+Δ)-minimal model program by suggesting the flowchart for such a program. We will also discuss the possible outcomes of the program. END:VEVENT BEGIN:VEVENT DTSTART:20240821T100000 DTEND:20240821T120000 DTSTAMP:20240820T150000Z UID:313bfaff7bf1e35fd728f5cb34f00691@cgp.ibs.re.kr SUMMARY:An introductory course on mixed Hodge modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: This course gives an introduction to Morihiko Saito's theory of mixed Hodge modules. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. The main goal of this course is to understand how D-modules come into the theory and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry. The course goes as follows:Lecture 1: D-modules and perverse sheavesLecture 2: The classical Hodge theory and variations of Hodge structuresLecture 3: Hodge modulesLecture 4: Two important theorems END:VEVENT BEGIN:VEVENT DTSTART:20240821T140000 DTEND:20240821T150000 DTSTAMP:20240820T150000Z UID:419b114dc1d69edd89d29617a4d1d2c3@cgp.ibs.re.kr SUMMARY:K-stability of weighted del pezzo hypersurfaces LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Joonyeong Won\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: For an importance of the existence problem of Sasaki-Einstein metrics on 5-dimensional manifolds, Kollar started to consider the existence problem of the Kaehler-Einstein metric of weighted del Pezzo hypersurfaces that was verified in low index cases. We discuss recent development of that problem. END:VEVENT BEGIN:VEVENT DTSTART:20240822T100000 DTEND:20240822T120000 DTSTAMP:20240821T150000Z UID:be7522bbbf73ed5f5ba081c76bba3ca8@cgp.ibs.re.kr SUMMARY:An introductory course on mixed Hodge modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: This course gives an introduction to Morihiko Saito's theory of mixed Hodge modules. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. The main goal of this course is to understand how D-modules come into the theory and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry. The course goes as follows:Lecture 1: D-modules and perverse sheavesLecture 2: The classical Hodge theory and variations of Hodge structuresLecture 3: Hodge modulesLecture 4: Two important theorems END:VEVENT BEGIN:VEVENT DTSTART:20240822T143000 DTEND:20240822T153000 DTSTAMP:20240821T150000Z UID:fef770502ba456b650bcf5ba77ce4bd9@cgp.ibs.re.kr SUMMARY:Relative Castelnuovo-de Franchis Theorem and monodromy of local systems associated to a VHS LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Luca Rizzi\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: Consider a semistable fibration between non-singular complex projective varieties. The relative holomorphic differential forms which are locally liftable to closed holomorphic forms naturally define local systems contained in the kernel of the variation of Hodge structure on the smooth part of the fibration.In this setting, we present a relative version of a theorem by Castelnuovo and de Franchis and use it to show the existence, up to base change, of higher irrational pencils and the finiteness of the monodromy representations associated to these local systems.We interpret these results in light of the so called second Fujita decomposition of the direct image of the relative dualizing sheaf and of the semiampleness of this vector bundle. END:VEVENT BEGIN:VEVENT DTSTART:20240823T100000 DTEND:20240823T120000 DTSTAMP:20240822T150000Z UID:64dab27ffadc29a64cc39dea8d9530e5@cgp.ibs.re.kr SUMMARY:An introductory course on mixed Hodge modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seung-Jo Jung\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: This course gives an introduction to Morihiko Saito's theory of mixed Hodge modules. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. The main goal of this course is to understand how D-modules come into the theory and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry. The course goes as follows:Lecture 1: D-modules and perverse sheavesLecture 2: The classical Hodge theory and variations of Hodge structuresLecture 3: Hodge modulesLecture 4: Two important theorems END:VEVENT BEGIN:VEVENT DTSTART:20240823T140000 DTEND:20240823T150000 DTSTAMP:20240822T150000Z UID:2170329cc2fad58d5a102dce247ab857@cgp.ibs.re.kr SUMMARY:Spectrum of non-degenerate functions LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: In-kyun Kim\n\nEvent: Summer Mini-school on Algebraic Geometry\n\nAbstract: The spectrum of an isolated singularity is a set of rational numbers, which is its most important discrete invariant. It describes the relationship between the semisimple part of the monodromy and the Hodge filtration of the mixed Hodge structure. In this talk, we discuss Steenbrink’s formula for the spectrum of convenient Newton non-degenerate functions, and prove the symmetry of combinatorial polynomials in the simplicial case. END:VEVENT BEGIN:VEVENT DTSTART:20240626T161500 DTEND:20240626T181500 DTSTAMP:20240625T150000Z UID:9580bc53aa0c4de51df124990b9657de@cgp.ibs.re.kr SUMMARY:Sheridan's homological mirror symmetry for pairs of pants, part 1 LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: We will begin discussing Sheridan's paper "On the homological mirror symmetry conjecture for pairs of pants" by discussing the A-side for the 1-dimensional case, i.e. the appropriate Fukaya category for the traditional pair of pants. If there is time, we will begin discussing the n-dimensional case; otherwise, we will discuss the n-dimensional case in part 2. END:VEVENT BEGIN:VEVENT DTSTART:20240704T161500 DTEND:20240704T181500 DTSTAMP:20240703T150000Z UID:c9ebf7883bc17be6e5eef26235eff019@cgp.ibs.re.kr SUMMARY:Cluster structure on the moduli space of toric vector bundles over toric surfaces via mirror symmetry LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: CGP Seminar\n\nAbstract: In this talk, I will explain how cluster structure shows up on the moduli space of toric vector bundles over toric surfaces based on spectral networks and mirror symmetry. END:VEVENT BEGIN:VEVENT DTSTART:20240723T161500 DTEND:20240723T181500 DTSTAMP:20240722T150000Z UID:2ae228fa5b375274de0ad2fdc4990eef@cgp.ibs.re.kr SUMMARY:Two topics in general relativity LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: SungJin Oh\n\nEvent: Mathematical Physics Seminar\n\nAbstract: In this two-hour, two-part talk, I will discuss two mathematical problems in general relativity. 1. The subject of the first part will be general relativistic initial data sets (i.e., fixed-time configurations), which are required to satisfy underdetermined PDEs called constraint equations. Our focus will be to elucidate the flexibility of these objects; specific results to be presented include extension, gluing, asymptotics-prescription, and parametrization of asymptotically flat initial data sets, often with sharp assumptions. Basic to our approach is a novel way to construct solution operators for divergence-type equations with prescribed support properties, which should be of independent interest. This part is based on joint work with Phil Isett (Caltech), Yuchen Mao (UC Berkeley), and Zhongkai Tao (UC Berkeley).2. The second part will concern the time evolution problem. More specifically, I will present a new method for determining the late-time tails of solutions to a fairly general class of nonlinear wave equations on dynamic spacetimes with odd space dimensions. The new methodology generalizes the existing predictions in the linear stationary case, referred to as Price's law. Furthermore, it shows that different, slower late-time tails arise in the presence of (arbitrarily small) nonlinearity or nonstationarity in the problem. Time permitting, I will explain how this problem relates to the question of the nature of singularities inside spinning black holes (Strong Cosmic Censorship Conjecture). This part is based on joint work with Jonathan Luk (Stanford). END:VEVENT BEGIN:VEVENT DTSTART:20240718T161500 DTEND:20240718T181500 DTSTAMP:20240717T150000Z UID:9894277b4fb3c86005199b4fc65d9dfd@cgp.ibs.re.kr SUMMARY:Floer theory of higher rank spectral networks LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yoon Jae Nho\n\nEvent: CGP Seminar\n\nAbstract: In this talk, we will discuss GMN higher rank spectral networks. We introduce the class of Lagrangian spectral curves and introduce the notion of generic Morse spectral networks for Lagrangian spectral curves. We describe GMN non-abelianization map and show that in the presence of a generic energy-finite Morse spectral network, holomorphic strips between a cotangent fibre and a Lagrangian spectral curve degenerate to partial Morse flowtrees contained in the Morse spectral network. We then state how in the case of exact Lagrangian spectral curves, there exists a finite generic Morse spectral network. We then explain the relationship between GMN non-abelianization and family Flore local system, first for exact spectral curves for which they turn out to be the same, and if time permitting, for finite Morse and energy-finite Morse spectral networks. This is based on joint work with Casals and Weng. END:VEVENT BEGIN:VEVENT DTSTART:20240703T161500 DTEND:20240703T181500 DTSTAMP:20240702T150000Z UID:139206c7cf217c6de281962f07e052d8@cgp.ibs.re.kr SUMMARY:Sheridan's homological mirror symmetry for pairs of pants, part 2 LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Sam Bardwell-Evans\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: We will begin discussing Sheridan's paper "On the homological mirror symmetry conjecture for pairs of pants" by discussing the A-side for the n-dimensional case, i.e. the appropriate