Program

	Mar 24 (Mon)	Mar 25 (Tue)	Mar 26 (Wed)	Mar 27 (Thu)	Mar 28 (Fri)
09:20 – 09:40	Welcome and Registration
09:40 – 10:30	Jun-Muk Hwang	Yuri Prokhorov	Adrien Dubouloz	Frederic Mangolte	Jungkai Chen
10:30 – 11:00	Break / Teatime
11:00 – 11:50	Hamid Abban	Paolo Cascini	Takashi Kishimoto	Robert Smiech	Yongnam Lee
11:50 – 14:00	Lunch
14:00 – 14:50	Tiago Duarte Guerreiro	Anne-Sophie Kaloghiros	Free Discussion	Constantin Loginov	Constantin Shramov
14:50 – 15:20	Break / Teatime			Break / Teatime	Closing & Free Discussion
15:20 – 16:10	Taro Sano	Kento Fujita		Sung Rak Choi
16:10 – 16:40	Free Discussion	Break / Teatime		Break / Teatime
16:40 – 17:30		Luca Tasin		Andrea Petracci
17:30 – 19:30				Photo Session& Banquet

Abstract

Monday, March 24

Time	Speaker	Title & Abstract
09:40 – 10:30	Jun-Muk Hwang (Center for ComplexGeometry, IBS)	Minimal rational curves on equivariant group compactifications 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.
11:00 – 11:50	Hamid Abban (University of Nottingham)	A pointless approach to K-stability 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.
14:00 – 14:50	Tiago Duarte Guerreiro (Paris-Saclay University)	On hypersurfaces in projective bundles 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.
15:20 – 16:10	Taro Sano (Kobe University)	On Hodge structures of compact complex manifolds with semistable degeneration 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.

Tuesday, March 25

Time	Speaker	Title & Abstract
09:40 – 10:30	Yuri Prokhorov (Steklov MathematicalInstitute)	On the birational geometry of termial Fano threefolds of large Fano index 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.
11:00 – 11:50	Paolo Cascini (Imperial College London)	On the birational geometry of algebraically integrable foliations I will report regarding some recent results on the Minimal Model Program for algebraically integrable foliations and some of their applications.
14:00 – 14:50	Anne-Sophie Kaloghiros (Brunel University London)	Wall crossing for K-moduli of Fano threefolds 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 $(P^1,cX)$ where $X$ is a Fano 3-fold in family 4.1, as c varies 0<c<2, and discuss wall crossing for these.
15:20 – 16:10	Kento Fujita (Osaka University)	On the coupled Ding stability and the Yau-Tian-Donaldson correspondence for Fano manifolds We interpret the reduced coupled Ding stability of Fano manifolds in the notion of reduced coupled stability thresholds. As a corollary, we solve a modified version of the conjecture by Hultgren and Witt Nystroem for coupled Kaehler-Einstein metrics on Fano manifolds. This is a joint work with Yoshinori Hashimoto.
16:40 – 17:30	Luca Tasin (University of Milan)	K-stability of Fano weighted hypersurfaces I will report on recent progress in determining the K-stability of Fano hypersurfaces in weighted projective space. In particular, I will explain how to prove K-stability in the index one case under suitable assumptions. This is based on joint work with Taro Sano.

Wednesday, March 26

Time	Speaker	Title & Abstract
09:40 – 10:30	Adrien Dubouloz (University of Poitiers)	Smooth prime Fano threefolds of degree 22 with infinite automorphism groups (Joint work with Kento Fujita and Takashi Kishimoto) Smooth prime Fano threefolds of degree 22 with infinite automorphism groups have been studied and classified by Kuznetsov-Prokhorov-Shramov, Kuznetsov-Prokhorov. In this talk I will present an alternative complementary viewpoint on this classification building on the study of pencils of rational normal quintic curves with infinite stabilizers in non-normal hyperplane sections of the quintic del Pezzo threefold.
11:00 – 11:50	Takashi Kishimoto (Saitama University)	Forms of smooth prime Fano threefolds of degree 22 with infinite automorphism groups As explained in Dubouloz's talk, smooth prime Fano threefolds $X_{22}$ of degree 22 with infinite automorphism groups, which have been initially studied by Kuznetsov-Prokhorov-Shramov, Kuznetsov-Prokhorov by a different viewpoint, can be reconstructed by means of linear pencils of special type on the Hirzebruch surface of degree three. This observation allows us to look into their forms. In the talk, beginning with forms of the smooth quintic del Pezzo threefold, we will clarify the behavior of forms of $X_{22}$ having infinite automorphism groups depending on the type of connected components. This is based on a joint work with Adrien Dubouloz and Kento Fujita.

