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| 8:30–9:00 | 会议注册 |
| 9:00–10:00 | Some new advances on birational geometry of varieties of general type |
| 陈猛 | |
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In this lecture, we introduce some new advances on induction and lifting property of canonical stability index of varieties of general type. The content covers my joint work with Zhi Jiang and Hexu Liu. |
| 10:00–10:30 | 合影、茶歇 |
| 10:30–11:30 | Algebraic vector bundles on Grassmannians in positive characteristics |
| 杜荣 | |
| Algebraic vector bundles over projective spaces or even Grassmannians in positive characteristic exhibit notable distinctions from those in characteristic zero. In this talk, I will talk about several dissimilarities regarding this issue. This talk is based on the joint works with Xinyi Fang and Yuhang Zhou. |
| 中午 | 午餐 |
| 14:00–15:00 | On Severi type inequalities and equalities |
| 江智 | |
| We will report a method initiated by Barja-Pardini-Stoppino to prove Severi type inequalities. By combining calculations of cohomological rank function, we can apply these inequalities to classify irregular varieties with small birational invariants |
| 15:00–15:20 | 茶歇 |
| 15:20–16:20 | The algebra of symmetric tensors and symplectic geometry of cotangent bundles |
| 刘杰 | |
| The algebra of symmetric tensors of a projective manifold is a graded \(\mathbb{C}\)-algebra, which is canonically isomorphic to the ring of regular functions over the total space of the cotangent bundle. Despite its simple definition, this is an intriguing object and it is less studied in the literature. In this talk I will discuss it by some typical examples, focusing on its interaction with symplectic geometry of cotangent bundles. |
| 16:20–16:40 | 茶歇 |
| 16:40–17:40 | On dynamical Iitaka fibration |
| 孟晟 | |
| Dynamical Iitaka fibration is used to create a new equivariant fibration when the birational equivariant minimal model program fails. I shall mainly explain this technique in this talk. If we still have time, I shall further introduce a bit the applications.This talk is based on a joint work with De-Qi Zhang. |
| 18:00 | 晚宴 |
| 09:00–10:00 | A finite dimensional proof of the Verlinde formula |
| 孙笑涛 | |
|
A formula of dimensions for the spaces of generalized theta functions on moduli spaces of parabolic bundles on a curve of genus g , the so called Verlinde formula, was predicted by Rational Conformal Field Theories. The proof of Verlinde formula by identifying the spaces of generalized theta functions with the spaces of conformal blocks from physics was given in last century mainly by Beauville and Faltings (so called infinite dimensional proof). Under various conditions, many mathematicians tried to give proofs of Verlinde formula without using of conformal blocks, which are called finite dimensional proofs by Beauville. In this talk, we give unconditionally a purely algebro-geometric proof of Verlinde formula. Our proof is based on two recurrence relations, one of which establishes an inductive procedure for the genus of curves, another one provides an inductive procedure for the number of parabolic points. This is a joint work with Mingshuo Zhou. |
| 10:00–10:30 | 茶歇 |
| 10:30–11:30 | Orbifold modification of complex analytic varieties |
| 欧文浩 | |
| We prove that if \(X\) is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism \(f\colon Y\to X\), such that \(Y\) has quotient singularities, and that the indeterminacy locus of \(f^{-1}\) has codimension at least 3 in \(X\). As an application, we deduce the Bogomolov-Gieseker inequality on orbifold Chern classes for stable reflexive coherent sheaves on compact Kaehler varieties which have quotient singularities in codimension 2. |
| 中午 | 午餐 |
| 14:00–15:00 | An effective upper bound for anti-canonical volumes of singular Fano 3-folds |
| 江辰 | |
| Fano varieties are natural geometric objects in algebraic geometry and differential geometry. Motivated by the classifications theory, we are interested in certain boundedness properties of Fano varieties. In this talk, I will explain recent progress on the study of anti-canonical volumes of Fano 3-folds. We show that for a Fano 3-fold with e-lc singularities, the anti-canonical volume is at most \(3200/e^4\). This is based on a joint work with Yu Zou. |
| 15:00–15:20 | 茶歇 |
| 15:20–16:20 | K3 surface entropy and automorphism groups |
| 余讯 | |
| In this talk, we give a characterization of the complex projective K3 surfaces admitting automorphisms of positive entropy and we explain how to classify the projective K3 surfaces of zero entropy with infinite automorphism groups. As an application, we determine the projective K3 surfaces of Picard number at least five with almost abelian automorphism groups. This answers a question of Nikulin. |
| 16:20–16:40 | 茶歇 |
| 16:40–17:40 | Positivity of line bundles on toric varieties |
| 朱智贤 | |
| In this talk, we first characterize the jet ampleness of line bundles on a toric variety, in terms of the lattice length of their associated polytopes. As an application, we prove a \(k\)-jet generalization of Fujita's conjectures. Inspired by the Mukai conjecture, which naturally generalizes Fujita's conjectures, we make a conjecture regarding the higher syzygies in terms of the lattice length and report our progress in this conjecture. Part of the talks is based on joint work with Jose Gonzalez and joint work in progress with Lei Song and Huanqi Wen. |
| 18:00 | 晚餐 |