Fukaya category for the traditional pair of pants. END:VEVENT BEGIN:VEVENT DTSTART:20240829T154000 DTEND:20240829T161000 DTSTAMP:20240828T150000Z UID:406b35982c12316ccba6abfb813585ea@cgp.ibs.re.kr SUMMARY:State integrals over local field and A-polynomials LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Honghuai Fang\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: We focus on the generalized Teichmüller TQFT over local field constructed by Garoufalidis and Kashaev. This new TQFT with infinite-dimensional Hilbert spaces is conjecturally related to point counting of the A-polynomial curve, similar to what has been observed in the mirror symmetry of Calabi-Yau manifolds. We will show how these relevant topological invariants relate to A-polynomials of knots. END:VEVENT BEGIN:VEVENT DTSTART:20240826T100000 DTEND:20240826T105000 DTSTAMP:20240825T150000Z UID:45aaea6bb13aa5d780cc6ee924ca8b12@cgp.ibs.re.kr SUMMARY:Complex Kuranishi structures LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Jeongseok Oh\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts.We apply the theory to projective moduli spaces M of stable sheaves on Calabi-Yau 4-folds. Using real derived differential geometry, Borisov- Joyce produced a virtual homology cycle on M. In the prequel work we constructed an algebraic virtual cycle on M. We prove the cycles coincide in homology after inverting 2 in the coefficients. In particular, when Borisov-Joyce’s real virtual dimension is odd, their virtual cycle is torsion.This is a joint work with Richard Thomas. END:VEVENT BEGIN:VEVENT DTSTART:20240826T111000 DTEND:20240826T120000 DTSTAMP:20240825T150000Z UID:98b09ea21c86f02d160d9f91ff68cebc@cgp.ibs.re.kr SUMMARY:TBA LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Jian Zhou\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: TBA END:VEVENT BEGIN:VEVENT DTSTART:20240826T140000 DTEND:20240826T145000 DTSTAMP:20240825T150000Z UID:3bd5dfe52b20e2c7eb75c997c7b9e9d5@cgp.ibs.re.kr SUMMARY:Quantum K-theory LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Yuan-Pin Lee\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Quantum K-theory is a K-theoretic version of the (cohomological) Gromov-Witten theory. In this talk, I will present some thoughts on quantum K-theory, including some old results and some new ones. END:VEVENT BEGIN:VEVENT DTSTART:20240827T100000 DTEND:20240827T105000 DTSTAMP:20240826T150000Z UID:f5cf3ca96c824e3e2ff2db9eaf6f7568@cgp.ibs.re.kr SUMMARY:Mirror symmetry for certain blowup of Grassmannians LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Changzheng Li\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: In this talk, we will discuss the Fano property of the blowup of a complex Grassmannian Gr(k, n) along a sub-Grassmannian Gr(r, m). We will study the quantum cohomology when (r, m)=(k, n-1), and will further discuss the mirror symmetry when k=2. This is based on my work in progress joint with Jianxun Hu, Huazhong Ke and Lei Song. END:VEVENT BEGIN:VEVENT DTSTART:20240827T111000 DTEND:20240827T120000 DTSTAMP:20240826T150000Z UID:97c576a00bea7dcb9ea4f323a1fd012e@cgp.ibs.re.kr SUMMARY:KP integrability in topological recursion through the x-y swap relation LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Alexander Aleksandrov\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Topological recursion is a surprisingly universal mathematical physics tool, that has numerical applications in mathematics,for instance in combinatorics, enumerative geometry, and knot invariants. I will discuss a universal relation sometimes called the x-y swap relation, which plays a prominent role in the theory of topological recursion. In particular, the x-y swap relation is natural for the KP integrability and can be described by certain integral transforms, leading to the Kontsevich-like matrix models. This allows us to establish general KP integrability properties of the topological recursion differentials. This talk is based on a joint work with Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, and Sergey Shadrin. END:VEVENT BEGIN:VEVENT DTSTART:20240827T140000 DTEND:20240827T145000 DTSTAMP:20240826T150000Z UID:454129e1c8d2a3e557c3a962a3483297@cgp.ibs.re.kr SUMMARY:Counting embedded curves in 3-folds LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Eleny Ionel\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: There are several ways of counting (pseudo)-holomorphic curves in Calabi-Yau 3-folds. Counting them as maps gives rise to the Gromov-Witten invariants. This overcounts multiple covers and gives rise to non-integer invariants due to their symmetries. But one can consider instead images of such maps (possibly with multiplicity), regarded either as subsets or as integral currents. This allowed us to prove a structure theorem for the GW invariants of symplectic 6-manifolds and the Gopakumar-Vafa conjecture. The latter states that the GW invariants of CY 3-folds are obtained, by a specific transform, from another set of invariants called BPS states which have better properties: integrality and finiteness. The integrality statement was proved earlier in joint work with Thomas Parker and the finiteness recently in joint work with Aleksander Doan and Thomas Walpuski.This talk presents some of the background and main ingredients of our proof, as well as recent progress, joint with Penka Georgieva, towards proving that a similar structure theorem holds for the real GW invariants of Calabi-Yau 3-folds with an anti-symplectic involution. END:VEVENT BEGIN:VEVENT DTSTART:20240828T100000 DTEND:20240828T105000 DTSTAMP:20240827T150000Z UID:c6338e19a8acf35da64c0de56ae1e8eb@cgp.ibs.re.kr SUMMARY:Virasoro constraints for cohomological field theory LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Shuai Guo\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Virasoro constraints are a hypothetical framework that arises in many enumerative geometry problems. In this talk, we will investigate the properties and applications of the Virasoro constraints for all genera. First, we will derive the ancestor form of the Virasoro constraints, which leads to a polynomial recursion relation. For semisimple cases, this recursion completely determines the generating series of higher genus invariants, extending Gathmann's result. Then, we will propose a generalized Virasoro conjecture for the CohFTs with non- flat units. For semisimple theories, we will prove this conjecture by using the Givental-Teleman reconstruction theorem. This talk is based on joint work with Qingsheng Zhang. END:VEVENT BEGIN:VEVENT DTSTART:20240828T111000 DTEND:20240828T120000 DTSTAMP:20240827T150000Z UID:59c0838b0a99c0640790acbc108b9c27@cgp.ibs.re.kr SUMMARY:Quantum cohomology of blowups LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Hiroshi Iritani\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Quantum cohomology is a deformation of the cohomology ring of a smooth projective variety defined by counting rational curves. The relationship between quantum cohomology and birational geometry has attracted much interest. In this talk, I will explain the following decomposition theorem for quantum cohomology of blowups: the quantum cohomology of the blowup of X along a smooth subvariety Z is a direct sum of the quantum cohomology of X and (codim(Z)-1) copies of the quantum cohomology of Z. The proof idea is based on a D-module version of Teleman's conjecture, which relates the quantum cohomology of a GIT quotient to the equivariant quantum cohomology of the original manifold via Fourier transformation. END:VEVENT BEGIN:VEVENT DTSTART:20240829T100000 DTEND:20240829T105000 DTSTAMP:20240828T150000Z UID:707d87d04cce7b5c5f1c1268ab6c7f56@cgp.ibs.re.kr SUMMARY:Some recent progress on Gamma conjectures LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Jianxun Hu\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Gamma conjectures, proposed by V. Golyshev, S. Galkin and H. Iritani, consists of conjecture O, Gamma conjecture I and II. Previous answers are affirmative.In this talk, I will talk about some counter-examples to conjecture O and Gamma conjecture I. This talk is based on a joint work with S. Galkin, H. Iritani, H. Ke, C. Li and Z. Su. END:VEVENT BEGIN:VEVENT DTSTART:20240829T111000 DTEND:20240829T120000 DTSTAMP:20240828T150000Z UID:ecbc28e3da42394fb5236eda73900a40@cgp.ibs.re.kr SUMMARY:Tropical Descent and Hodge Number Duality LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Sukjoo Lee\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: In this talk, I will present a tropical framework for computing Hodge-Deligne numbers of quasi-projective varieties, which we refer to as tropical descent theory. I will show that tropical descent holds for quasi-smooth toric hypersurfaces, which partially extends the work of Itenberg, Katzarkov, Mikhalkin, and Zharkov to non-smooth cases. This framework also yields significant applications in mirror symmetry: Hodge number duality holds for orbifold Clarke mirror pairs, providing a proof of a conjecture by Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. If time permits, I will discuss several additional applications, including the functoriality in Fano mirror symmetry and Hodge number duality for singular varieties. This is joint work with Andrew Harder. END:VEVENT BEGIN:VEVENT DTSTART:20240829T140000 DTEND:20240829T145000 DTSTAMP:20240828T150000Z UID:eef8ab626f847759855d7f6dbdbd76a4@cgp.ibs.re.kr SUMMARY:Open Gromov-Witten invariants: Lagrangian cobordisms and the Fukaya category LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Kai