Thursday, March 27

Time	Speaker	Title & Abstract
09:40 – 10:30	Frederic Mangolte (Aix-Marseille University)	Real loci of rational Fano threefolds From the classification of real rational surfaces worked out by Comessatti at the beginning of the 20th century we get the following striking characterization of real rational surfaces: a geometrically rational real surface is rational if and only if its real locus is non-empty and connected. In a work in progress with Andrea Fanelli, we explore real loci of geometrically rational Fano threefolds in relation to their rationality. I this talk I will focus on the construction of real Fano manifolds with disconnected real loci.
11:00 – 11:50	Robert Smiech (University of Edinburgh)	K-stability and K-moduli of Fano 3.11 revisited The introduction of the Abban-Zhuang method allowed to achieve rapid progress in determining the K-stability and constructing K-moduli spaces of Fano threefolds. In my talk, I will present the family 3.11, whose smooth members are constructed as follows: consider a smooth complete intersection of two quadrics in projective space of dimension 3 - i.e. an elliptic curve. Pick up a point on it and blow it up, then blow up the strict transform of the elliptic curve. K. Fujita showed that a particular member of this family is K-stable, so consequently - by the openness of the K-stability - most of the members of the family are K-stable. Unfortunately, we do not yet have a complete understanding of the K-moduli of the family. I will present a conjectural characterization of this moduli space, based on the joint work in progress with I. Cheltsov, A.-S. Kaloghiros and J. Zhao.
14:00 – 14:50	Constantin Loginov (Steklov MathematicalInstitute)	Finite Abelian Subgroups in the Space Cremona Group Finite abelian groups are one of the simplest objects studied in algebra. Rational varieties form a reasonably simple class of varieties considered in algebraic geometry. However, the question of which finite abelian groups can act on rational (or rationally connected) varieties, is far from being an easy question. In dimension 2 the answer to this question was given by A. Beauville and J. Blanc. We will consider this question in dimension three.
15:20 – 16:10	Sung Rak Choi (Yonsei University)	A valuative approach to the -K-MMP For We study the geometry of the triple which consists of a usual pair and a pseudoeffective divisor. We define the log canonical threshold to such triples and prove that there exists a quasi-monomial valuation which computes the log canonical threhold if the triple is klt. As a by product, we show that in such a case, we can run the -K-MMP. This is a report on the joint work with S.Jang, D.Kim, and D.Lee.
16:40 – 17:30	Andrea Petracci (University of Bologna)	On deformations of monomial schemes Deformation theory is a well-established part of algebraic geometry and is essential to study local properties of moduli spaces. Nonetheless explicitly computing deformations of algebraic varieties (affine or projective) is usually very hard, and most of the times impossible. In this talk, I will present some partial results of work in progress with Nathan Ilten and Francesco Meazzini about (even derived) deformation theory of affine varieties defined by monomial ideals. The combinatorics of monomial ideals and the torus action allow us to reduce certain deformation-theoretic computations about differential graded Lie algebras and about the cotangent complex to combinatorial computations.

Friday, March 28

Time	Speaker	Title & Abstract
09:40 – 10:30	Jungkai Chen (National Taiwan University)	On threefolds of general type with small volume and genus. It is now known that for threefolds of general type, their volume and genus satisfies the Noether inequality. Following these recent developments, it is known that volume greater or equal to 1 (resp. 2 and 7/2) if genus is 3 (resp. 4 and 5). The canonical models of threefolds with (vol, pg)=(1.3) and (2,4) can be realized as weighted hypersurfaces or weighted complete intersection. In this talk, we are going to introduce the abovementioned work of Chen-Hu-Jiang and also provide more details about their minimal models. Part of the talk is a joint work in progress with Hsin-Ku Chen.
11:00 – 11:50	Yongnam Lee (Center for Complex Geometry, IBS)	Morphisms from a very general hypersurface In this talk, we will talk about a non-binational surjective morphism from a very general hypersurface X to a normal projective variety Y. We first show Y is a Fano variety if the degree of the morphism is bigger than a constant C where C depends on the dimension and degree of X. Next we prove an optimal upper bound of the morphism which is degree of X provided that Y is factorial, degree of the morphism is prime and bigger than a constant E where E depends only on the dimension of X. Also, we will show that Y is a projective space under some conditions. This is a joint work with Yujie Luo and De-Qi Zhang.
14:00 – 14:50	Constantin Shramov (Steklov Mathematical Institute)	Pluricanonical representations of automorphism groups. Let X be a compact complex manifold, and let Y be the image of its pluricanonical map. According to a theorem due to Deligne and Ueno, the image of the automorphism group of X in the automorphism group of Y is finite if X is Moishezon. I will discuss an approach to possible generalizations of this result for the case of arbitrary compact complex manifolds.The talk is based on a joint work with Konstantin Loginov.

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Room Type	POSCO Int'l Center	Hotel Yeongildae	Apple Tree Hotel	Tour de Pohang (Woman's Safety Sohotel)
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