东南代数几何研讨班III

：2022-11-26 09:00 —— 2022-11-27 17:00
：腾讯会议ID：854 4675 3910 （密码：112627）

 

一、 日程表

 

日期		报告人	主持人
11 月 26 日	09:00-10:00	陆俊（华东师范大学）Riccati foliations and double Riccati foliations	刘文飞
	休息
	10:10-11:10	徐万元（上海师范大学）On the sum of the non-negative Lyapunov exponents for a Teichmüller   curve	刘文飞
	休息
	14:00-15:00	李长征（中山大学）Plücker coordinate superpotential for flag varieties of Lie type A	宋雷
	休息
	15:10-16:10	赵以庚（西湖大学）On characteristic classes of constructible étale sheaves	宋雷

 

日期		报告人	主持人
11 月 27 日	09:00-10:00	许金兴（中国科学技术大学）A   higher-dimensional Chevalley restriction theorem for orthogonal groups	于飞
	休息
	10:10-11:10	李思辰（华东理工大学）Kawaguchi-Silverman conjecture on birational automorphisms of   projective threefolds	于飞
	休息
	14:00-15:00	李展（南方科技大学）Morrison-Kawamata   cone conjecture for Calabi-Yau fiber spaces	刘海东
	休息
	15:10-16:10	陈国度（西湖大学）On effective log Iitaka fibrations	刘海东

 

二、学术报告题目与摘要

  

On effective log Iitaka fibrations

陈国度（西湖大学）

We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. We show the effective log Iitaka fibration conjeture for threefold pairs. This is an ongoing joint work with Jingjun Han and Jihao Liu.

 

 

Plücker coordinate superpotential for flag varieties of Lie type A

李长征（中山大学）

In this talk, I will give a brief review on the mirror symmetry for partial flag varieties. I will explain how to interpret Rietsch's Lie theoretic superpotential in terms of Plücker coordinates. I will also discuss the mirror symmetry expectation that the first Chern class is sent to the class of the superpotential in the Jacobi ring under the mirror map. This is based on a work-in-progress, joint with Konstanze Rietsch, Mingzhi Yang and Chi Zhang.

 

 

 

Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces

李展（南方科技大学）

In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to establish the existence of (weak) fundamental domains for movable cones. This is joint work with Hang Zhao.

 

 

Riccati foliations and double Riccati foliations

陆俊（华东师范大学）

In this talk, we will give some results about Riccati foliations and  double Riccati foliations. Our discussion will be divided into two parts.

(I)  We will answer Poincaré's question in the case of Riccati foliations: is it possible to decide if a holomorphic foliation in P^2 is algebraic? Some criteria on the algebraicity of Riccati foliations will be given (joint work with Cheng Gong and Sheng-Li Tan).  As an interesting application, we will get a counter-example to Gurjar-Zhang's conjecture, i.e., a fibration with two multiple fibers on a rational surface (joint work with Xiaohang Wu).

(II)  We will talk about the geography of double Riccati foliations.  By using Chern numbers of  a foliation, we can get a slope inequality of  double Riccati foliations.

 

 

A higher-dimensional Chevalley restriction theorem for orthogonal groups

许金兴（中国科学技术大学）

The classical Chevalley restriction theorem asserts that for a semisimple complex Lie group G, the ring of G-invariant polynomials on the Lie algebra g is isomorphic through restriction to the ring of Weyl group invariant polynomials on the Cartan subalgebra. In studying the Hitchin morphism of Higgs bundles over higher dimensional varieties, Chen and Ngo conjectured a multi-variable generalization of the Chevalley restriction theorem, and they proved the GL and Sp cases. We then prove the orthogonal group case and our treatment can apply to the GL and Sp cases in a uniform way. As a corollary, we can prove a multiplicative property of Pfaffians for commutative skew symmetric matrices over an arbitrary char. 0 commutative ring. This is a joint work with Lei Song and Xiaopeng Xia.

 

 

On the sum of the non-negative Lyapunov exponents for a Teichmüller curve

徐万元（上海师范大学）

In this talk, I will talk about some numerical bounds of the sum of the non-negative Lyapunov exponents for a Teichmüller curve. We compute all Harder-Narasimahn polygon when Teichmüller curves reached the upper bound of the sum. We also compute all Lyapunov exponents for those Teichmüller curves in principal strata, which is not from computer numerical and Kontsevich-Forni formula. This work is in progress with Fei Yu.

 

 

On characteristic classes of constructible étale sheaves

赵以庚（西湖大学）

Characteristic classes can be thought of as natural transformations from Grothendieck K-groups of geometric objects to their cohomology groups. It has been well-studied for vector bundles on manifolds. In this talk, we first review Abbes-Saito's construction of characteristic classes for constructible étale sheaves on smooth varieties in positive characteristics. Then we generalize this formalism to relative cases under certain transversality conditions. We finally study the relationship between these two notions. This talk is based on joint work with Enlin Yang.