Hugtenberg\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: This talk reports on two projects. The first work (in progress), joint with Amanda Hirschi, constructs (genus 0) open Gromov-Witten invariants for any Lagrangian submanifold using a global Kuranishi chart construction. We also prove a relation between open Gromov-Witten invariants of Lagrangians related by a Lagrangian cobordism. Time permitting, I will discuss the second project, which concerns obtaining open Gromov-Witten invariants from the Fukaya category via an extension of the variation of Hodge structures associated to quantum cohomology. END:VEVENT BEGIN:VEVENT DTSTART:20240829T151000 DTEND:20240829T154000 DTSTAMP:20240828T150000Z UID:df3ddb96fe5fdac217a2b03cd8cceb5c@cgp.ibs.re.kr SUMMARY:On A Tautological Relation Conjectured By Buryak-Shadrin LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Chongyu Wang\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: Tautological relations on moduli spaces $\overline{\mathcal{M}}_{g,n}$ of stable curves are important topics. Recently, Buryak and Shadrin conjectured a tautological relation which has the form $B^m_{g, \textbf{d}=0}$ where $m \geq 2, n \geq 1$ and $|\textbf{d}| \geq 2g+m-1$.We proved that the conjecture holds if it is true for the $m=2$ and $|\textbf{d}| = 2g+1$ case. This reduces the proof of this conjecture to checking finitely many cases for each genus $g$. In particular, we proved the conjecture for the $g=1$ case.I will explain our proof and some calculations in this report. This is a joint work with Prof. Xiaobo Liu. END:VEVENT BEGIN:VEVENT DTSTART:20240830T100000 DTEND:20240830T105000 DTSTAMP:20240829T150000Z UID:dd0ea5ef9b766613ef1e59235453eaa4@cgp.ibs.re.kr SUMMARY:Mirror symmetric Gamma conjecture for toric Calabi-Yau 3-orbifolds LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Bohan Fang\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: I will explain the correspondence between K-theoretic framing of a toric Calabi-Yau 3-orbifold and Lagrangian cycles on the mirror curve. Under such correspondence the oscillatory integral on the mirror curve produces the expected genus zero Gromov-Witten invariants. By Givental-Teleman's graph sum expression for Gromov-Witten invariants, this further gives an all-genus descendant formula using the topological recursion. END:VEVENT BEGIN:VEVENT DTSTART:20240830T111000 DTEND:20240830T120000 DTSTAMP:20240829T150000Z UID:ad2b7f5da9511f684f916f4ace69434d@cgp.ibs.re.kr SUMMARY:Gromov-Witten invariants for branched covers LOCATION:Uni Hotel Jeju, Jeju Island, Korea DESCRIPTION:Speaker: Young-Hoon Kiem\n\nEvent: 2024 BICMR-IBSCGP Conference on Gromov-Witten Theory and Related Topics\n\nAbstract: A fundamental idea for computing Gromov-Witten invariants is to push the computation to simpler spaces like projective spaces. When the target manifold X is a complete intersection in a projective space P, the virtual fundamental class of the moduli space M(X) of stable maps to X coincides with the cosection localized virtual fundamental class of the moduli space of stable maps to P with an additional field. Hence we can enumerate curves in X by studying certain decorated moduli spaces of curves in P. In this talk, I will extend this idea to the case where the targent manifolds are branched covers of simpler spaces. Based on a joint work with Hyeonjun Park. END:VEVENT BEGIN:VEVENT DTSTART:20240805T161500 DTEND:20240805T181500 DTSTAMP:20240804T150000Z UID:70f12ff90ffbc3a30d0864ba4f4dbe0a@cgp.ibs.re.kr SUMMARY:A spectral analog of a formula of Bezrukavnikov-Kaledin LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Semon Rezchikov\n\nEvent: Symplectic Monday Seminar\n\nAbstract: In the talk, I will explain a generalization of a formula about calculus in characteristic p to the setting of stable infinity-categories. While the result is purely algebraic, this formula captures the relationship between the cyclotomic structure on symplectic cohomology, which I have introduced in an earlier work, and the quantum steenrod operations in symplectic topology. I will explain the relevant background on Topological Hochschild Homology and the expected connections to symplectic geometry (including a sketch of a `symplectic proof' of the main result). END:VEVENT BEGIN:VEVENT DTSTART:20240930T090000 DTEND:20240930T101500 DTSTAMP:20240929T150000Z UID:9015c9ed77e6877f0ecb382c6da2a23a@cgp.ibs.re.kr SUMMARY:[Mini-course A] A combinatorial approach to knotted surfaces in 4-space I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jean-Baptiste Meilhan\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: The aim of this mini-course is to introduce the notion of cut-diagrams, and present some of its applications to the study of surfaces in 4-space up to concordance and link-homotopy. We shall begin in Lecture 1 with reviewing the classical notion of broken surface diagrams and Roseman moves for studying knotted surfaces in 4-space, which leads to the theory of cut-diagrams and cut-moves. The latter is a diagrammatic generalization of surfaces in 4-space, which we will use in Lecture 2 to construct a family of concordance invariants. Lastly, Lecture 3 will show how cut-diagrams can be used to define link-homotopy invariants of link maps, generalizing works of P. Kirk. Several concrete topological application will be given in both Lectures 2 and 3. No prior knowledge on 4-dimensional topology is needed for these lectures, which are based on a series of joint works with B. Audoux and A. Yasuhara. END:VEVENT BEGIN:VEVENT DTSTART:20240822T161500 DTEND:20240822T181500 DTSTAMP:20240821T150000Z UID:117909ad4a949633a8635f870d6786a8@cgp.ibs.re.kr SUMMARY:Kontsevich's invariants of disk fiber bundles, and a "product formula" LOCATION:CGP Delta DESCRIPTION:Speaker: Xujia Chen\n\nEvent: CGP Seminar\n\nAbstract: In topology, the difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". The recent work of Watanabe (2018) uses the tool "Kontsevich's invariants" to detect exotic-ness in the group of diffeomorphisms of the 4-dimensional ball. The first part of the talk will be an introduction to Kontsevich's invariants, which are invariants of (certain) 3-manifolds / fiber bundles / knots and links, and were defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory. I will end the first part by giving a perspective on how to understand the role smooth structure plays in these invariants. In the second part of the talk (based on joint work in progress with Robin Koytcheff and Sander Kupers), I will talk about a "product" operation on the space of smooth, framed fiber bundles whose fibers are disks, and a formula relating the Kontsevich invariants of the resulting product bundle with the Kontsevich invariants of the two input bundles. END:VEVENT BEGIN:VEVENT DTSTART:20241011T161500 DTEND:20241011T171500 DTSTAMP:20241010T150000Z UID:e81d05c87591ff6b3eb6361287c6e101@cgp.ibs.re.kr SUMMARY:On Legendre-type transformations of a Frobenius manifold LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Di Yang\n\nEvent: Mathematical Physics Seminar\n\nAbstract: Frobenius manifold was introduced by Dubrovin to give a coordinate free description of WDVV (Witten--Dijkgraaf--Verlinde--Verlinde) equations that appeared in 2D topological field theories. Through investigating symmetries of WDVV equations, Dubrovin introduced Legendre-type transformations for a Frobenius manifold. In this work, we show that these Legendre-type transformations share the same monodromy data. We also present several applications of this result. A typical example, which was also the main motivation of our study, gives the relationship (originally discovered by Dubrovin) between the GUE (Gaussian--Unitary--Ensemble) partition function and the partition function of Gromov--Witten invariants of the complex projective line. END:VEVENT BEGIN:VEVENT DTSTART:20240927T150000 DTEND:20240927T170000 DTSTAMP:20240926T150000Z UID:cd0150b678a5f94c278e84f28db5b1a9@cgp.ibs.re.kr SUMMARY:[IBS-CGP&POSTECH-Math Colloquium] Poincaré duality in non-archimedean geometry LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: ShiZhang Li\n\nEvent: Seminar\n\nAbstract: We will start by introducing basics of non-archimedean geometry, then we will review the history of etale cohomology theory in non-archimedean geometry. After explaining some recent developments for p-adic etale cohomology of p-adic non-archimedean spaces, we end the talk with speaker's new joint work with Emanuel Reinecke and Bogdan Zavyalov concerning various Poincaré duality statements in p-adic geometry. END:VEVENT BEGIN:VEVENT DTSTART:20240923T161500 DTEND:20240923T181500 DTSTAMP:20240922T150000Z UID:465373726d3ba5ad5d8d50130c413907@cgp.ibs.re.kr SUMMARY:Equivariant Lagrangian correspondence and Teleman's conjectures LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yan-Lung Li\n\nEvent: Symplectic Monday Seminar\n\nAbstract: "In this talk, we will report a joint work with Lau and Leung on resolving a conjecture of Teleman on the mirror constructions of Hamiltonian G-spaces and their smooth symplectic quotients, using equivariant Lagrangian correspondences between them. The key technical ingredient is an equivariant extension of Fukaya's correspondence tri-modules over equivariant Floer complexes. Time permitting, we will discuss an ongoing joint work with Choa, Hu and Lau on Teleman's conjectures for singular quotients in the sense of Lekili-Segal.” END:VEVENT BEGIN:VEVENT DTSTART:20240926T161500 DTEND:20240926T181500 DTSTAMP:20240925T150000Z UID:fd93b39d4a9aa6079c25cb23064fe2dd@cgp.ibs.re.kr SUMMARY:An introduction to isolated singular points of complete