2025秋季上海几何拓扑研讨会/2025 Fall Shanghai Geometry and Topology workshop

2025秋季上海几何拓扑研讨会/2025 Fall Shanghai Geometry and Topology workshop

时间：9月19日-9月21日

报告会场：上海科技大学张江校区

图书馆302报告厅

报告人：苏阳（中国科学院）

余斌（同济大学）

马烺特（上海交通大学）

王晁（华东师范大学）

王炜飚(中南大学)

组织人：陈文钊，皇甫振国，汪湜

会议议程：

9月19日（周五）        

9月20日（周六）  地点：上海科技大学图书馆302报告厅

9月21日（周日）        地点：数学科学研究所（创意与艺术学院南楼S408）

报告标题与摘要

Tittle： Diffeomorphism classification of simply connected 3 dimensional Mori fiber spaces

Speaker： 苏阳（中国科学院）

Abstract: Mori fiber spaces form a special class of complex projective varieties. They appear naturally in the minimal model program. In this talk I will describe a diffeomorphism classification of 3 dimensional simply connected Mori fiber spaces. This is based on the knowledge of the classification of simply connected 6-manifolds. Interestingly, the diffeomorphism types of these objects are determined by algebro-topological and algebro-geometrical numerical invariants such the Euler characteristic, the holomorphic Euler characteristic, the cube of the canonical divisor, etc. This is a joint work with HAO Feng and YANG Jianqiang.

Tittle: Self-orbit equivalences of a class of three dimensinal Anosov flows

余斌（同济大学）

Abstract: In this talk, starting from constructing examples, we will show that:

Theorem 1. For every , there exists a closed orientable hyperbolic 3-manifold M such that:

(1) 

(2) For every  with , there exists a nonn--covered Anosov flow  such that  

.Here, is the mapping class group of M, and is the sub-group of

 generated by the self orbit equivalences of . There are two intersting applications of this theorem:

 If we take , then the consequence of this theorem positively answer a question due to Barthelme and Mann: Does there exist an Anosov flow on a hyperbolic 3–manifold M such that the only self-orbit equivalences are isotopic to the identity?

 As a direct consequence of the theorem, we have: for every , there exists a hyperbolic 3-manifold M that carries at least k pairwise orbitally non-equivalent non--covered Anosov flows. This is the second way in history to construct this type of examples. The point is: we use as invariants, which we believe that the effective use of these dynamic invariants will inspire future related works.

This is the final part of a joint work with Francois Beguin and Christian Bonatti.

Tittle: Instantons on Product Manifolds  

Speaker: 马烺特（上海交通大学）

Abstract: In the late 90s, Donaldson-Segal proposed the framework of instantons over higher dimensional manifolds for the purpose of studying metrics with special holonomy. In this talk, I will discuss how to construct instantons on  product manifolds from those on the factor manifolds. In favorable caese, such instantons can be classified completely.  This is joint work with Dylan Galt.  

Tittle: Equivariant embeddings of Riemann surfaces into Euclidean spaces

Speaker:王晁（华东师范大学）

Abstract: Let S be a closed Riemann surface of genus g>1, and let G be the automorphism group of S. It is known that there exists a smooth G-equivariant embedding from S to some Euclidean space E, where G acts orthogonally on E. Let n be the minimal possible dimension of such E. We will show that n is at most 12(g-1). This is a joint work with Zhongzi Wang.

Tittle: Embeddability of non-orientable surfaces  in torus bundles over the circle

Speaker: 王炜飚(中南大学)

Abstract. For a given 3-manifold, which non-orientable closed surfaces can be embedded in it? For any lens space, or the product of any surface and the circle, the answer is known, mainly by the work of Bredon and Wood, as well as those of Jaco, End, Rannard, and so on. In joint work with Xiaoming Du, we answer this question for torus bundles over the circle, using the curve complex on torus of intersection number 2. Moreover, we determine the mod 2 Thurston norm of each mod 2 homology class for any torus bundle over the circle.