intersections LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: In this talk, I will give a gentle introduction to the theory of isolated singular points of complete intersections. END:VEVENT BEGIN:VEVENT DTSTART:20241001T103000 DTEND:20241001T114500 DTSTAMP:20240930T150000Z UID:03cabaae6ceacf9dac901db03ec40e5f@cgp.ibs.re.kr SUMMARY:[Mini-course A] A combinatorial approach to knotted surfaces in 4-space II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jean-Baptiste Meilhan\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: The aim of this mini-course is to introduce the notion of cut-diagrams, and present some of its applications to the study of surfaces in 4-space up to concordance and link-homotopy. We shall begin in Lecture 1 with reviewing the classical notion of broken surface diagrams and Roseman moves for studying knotted surfaces in 4-space, which leads to the theory of cut-diagrams and cut-moves. The latter is a diagrammatic generalization of surfaces in 4-space, which we will use in Lecture 2 to construct a family of concordance invariants. Lastly, Lecture 3 will show how cut-diagrams can be used to define link-homotopy invariants of link maps, generalizing works of P. Kirk. Several concrete topological application will be given in both Lectures 2 and 3. No prior knowledge on 4-dimensional topology is needed for these lectures, which are based on a series of joint works with B. Audoux and A. Yasuhara. END:VEVENT BEGIN:VEVENT DTSTART:20241004T103000 DTEND:20241004T104500 DTSTAMP:20241003T150000Z UID:7325bd8f51e5d97a03e11dc62c93dc3f@cgp.ibs.re.kr SUMMARY:[Mini-course A] A combinatorial approach to knotted surfaces in 4-space III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Jean-Baptiste Meilhan\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: The aim of this mini-course is to introduce the notion of cut-diagrams, and present some of its applications to the study of surfaces in 4-space up to concordance and link-homotopy. We shall begin in Lecture 1 with reviewing the classical notion of broken surface diagrams and Roseman moves for studying knotted surfaces in 4-space, which leads to the theory of cut-diagrams and cut-moves. The latter is a diagrammatic generalization of surfaces in 4-space, which we will use in Lecture 2 to construct a family of concordance invariants. Lastly, Lecture 3 will show how cut-diagrams can be used to define link-homotopy invariants of link maps, generalizing works of P. Kirk. Several concrete topological application will be given in both Lectures 2 and 3. No prior knowledge on 4-dimensional topology is needed for these lectures, which are based on a series of joint works with B. Audoux and A. Yasuhara. END:VEVENT BEGIN:VEVENT DTSTART:20240930T103000 DTEND:20240930T114500 DTSTAMP:20240929T150000Z UID:78cb1b5af7075d4083b63f29bb115791@cgp.ibs.re.kr SUMMARY:[Mini-course B] Introduction to the Kauffman bracket skein algebra I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Helen Wong (Claremont McKenna College)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: We will give an introduction to the Kauffman bracket skein algebra of a surface and discuss its relationship with hyperbolic geometry. The skein algebra is a generalization of the Jones polynomial for links that plays a key role in the skein-theoretic version of the topological quantum field theory associated with the Witten-Reshetikhin-Turaev invariant for 3-manifolds. Although little is generally known about the topological or geometric content of the Jones polynomial and Witten-Reshetikhin-Turaev invariants, the relationship between the skein algebra and hyperbolic geometry is more established. In particular, the skein algebra is a quantization of the $SL_2(C)$ character variety, which contains a copy of the Teichmuller space of the surface. In this series of lectures, we will discuss recent progress about the representation theory of the skein algebra and the geometric ramifications. If time permits, we will also discuss generalizations of the skein algebra, as well as open conjectures related to the skein algebra. END:VEVENT BEGIN:VEVENT DTSTART:20241001T140000 DTEND:20241001T151500 DTSTAMP:20240930T150000Z UID:2d83280a88a741d2f756d766c7c5e8dd@cgp.ibs.re.kr SUMMARY:[Mini-course B] Introduction to the Kauffman bracket skein algebra II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Helen Wong (Claremont McKenna College)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: We will give an introduction to the Kauffman bracket skein algebra of a surface and discuss its relationship with hyperbolic geometry. The skein algebra is a generalization of the Jones polynomial for links that plays a key role in the skein-theoretic version of the topological quantum field theory associated with the Witten-Reshetikhin-Turaev invariant for 3-manifolds. Although little is generally known about the topological or geometric content of the Jones polynomial and Witten-Reshetikhin-Turaev invariants, the relationship between the skein algebra and hyperbolic geometry is more established. In particular, the skein algebra is a quantization of the $SL_2(C)$ character variety, which contains a copy of the Teichmuller space of the surface. In this series of lectures, we will discuss recent progress about the representation theory of the skein algebra and the geometric ramifications. If time permits, we will also discuss generalizations of the skein algebra, as well as open conjectures related to the skein algebra. END:VEVENT BEGIN:VEVENT DTSTART:20241002T090000 DTEND:20241002T101500 DTSTAMP:20241001T150000Z UID:84ab429a4e6bcde949b89244dd9a79a2@cgp.ibs.re.kr SUMMARY:[Mini-course B] Introduction to the Kauffman bracket skein algebra III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Helen Wong (Claremont McKenna College)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: We will give an introduction to the Kauffman bracket skein algebra of a surface and discuss its relationship with hyperbolic geometry. The skein algebra is a generalization of the Jones polynomial for links that plays a key role in the skein-theoretic version of the topological quantum field theory associated with the Witten-Reshetikhin-Turaev invariant for 3-manifolds. Although little is generally known about the topological or geometric content of the Jones polynomial and Witten-Reshetikhin-Turaev invariants, the relationship between the skein algebra and hyperbolic geometry is more established. In particular, the skein algebra is a quantization of the $SL_2(C)$ character variety, which contains a copy of the Teichmuller space of the surface. In this series of lectures, we will discuss recent progress about the representation theory of the skein algebra and the geometric ramifications. If time permits, we will also discuss generalizations of the skein algebra, as well as open conjectures related to the skein algebra. END:VEVENT BEGIN:VEVENT DTSTART:20240930T115000 DTEND:20240930T123000 DTSTAMP:20240929T150000Z UID:87035d05f1b52aa5dc9908f7400d8488@cgp.ibs.re.kr SUMMARY:Candidate for the contact first Kirby move LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Prerak Deep (IISER Bhopal)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: This talk is based on my article titled, "On a potential contact analogue of Kirby move of type 1". I will start the talk with giving necessary conditions for a contact surgery diagram to be a contact analogue of the first Kirby move. Then we will prove that contact positive integral surgery on Legendrian unknot of specific type has one presentation satisfying the necessary conditions. Thus, we get a collection of contact surgery diagrams as potential candidate for the contact first Kirby move. END:VEVENT BEGIN:VEVENT DTSTART:20241213T161500 DTEND:20241213T171500 DTSTAMP:20241212T150000Z UID:6e36265eb8c6e0ad4df55c1314583bb8@cgp.ibs.re.kr SUMMARY:Integrable systems associated to cohomological field theories LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sergey Shadrin\n\nEvent: Mathematical Physics Seminar\n\nAbstract: There are several constructions of integrable systems that can be associated to cohomological field theories:(1) Dubrovin-Zhang hierarchy (defined by Dubrovin and Zhang only for homogeneous CohFTs, but then extended by other people to arbitrary CohFTs). It its most general formulation it deals with partition function coupled to gravity.(2) Buryak's double ramification hierarchy is designed to imitate in the realm of algebraic geometry the ideas coming from the symplectic field theory. It is defined through is Hamiltonians computed as the integrals over the double ramification cycles.(3) A new construction by Blot et al that works for a new kind of parition functions. It uses essentially the so-called Omega classes corresponding to the roots of the tensor powers of the canonical line bundle.All three constructions use very deeply various aspects of geometry of the moduli spaces of curves, and appear to be Miura equivalent to each other.In the talk I'll try to survey some aspects of this theory. END:VEVENT BEGIN:VEVENT DTSTART:20240930T140000 DTEND:20240930T150000 DTSTAMP:20240929T150000Z UID:578060e9632bfab8866294bbb70ad3e0@cgp.ibs.re.kr SUMMARY:The covolumes of the mapping class group actions on many higher Teichmuller spaces are infinite LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hongtaek Jung (Seoul National University)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: For many higher Teichmuller spaces, we show that the quotient spaces of these spaces by the mapping class group action have infinite Atiyah-Bott-Goldman volume. Our result covers G-Hitchin components for $G=PSL(n+1,R), PSO(n+1,n)$ and $PSp(2n,R)$ with $n>1$ and the space of $Sp(2n,R)$-maximal representations with $n>1$. END:VEVENT BEGIN:VEVENT DTSTART:20240930T150000 DTEND:20240930T160000 DTSTAMP:20240929T150000Z UID:b2175878a057f01f7844a978d6623a32@cgp.ibs.re.kr SUMMARY:Unbounded $sl(3)$-laminations and their shear coordinates LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Shunsuke Kano (Tohoku University)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: Generalizing the work of Fock$-$Goncharov on rational unbounded laminations, we give a geometric model of the tropical points of the moduli space $\mathcal{X}_{PGL_3,\Sigma}$ of framed $PGL_3$-local systems on a marked surface $\Sigma$ based on the Kuperberg's $\mathfrak{sl}_3$-webs.We introduce their tropical cluster coordinates as an $\mathfrak{sl}_3$-analogue of the Thurston's shear coordinates associated with any ideal triangulation.We also describe tropical points of Goncharov$-$Shen's moduli space $\mathcal{P}_{PGL_3,\Sigma}$.Then we give a tropical analogue of gluing morphisms among the moduli spaces as a geometric gluing procedure of $\mathfrak{sl}_3$-laminations with "shearings".We also investigate a relation to the graphical basis of the $\mathfrak{sl}_3$-skein algebra by Ishibashi$-$Yuasa, which conjecturally leads to a quantum duality map.This is a joint work with Tsukasa Ishibashi. END:VEVENT BEGIN:VEVENT DTSTART:20240930T163000 DTEND:20240930T173000 DTSTAMP:20240929T150000Z UID:222b5178d672e09d035dbee4421ea4f9@cgp.ibs.re.kr SUMMARY:Combinatorics of the product between a dendroidal set and a simplicial set LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Eric Dolores Cuenca (Pusan National University)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: A dendroidal set is a contravariant functor from a category, whose objects are trees, to the category of sets. When we identify linear trees with simplices dendroidal sets generalize simplicial sets. In this talk we describe the combinatorics of the product of a dendroidal sets and a simplicial set. Our work brings us a step closer to understand the tensor product of dendroidal sets, which, via a Quillen equivalence between dendroidal sets and topological operads, induces the derived tensor product of topological operads. END:VEVENT BEGIN:VEVENT DTSTART:20241001T090000 DTEND:20241001T101500 DTSTAMP:20240930T150000Z UID:9d162ac36825b28b5144f67c28b4f3b1@cgp.ibs.re.kr SUMMARY:[Mini-course C] K-symplectic geometry I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Vladimir Fock (University of Strasbourg)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: For any three-dimensional manifold with boundary one can associate the symplectic space of flat connections on its boundary and a Lagrangian subvariety of flat connections extendible to the three-manifold. Many constructions in three-dimensional topology uses this construction.The aim of the mini-course is to introduce a refinement of the notions of symplectic structure and of Lagrangian subvariety using the algebraic K-theory (which is not supposed to be known). This structure is on one side related to geometry, in particular to Dehn invariant and hyperbolic volume of polyhedra, and on the other hand to number theory such as Gauss reciprocity. Finally we will describe what this structure give more fine number-theoretic structure of invariants of knots and three-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20241002T103000 DTEND:20241002T104500 DTSTAMP:20241001T150000Z UID:90fbc9270388869fd4aee4021afbb717@cgp.ibs.re.kr SUMMARY:[Mini-course C] K-symplectic geometry II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Vladimir Fock (University of Strasbourg)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: For any three-dimensional manifold with boundary one can associate the symplectic space of flat connections on its boundary and a Lagrangian subvariety of flat connections extendible to the three-manifold. Many constructions in three-dimensional topology uses this construction.The aim of the mini-course is to introduce a refinement of the notions of symplectic structure and of Lagrangian subvariety using the algebraic K-theory (which is not supposed to be known). This structure is on one side related to geometry, in particular to Dehn invariant and hyperbolic volume of polyhedra, and on the other hand to number theory such as Gauss reciprocity. Finally we will describe what this structure give more fine number-theoretic structure of invariants of knots and three-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20241004T090000 DTEND:20241004T101500 DTSTAMP:20241003T150000Z UID:44120cd2784a7cd220293978f6731cb0@cgp.ibs.re.kr SUMMARY:[Mini-course C] K-symplectic geometry III LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Vladimir Fock (University of Strasbourg)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: For any three-dimensional manifold with boundary one can associate the symplectic space of flat connections on its boundary and a Lagrangian subvariety of flat connections extendible to the three-manifold. Many constructions in three-dimensional topology uses this construction.The aim of the mini-course is to introduce a refinement of the notions of symplectic structure and of Lagrangian subvariety using the algebraic K-theory (which is not supposed to be known). This structure is on one side related to geometry, in particular to Dehn invariant and hyperbolic volume of polyhedra, and on the other hand to number theory such as Gauss reciprocity. Finally we will describe what this structure give more fine number-theoretic structure of invariants of knots and three-manifolds. END:VEVENT BEGIN:VEVENT DTSTART:20241001T115000 DTEND:20241001T123000 DTSTAMP:20240930T150000Z UID:d9f7fac43f5e783c067dbf55b2bcc231@cgp.ibs.re.kr SUMMARY:Parameterization and non-triviality of ribbon torus knots LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tumpa Mahato (Indian Institute of Science Education and Research Pune)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: In this talk, we will discuss a method to provide a parameterization for a special class of knotted surfaces, called ribbon torus knots using elementary functions. We will also discuss if the parameterized ribbon torus knot is non-trivial. This uses the connection of ribbon torus knots with welded knots given by S. Satoh’s Tube map. We will explore the non-triviality of welded knots by studying a welded knot invariant, called welded unknotting number and utilize those results to examine the non-triviality of ribbon torus knots. END:VEVENT BEGIN:VEVENT DTSTART:20241001T154500 DTEND:20241001T164500 DTSTAMP:20240930T150000Z UID:2ae7ce58f2d8bbbe55971b87e293dc79@cgp.ibs.re.kr SUMMARY:On knots in $S_{g} \times S^{1}$ and its invariant LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Seongjeong Kim (Jilin university)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: In knot theory not only classical knots, which are embedded circles in S^{3} up to isotopy, but also knots in other 3-manifolds are interesting for mathematicians. In particular, virtual knots, which are knots in thickened surface $S_{g} \times [0,1]$ with an orientable surface $S_{g}$ of genus $g$, are studied and they provide interesting properties. In this talk, we will talk about knots in $S_{g} \times S^{1}$ where $S_{g}$ is an oriented surface of genus $g$. We introduce basic notions and properties for them. In particular, for knots in $S_{g} \times S^{1}$ one of important information is “how many times a half of a crossing turns around $S^{1}$”, and we call it winding parity of a crossing. We extend this notion more generally and introduce a topological model. In the end we apply it to classify knots in $S_{g}\times S^{1}$ with small number of crossings. END:VEVENT BEGIN:VEVENT DTSTART:20241002T115000 DTEND:20241002T123000 DTSTAMP:20241001T150000Z UID:039bb46246b3e549d22cb3329a8e9bc2@cgp.ibs.re.kr SUMMARY:(Co)Homology of symmetric quandles over homogeneous Beck modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Deepanshi Saraf (IISER Mohali)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily oriented. In this talk, I will intro- duce the category of symmetric quandle modules and will see that these modules completely determine the Beck modules in the category of symmetric quandles. Consequently, this establishes suitable coefficient objects for constructing appropriate (co)homology theories. We develop an extension theory of modules over symmetric quandles and propose a generalized (co)homology theory for symmetric quandles with coefficients in a homogeneous Beck module, which also recovers the symmetric quandle (co)homology developed by Kamada and Oshiro [Trans. Amer. Math. Soc. (2010)]. Our constructions also apply to symmetric racks. This is a joint work with Biswadeep Karmakar and Dr. Mahender Singh. END:VEVENT BEGIN:VEVENT DTSTART:20241002T140000 DTEND:20241002T150000 DTSTAMP:20241001T150000Z UID:5acdac73483bea3aab694e9b32680eec@cgp.ibs.re.kr SUMMARY:Khovanov-instanton Floer theory and immersed cobordism maps LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hayato Imori (KAIST)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: Khovanov homology theory and instanton Floer theory have provided powerful tools with functorial properties in knot theory. Kronheimer and Mrowka constructed a spectral sequence linking Khovanov homology and instanton Floer homology to demonstrate that Khovanov homology detects the unknot. Furthermore, Baldwin, Hedden, and Lobb showed that this spectral sequence is functorial with respect to embedded surface cobordisms. In this talk, we show that Kronheimer--Mrowka's spectral sequence is also functorial for immersed surface cobordisms. We also provide several topological applications using the functoriality of the spectral sequence for immersed surfaces. This talk is based on a joint work with Taketo Sano, Kouki Sato, and Masaki Taniguchi. END:VEVENT BEGIN:VEVENT DTSTART:20241002T150000 DTEND:20241002T160000 DTSTAMP:20241001T150000Z UID:1d66275398dd3ebdbf9569be70fd26b8@cgp.ibs.re.kr SUMMARY:Center of stated $SL(n)$-skein algebras LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hiroaki Karuo (Gakushuin University)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: To understand the representation theory of non-commutative algebras, the Unicity theorem is helpful and implies the importance of understanding of their centers. Since there exists the quantum trace map, an embedding of the (reduced) stated $SL(n)$-skein algebra into the (extended) Fock$-$Goncharov algebra (a quantum torus), we can use some properties of quantum tori to understand the properties of the skein algebra. In the talk, I will give the center of the (reduced) stated $SL(n)$-skein algebra using that of the Fock$-$Goncharov algebra. Consequently, thanks to the Unicity theorem, we can access to the representation theory of (reduced) stated $SL(n)$-skein algebras potentially related to quantum moduli algebras and quantum cluster algebras. END:VEVENT BEGIN:VEVENT DTSTART:20241002T163000 DTEND:20241002T173000 DTSTAMP:20241001T150000Z UID:a0f6f76e6aa9b78295b9ead9110530eb@cgp.ibs.re.kr SUMMARY:The moduli space of decorated G-local systems and skein algebras LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Tsukasa Ishibashi (Tohoku University)\n\nEvent: Autumn School on Low-dimensional Topology and Related Topics\n\nAbstract: The moduli space of decorated (twisted) G-local systems on a marked surface, originally introduced by Fock–Goncharov, is known to have a natural cluster $K_2$ structure. In particular, it admits a quantization via the framework of quantum cluster algebras, due to Berenstein—Zelevinsky and Goncharov—Shen.In this talk, I will explain its connection to the skein algebras: we have two generating sets of the function ring of the moduli space - cluster variables and matrix coefficients of Wilson lines - and the quantum lift of their relations would lead to an isomorphism between two types of skein algebras.This talk is based on several joint works with Hironori Oya, Linhui Shen, and with Wataru Yuasa. END:VEVENT BEGIN:VEVENT DTSTART:20241015T151500 DTEND:20241015T164500 DTSTAMP:20241014T150000Z UID:4e58948d18a6a70dc0edb5cff3b7874c@cgp.ibs.re.kr SUMMARY:Recent advances on categorical Torelli problems LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Shizhuo Zhang\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Let X be a Fano variety(not necessarily smooth) and denote the non-trivial semi-orthogonal component by $Ku(X)$, known as the Kuznetsov component. The categorical Torelli problem asks if $Ku(X)$ determines the isomorphism class of $X$. I will briefly talk about the history of this topic, including the known results and popular strategies to prove these results(Hodge theoretic, moduli space theoretic and Chow theoretic). Then, I will survey the recent advances for (weighted) hypersurfaces, a cubic threefold with a geometric involution, del Pezzo threefold of Picard rank one, and a class of nodal prime Fano threefolds. Meanwhile, I will talk about infinitesimal version of categorical Torelli problem. If time permits, I will also speak about categorical Torelli problems for a class of index one prime Fano threefold as the double cover of del Pezzo threefolds. This talk is based on a series of works with Daniele Faenzi,Xun Lin, Zhiyu Liu, Soheyla Feyzbakhsh, Jorgen Renneomo, Xianyu Hu, Sabastian-Casalaina Martin, and Zheng Zhang. END:VEVENT BEGIN:VEVENT DTSTART:20241016T161500 DTEND:20241016T181500 DTSTAMP:20241015T150000Z UID:f18694fd9e3e7c77bb45ad320ee1d358@cgp.ibs.re.kr SUMMARY:An introduction to isolated singular points of complete intersections-continue LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: In this talk, I will give a gentle introduction to the theory of isolated singular points of complete intersections. END:VEVENT BEGIN:VEVENT DTSTART:20241126T161500 DTEND:20241126T181500 DTSTAMP:20241125T150000Z UID:67b98b2a2bae6d0130faa87dd1ea668a@cgp.ibs.re.kr SUMMARY:Coregularity LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Victor Przyjalkowski\n\nEvent: Algebraic Geometry Seminar\n\nAbstract: Coregularity means how ``big'' a complement on an algebraic variety can be.More precise, having a log Calabi--Yau (X,B) with coefficients of the boundary B between 0 and 1, one can construct its log resolution, pick those divisors of the boundary that have coefficients 1, and consider dual complex for the divisors. If it has dimension k, then the corresponding coregularity is equal to dim(X)-k-1. In particular, coregularity 0 means that the dimension of the dual complex is maximal. Coregularity of X is the minimum of coregularitiesof (X,B) over all B. We will discuss how coregularity is related to other algebro-geometric invariants,and will say some words about its relations with Mirror Symmetry.We also discuss how to compute coregularity for del Pezzo surfaces and Fano threefolds.Finally, we will introduce G-coregularity, compute it in some cases, and discuss how it is relatedto invariants of singularities.The talk was prepared within the framework of the project “International academic cooperation” HSE University. END:VEVENT BEGIN:VEVENT DTSTART:20241021T100000 DTEND:20241021T110000 DTSTAMP:20241020T150000Z UID:4a0799f56791ee0a2c426c71a6b2740a@cgp.ibs.re.kr SUMMARY:A Plücker coordinate mirror for partial flag varieties and quantum Schubert calculus LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Changzheng Li\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: In this talk, we will review the current study of mirror symmetry for flag varieties. We will focus more on the construction of the Landau–Ginzburg model, and discuss a folklore mirror symmetry expectation on the eigenvalues of the first Chern class, using concrete examples of flag varieties of Lie type A. This is based on a work-in-progress joint with Konstanze Rietsch, Mingzhi Yang, and Chi Zhang. END:VEVENT BEGIN:VEVENT DTSTART:20241021T113000 DTEND:20241021T123000 DTSTAMP:20241020T150000Z UID:2df847e0abc6c4510964ce0c1a2265f8@cgp.ibs.re.kr SUMMARY:An exploration of torus orbit closures LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Eunjeong Lee\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: A flag variety is a smooth projective homogeneous variety, denoted as $G/B$, where $G$ is a semisimple Lie group and B is a Borel subgroup. The maximal torus $T⊂B$ acts on $G/B$ via left multiplication. Considering the closures of torus orbits under this T-action, one can construct a family of toric varieties within $G/B$. For example, a permutohedral variety can be obtained in this manner. In this talk, we will explore these toric varieties. This talk is based on joint work with Sujin Cho and Jaehyun Hong, as well as several collaborations with Seonjeong Park and Masuda. END:VEVENT BEGIN:VEVENT DTSTART:20241021T140000 DTEND:20241021T150000 DTSTAMP:20241020T150000Z UID:a8db790d1107f8b288b0e92609b9036a@cgp.ibs.re.kr SUMMARY:Relative simplicity of the universal coverings of transformation groups LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Morimichi Kawasaki\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: Many transformation groups on manifolds are simple, but their universal coverings are not. In this talk, we introduce the concept of the relative simplicity of groups instead of the simplicity of groups. We show that the universal coverings of many transformation groups (including the group of Hamiltonian diffeomorphisms) are relatively simple and we provide some applications. We note that one of the motivations of this study is symplectic geometry. This is a joint work with Mitsuaki Kimura (Osaka Dental University), Yoshifumi Matsuda (Aoyama Gakuin University), Takahiro Matsushita (Shinshu University), Ryuma Orita (Niigata University). END:VEVENT BEGIN:VEVENT DTSTART:20241021T153000 DTEND:20241021T163000 DTSTAMP:20241020T150000Z UID:388095e79c496bf7626bfb36632b07c5@cgp.ibs.re.kr SUMMARY:Rational torsion points on Jacobian varieties LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Hwajong Yoo\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: We introduce a famous conjecture of Andrew Ogg, which was proved by Mazur, and discuss its generalization. END:VEVENT BEGIN:VEVENT DTSTART:20241022T100000 DTEND:20241022T110000 DTSTAMP:20241021T150000Z UID:64541e5db8843ed677228f31d3774af0@cgp.ibs.re.kr SUMMARY:Cluster structure on the moduli space of toric vector bundles over toric surfaces LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yat-Hin Suen\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: We use spectral networks and non-abelianization to construct toric vector bundles over toric surfaces and prove that the moduli space of rank 2 toric vector bundles over any complete toric surface admits a cluster structure. END:VEVENT BEGIN:VEVENT DTSTART:20241022T113000 DTEND:20241022T123000 DTSTAMP:20241021T150000Z UID:7add20f280636b2db2240c9b89421aa2@cgp.ibs.re.kr SUMMARY:My Journey of Mathematics after IBS-CGP LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Rui Wang\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: In this talk, I will describe my mathematical work over the past 10 years, which coincides with the time since I left Pohang. This includes research on Hamiltonian Gromov–Witten theory, orbifold Gromov–Witten theory, as well as reflections on my approach to mathematical education, drawing on knowledge and experiences from my time in Pohang. END:VEVENT BEGIN:VEVENT DTSTART:20241023T100000 DTEND:20241023T110000 DTSTAMP:20241022T150000Z UID:3bf6953066799edc94a8c4487c05b681@cgp.ibs.re.kr SUMMARY:Monotone Lagrangian tori via toric degeneration I LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yunhyung Cho\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: In this talk, I will explain a method of obtaining a family of monotone Lagrangian tori in a smooth Fano variety via toric degeneration. Our method is particularly useful when our variety is birational to a cluster variety such as a (partial) flag variety. Using our machinery, we obtain a family of infinitely many monotone Lagrangian tori in a full flag manifold. We also discuss how to generalize our machinery to an arbitrary Fano case. This is joint / partly joint work with Yoosik Kim, Myungho Kim, and Euiyong Park. END:VEVENT BEGIN:VEVENT DTSTART:20241023T113000 DTEND:20241023T123000 DTSTAMP:20241022T150000Z UID:94d81cc387d26fc0d8ec5d3888763ab0@cgp.ibs.re.kr SUMMARY:Monotone Lagrangian tori via toric degeneration II LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Yoosik Kim\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: This talk is a continuation of Yunhyung's talk. I will explain a method of obtaining a family of monotone Lagrangian tori in a smooth Fano variety via toric degeneration. Our method is particularly useful when our variety is birational to a cluster variety such as a (partial) flag variety. Using our machinery, we obtain a family of infinitely many monotone Lagrangian tori in a full flag manifold. We also discuss how to generalize our machinery to an arbitrary Fano case. This is joint / partly joint work with Yunhyung Cho, Myungho Kim, and Euiyong Park. END:VEVENT BEGIN:VEVENT DTSTART:20241023T140000 DTEND:20241023T150000 DTSTAMP:20241022T150000Z UID:92cfbbf3fdb54dd8f6d2827edc1e023c@cgp.ibs.re.kr SUMMARY:Symmetric products, Jacobians and moduli spaces of vector bundles of algebraic curves LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Kyoung-Seog Lee\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: Symmetric products, Jacobians and moduli spaces of vector bundles on curves are fundamental objects in the study of algebraic curves. In this talk, I will explain how they are related in the level of their derived categories and motives. This talk is based on several joint works with I. Biswas, T. Gomez, H.-B. Moon and M. S. Narasimhan. END:VEVENT BEGIN:VEVENT DTSTART:20241023T153000 DTEND:20241023T163000 DTSTAMP:20241022T150000Z UID:72832a90d2c37229edaba6a8a7c33900@cgp.ibs.re.kr SUMMARY:On the existence of anti-minimal model LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Sung Rak Choi\n\nEvent: 2024 IBS-CGP Reunion Workshop on Geometry and Physics\n\nAbstract: Due to the recent remarkable development of the minimal model program, it is known that there exist minimal models when the canonical divisor is big or effective in some occasions. In this talk, we report some recent progress on the existence of the anti-minimal model. The so-called anti-minimal model program does not run easily mainly because the classical results for the usual MMP fail to hold once we replace the canonical divisor with the anticanonical divisor. We will also try to explain how we can overcome the difficulties. END:VEVENT BEGIN:VEVENT DTSTART:20241205T161500 DTEND:20241205T181500 DTSTAMP:20241204T150000Z UID:fc0839b2df20e43ea2a17a9e2ce6beeb@cgp.ibs.re.kr SUMMARY:Analogues of hyperlogarithm functions on affine complex curves LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Benjamin Enriquez\n\nEvent: CGP Seminar\n\nAbstract: If $C$ is an affine complex curve, then iterated integration gives rise to an algebra morphism $\mathrm{Sh}(\Omega(C ))\to\mathcal O_{hol}(\tilde C)$, where $\mathrm{Sh}(-)$ is the (commutative) shuffle algebra over a vector space, $\Omega(C )$ is the space of regular differentials on $C$, and $\mathcal O_{hol}(\tilde C)$ is the algebra of multivalued holomorphic functions on $C$. We show that the image of this algebra morphism is isomorphic to the tensor product of the algebra $\mathcal O(C )$ of regular functions on $C$ with $\mathrm Sh(H^1(C))$, where $H^1(C )$ is the first de Rham cohomology group of $C$. We show that any nondegenerate element $J$ of $\Omega(C ) \otimes \mathbb Ll(H^1(C )^*)$ can be used for buiding up a morphism from $\mathcal O(C ) \otimes \mathrm Sh(H^1(C))$ to $\mathrm{im}(\mathrm{Sh}(\Omega(C ))\to\mathcal O_{hol}(\tilde C))$ by way of solving the equation $dF=JF$. The tool used for showing that this is an isomorphism involves the action of the fundamental group of $C$ on the subalgebra of $\mathcal O_{hol}(\tilde C)$ of functions with moderate growth at the cusps. (Joint work w. F. Zerbini.) END:VEVENT BEGIN:VEVENT DTSTART:20241119T161500 DTEND:20241119T181500 DTSTAMP:20241118T150000Z UID:7c395adf58715c35e7c4b81630d18df9@cgp.ibs.re.kr SUMMARY:3d Mirror Symmetry is Mirror Symmetry LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Kifung Chan\n\nEvent: Symplectic Monday Seminar\n\nAbstract: 3d mirror symmetry is a duality for certain hyperkähler manifolds. This talk will explore its connections with 2d mirror symmetry, as a 3d analog of ‘Mirror Symmetry is T-duality’ by Strominger, Yau, and Zaslow, which described 2d mirror symmetry via 1d dualities. Based on joint works with Naichung Conan Leung.Also, he will talk at Wednesday Noon Seminar (20 Nov, 12-13): Details would be determined later. END:VEVENT BEGIN:VEVENT DTSTART:20241120T120000 DTEND:20241120T130000 DTSTAMP:20241119T150000Z UID:4a98287a7a99ea79ab39d5f8c455aaa5@cgp.ibs.re.kr SUMMARY:3d Mirror Symmetry is Mirror Symmetry LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Kifung Chan\n\nEvent: Seminar\n\nAbstract: 3d mirror symmetry is a duality for certain hyperkähler manifolds. This talk will explore its connectionswith 2d mirror symmetry, as a 3d analog of ‘Mirror Symmetry is T-duality’ by Strominger, Yau, andZaslow, which described 2d mirror symmetry via 1d dualities. Based on joint works with NaichungConan Leung.* He will also speak on Nov 20, 12:00-13:00, at WNS (Wednesday Noon Seminar). Details would bedetermined later. END:VEVENT BEGIN:VEVENT DTSTART:20241127T161500 DTEND:20241127T181500 DTSTAMP:20241126T150000Z UID:03225c499878e4f4859b5b4be6fdd53f@cgp.ibs.re.kr SUMMARY:Unit normal correspondence of a smooth divisor complement LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongwook Choa\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: The main purpose of this talk is to introduce the notion of the symplectic divisor complement and to explore its Floer theory. This class of symplectic manifolds has drawn significant interest because the divisor and its complement interact through the Liouville flow. As a guiding example, I will illustrate the idea in the context of polarized Kähler manifolds accompanied by detailed computations. Additionally, these manifolds arise as Milnor fibers of quasi-homogeneous polynomials, which is one of the goals of this study. END:VEVENT BEGIN:VEVENT DTSTART:20241108T112000 DTEND:20241108T122000 DTSTAMP:20241107T150000Z UID:15d44498e57ab8dcc5d8d8849d9262ce@cgp.ibs.re.kr SUMMARY:Floer homotopy via flow modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: 2024 RIMS-IBSCGP Conference on Recent Developments in Symplectic Topology\n\nAbstract: I will describe joint work with Blumberg, starting with the results appearing in arXiv:2404.03193, whose goal is to build a foundation for the study of the interaction between generalised homology and Floer theory. The key idea is to interpret flow categories, due to Cohen-Jones-Segal, as objects of a category whose morphisms we call flow bimodules. While Morse and Floer complexes give rise to flow categories, continuation maps between them give rise to flow bimodules. These constructions have many flavours, as one can consider flow categories whose morphisms spaces are manifolds, equipped with various tangential structures, or more generally orbifolds or derived orbifolds. These variants are designed to accommodate specific Floer-theoretic applications, such as studying Floer theory on Liouville manifolds, or on general closed symplectic manifolds, as I will illustrate by discussing Hamiltonian Floer cohomology. END:VEVENT BEGIN:VEVENT DTSTART:20241107T100000 DTEND:20241107T110000 DTSTAMP:20241106T150000Z UID:600da02bed876be20f5840fbdde64794@cgp.ibs.re.kr SUMMARY:Floer homotopy via flow modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: 2024 RIMS-IBSCGP Conference on Recent Developments in Symplectic Topology\n\nAbstract: I will describe joint work with Blumberg, starting with the results appearing in arXiv:2404.03193, whose goal is to build a foundation for the study of the interaction between generalised homology and Floer theory. The key idea is to interpret flow categories, due to Cohen-Jones-Segal, as objects of a category whose morphisms we call flow bimodules. While Morse and Floer complexes give rise to flow categories, continuation maps between them give rise to flow bimodules. These constructions have many flavours, as one can consider flow categories whose morphisms spaces are manifolds, equipped with various tangential structures, or more generally orbifolds or derived orbifolds. These variants are designed to accommodate specific Floer-theoretic applications, such as studying Floer theory on Liouville manifolds, or on general closed symplectic manifolds, as I will illustrate by discussing Hamiltonian Floer cohomology. END:VEVENT BEGIN:VEVENT DTSTART:20241107T163000 DTEND:20241107T173000 DTSTAMP:20241106T150000Z UID:1f84eb7c659a840ef3ffbbeb238985ad@cgp.ibs.re.kr SUMMARY:Floer homotopy via flow modules LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Mohammed Abouzaid\n\nEvent: 2024 RIMS-IBSCGP Conference on Recent Developments in Symplectic Topology\n\nAbstract: I will describe joint work with Blumberg, starting with the results appearing in arXiv:2404.03193, whose goal is to build a foundation for the study of the interaction between generalised homology and Floer theory. The key idea is to interpret flow categories, due to Cohen-Jones-Segal, as objects of a category whose morphisms we call flow bimodules. While Morse and Floer complexes give rise to flow categories, continuation maps between them give rise to flow bimodules. These constructions have many flavours, as one can consider flow categories whose morphisms spaces are manifolds, equipped with various tangential structures, or more generally orbifolds or derived orbifolds. These variants are designed to accommodate specific Floer-theoretic applications, such as studying Floer theory on Liouville manifolds, or on general closed symplectic manifolds, as I will illustrate by discussing Hamiltonian Floer cohomology. END:VEVENT BEGIN:VEVENT DTSTART:20241206T150000 DTEND:20241206T170000 DTSTAMP:20241205T150000Z UID:336e49b60e147ff73a30c9e7a9126ad8@cgp.ibs.re.kr SUMMARY:[2024-2 IBS-CGP&POSTECH-Math Colloquium] Analysis of Conformal Fields LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Nam-Gyu Kang\n\nEvent: Seminar\n\nAbstract: Conformal field theory (CFT) was originally introduced to connect various critical statistical physics models with Virasoro representation theory. Since then, it has found applications in string theory, condensed matter physics, vertex operator algebras, and probability theory. Meanwhile, stochastic Loewner evolution (SLE), introduced by Schramm, emerged as the only possible candidates for scaling limits of interface curves in several critical lattice models. This development has led to rigorous proofs of significant conjectures in statistical physics, including some highly non-trivial predictions of CFT. After reviewing the evolution of these ideas, I will present the connections between CFT and SLE across various conformal frameworks. END:VEVENT BEGIN:VEVENT DTSTART:20241211T161500 DTEND:20241211T181500 DTSTAMP:20241210T150000Z UID:92baf775acf5063f7e203efd0ca4b6dc@cgp.ibs.re.kr SUMMARY:Unit normal correspondence of a smooth divisor complement-continue LOCATION:IBS POSTECH Campus Bldg. #301 DESCRIPTION:Speaker: Dongwook Choa\n\nEvent: Symplectic geomerty and biratonal geometry seminar\n\nAbstract: The main purpose of this talk is to introduce the notion of the symplectic divisor complement and to explore its Floer theory. This class of symplectic manifolds has drawn significant interest because the divisor and its complement interact through the Liouville flow. As a guiding example, I will illustrate the idea in the context of polarized Kähler manifolds accompanied by detailed computations. Additionally, these manifolds arise as Milnor fibers of quasi-homogeneous polynomials, which is one of the goals of this study. END:VEVENT BEGIN:VEVENT DTSTART:20250109T161500 DTEND:20250109T181500 DTSTAMP:20250108T150000Z UID:4dc447a50fb04e6fce4af62496f0f58c@cgp.ibs.re.kr SUMMARY:Bohr- Sommerfeld Surgeries on Lagrangian Submanifolds LOCATION:IBS POSTECH Campus Bldg. #301 Auditorium DESCRIPTION:Speaker: Soham Chanda\n\nEvent: CGP Seminar\n\nAbstract: We introduce a class of surgery operations on Lagrangian submanifolds which switch between two different fillings of Bohr-Sommerfeld Legendrians. We will discuss the effect of such a surgery operation on the disk potential in the setting of monotone Lagrangians. As an application we will prove that such surgery operations yield exotic monotone Lagrangian tori in projective spaces of dimension 3 and higher. END:VEVENT BEGIN:VEVENT DTSTART:20250324T094000 DTEND:20250324T103000 DTSTAMP:20250323T150000Z UID:03783dd386217e6caadd6570061b2761@cgp.ibs.re.kr SUMMARY:Minimal rational curves on equivariant group compactifications LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Jun-Muk Hwang\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: Let X be a nonsingular equivariant compactification of a simple algebraic group G. We show that minimal rational curves on X are orbit-closures of 1-parameter subgroups of G and the set of minimal rational curves through a general point is the closure of an adjoint orbit. This generalizes a result of Brion and Fu's on wonderful group compactifications to arbitrary equivariant group compactifications. This is a joint work with Qifeng Li. END:VEVENT BEGIN:VEVENT DTSTART:20250324T110000 DTEND:20250324T115000 DTSTAMP:20250323T150000Z UID:30eadabd12c8d36a876b6d10f0931cff@cgp.ibs.re.kr SUMMARY:A pointless approach to K-stability LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Hamid Abban\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: K-stability is a notion initially introduced to detect existence of Kähler-Einstein metrics on Fano manifolds. However, the notion proved fruitful beyond this by providing the correct platform to construct compact moduli spaces for Fano varieties over the complex numbers, amongst many other applications. In this talk I will uncover another facet of K-stability by exploring connections to existence of rational points over subfields of the complex numbers.This is based on a joint work with Ivan Cheltsov, Takashi Kishimoto, and Frederic Mangolte. END:VEVENT BEGIN:VEVENT DTSTART:20250324T140000 DTEND:20250324T145000 DTSTAMP:20250323T150000Z UID:c5f5c6a8afc5787db8b1d6c34b5847de@cgp.ibs.re.kr SUMMARY:On hypersurfaces in projective bundles LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Tiago Duarte Guerreiro\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: Mori dream spaces are a special kind of varieties introduced by Hu and Keel in 2000 that enjoy very good properties with respect to the minimal model program. On the other hand, not many classes of examples of these are known. In this talk we introduce general hypersurfaces in certain projective bundles of Picard rank 2 and show that (some of) these are Mori dream spaces, partially generalising Ottem's result on hypersurfaces in products of projective spaces. END:VEVENT BEGIN:VEVENT DTSTART:20250324T152000 DTEND:20250324T161000 DTSTAMP:20250323T150000Z UID:a0739298737a5abef2912c0927136964@cgp.ibs.re.kr SUMMARY:On Hodge structures of compact complex manifolds with semistable degeneration LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Taro Sano\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: Compact Käler manifolds satisfy several nice cohomological properties such as Hodge symmetry and Hodge-Riemann bilinear relations. Friedman and Li recently showed that non-Käler Calabi-Yau 3-folds which are obtained by conifold transitions of projective ones satisfy such properties. In this talk, I will present examples of non-Käler Calabi-Yau manifolds with such properties by smoothing normal crossing varieties. END:VEVENT BEGIN:VEVENT DTSTART:20250325T094000 DTEND:20250325T103000 DTSTAMP:20250324T150000Z UID:bb4254902772d283ba9bd221f41fbeb8@cgp.ibs.re.kr SUMMARY:On the birational geometry of termial Fano threefolds of large Fano index LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Yuri Prokhorov\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: A $\mathbb{Q}$-Fano threefold is a normal three-dimensional projective variety $X$ with only terminal $\mathbb Q$-factorial singularities, ample anticanonical class, and Picard rank~$1$. The Fano index of~$X$ is the maximal integer that divides the anticanonical class in the Weil divisor class group. I will discuss $\mathbb{Q}$-Fano threefolds of large Fano index in relation to rationality questions. END:VEVENT BEGIN:VEVENT DTSTART:20250325T110000 DTEND:20250325T115000 DTSTAMP:20250324T150000Z UID:48113503376acf350350e0594897607b@cgp.ibs.re.kr SUMMARY:On the birational geometry of algebraically integrable foliations LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Paolo Cascini\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: I will report regarding some recent results on the Minimal Model Program for algebraically integrable foliations and some of their applications. END:VEVENT BEGIN:VEVENT DTSTART:20250325T140000 DTEND:20250325T145000 DTSTAMP:20250324T150000Z UID:5fe486a01646760f4e0e2729d124e2d5@cgp.ibs.re.kr SUMMARY:Wall crossing for K-moduli of Fano threefolds LOCATION:IBS POSTECH Campus Bldg., Pohang, South Korea DESCRIPTION:Speaker: Anne-Sophie Kaloghiros\n\nEvent: Pohang Workshop on Birational Geometry\n\nAbstract: I will discuss joint work with Ivan Cheltsov, Maksym Fedorchuk and Kento Fujita. In this talk, I will describe the component of the K-moduli space of smoothable Fano threefolds of anticanonical degree 24 associated to the deformation family 4.1 in the classification due to Mori and Mukai. Smooth Fano threefolds in this family are hypersurfaces of multi degree (1,1,1,1) in $(P^1)^4$ (a product of four copies of P^1) and are K-polystable; I will describe singular K-polystable degenerations of these. I will relate this K-moduli space to K-moduli spaces of pairs ( $(P^1)^4$, cX) where X is a Fano 3-fold in family 4.1, as c varies 0