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会议时间、地点

2024.6.29，西安交通大学（兴庆校区）主楼A104教室

2024.6.30，西安交通大学（兴庆校区）数学楼 2-1会议室

日程表

报告题目、摘要

程志云（北京师范大学）

题目：Partial-dual genus polynomial and its categorification

摘要：The partial-dual genus polynomial of a ribbon graph is the generating function that enumerates all partial duals of the ribbon graph. In this talk, I will give a quick introduction to this polynomial and discuss the categorification of it. This is a joint work with Ziyi Lei.

冯可（电子科技大学）

题目：Some progress on geometric ideal triangulation

摘要：Gluing ideal tetrahedra plays a crucial role in the construction of hyperbolic 3-manifolds. While, it is still not known that whether a hyperbolic 3-manifold admits a geometric ideal triangulation. In this talk, we will show some progress to hyperbolize and further obtain geometric triangulations of 3-manifolds. To be precise, we will show the rigidity of hyperbolic polyhedral metrics on 3-manifolds, which is a joint work with Huabin Ge. And then, we will show the connections between 3D-combinatorial Ricci flows and Thurston's geometric ideal triangulations. At the same time, we will also give some topological conditions to guarantee the convergence of the combinatorial Ricci flows and furthermore the existence of geometric ideal triangulations.

马继明（复旦大学）

题目：Complex hyperbolic quadrangle groups

摘要：We report our recent work on complex hyperbolic quadrangle groups with two right angles.  We show the discreteness and faithfulness of the representations in some special cases. In turn, we obtain some complicated cusped hyperbolic 3-manifold admitting spherical CR uniformizations.

邱瑞锋（华东师范大学）

题目：Heegaard分解在三维流形理论中的应用

摘要：报告中我们将主要介绍Heegaard分解在纽结组合不变量可加性、三维流形的几何与拓扑结构、三维流形映射类群方面的应用。

苏阳（中国科学院）

题目：The mapping class group and the group of homotopy equivalences of certain 1-connected 6-manifolds

摘要：In this talk we will consider 1-connected 6-manifolds whose homology groups are isomorphic to that of 3-dimensional complex projective space. A classification of these manifolds is a classical theorem in manifold topology. I will describe the mapping class group of this class of manifolds. From this information we can basically determine the group of homotopy equivalences of these manifolds, which was initially studied by homotopy theorists. This is a joint work with M. Kreck.

王家军（北京大学）

题目：Shortest filling geodesics on hyperbolic surfaces

摘要：Among the moduli space of genus g hyperbolic surfaces, the shortest geodesics with certain properties have been extensively studied. We are interested in filling geodesics. We construct a candidate filling geodesic and show that it has minimal length under some assumptions. This is joint work with Yue Gao and Zhongzi Wang.

王诗宬（北京大学）

题目：曲面同胚的协边和不可压缩协边

摘要：本报告将介绍曲面同胚的协边和不可压缩协边的最新进展。

伍晓磊（上海数学中心）

题目：Triangle Artin Groups Part 2: Polyfreeness

摘要：I will discuss the question of when a triangle artin group is virtually poly-free. The idea is to make use of the free-splittings that have been constructed by Squier, Jankiewicz, Ye and myself. We can show most of them are virtually poly-free. This is a joint work with Shengkui Ye.

吴云辉（清华大学）

题目：On second eigenvalues of closed hyperbolic surfaces for large genus

摘要：In this work we obtain optimal lower and upper bounds for second eigenvalues of closed hyperbolic surfaces for large genus. Moreover, we also study their asymptotic behaviors on random hyperbolic surfaces. This is a joint work with Yuxin He.

杨文元（北京大学）

题目：Uniform exponential growth for groups with proper product actions on hyperbolic spaces

摘要：Uniform exponential growth of finitely generated groups has been a classical problem in geometric group theory. In recent years, there is an increasing interest in understanding the product set growth, which could be thought of as a stronger version of uniform exponential growth.  In this talk, I will discuss these two problems, provided that the finitely generated group under consideration acts properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing property on factors, we prove that any finitely generated non-virtually abelian subgroup has uniform exponential growth. These assumptions are full-filled in many hierarchically hyperbolic groups, including mapping class groups, specially cubulated groups and BMW groups.  Via a weakly acylindrical action on each factor, we are able to classify subgroups with product set growth in any group acting discretely on a simply connected manifold with pinched negative curvature, and in groups acting acylindrically on trees, and in 3-manifold groups. This is based on a joint work with Renxing Wan (PKU).

叶圣奎（上海纽约大学）

题目：Triangle Artin Groups Part 1: Splitting and Non-splitting

摘要：The triangle Artin group Art(m,n,p) is generated by 3 elements with 3 relators defined by the labels m,n,p. We consider the splitting of triangle Artin groups as a graph of free groups.  We show that Art(2,3,2n), n>2, is isomorphic to F_3 *_{F_7} F_4, the amalgamated product of the free groups F3, F4 over the subgroup F7.  Furthermore, the group Art(2,3,2n+1) cannot be split as a graph of free groups.  Combining the earlier work of Jankiewicz and Squier, this completely answers the question of splitting triangle Artin groups. This is a joint work with Xiaolei Wu.

于立（南京大学）

题目：Poincare-Lefschetz Duality between Weighted Simplicial Homology

and Cohomology of Orbifolds

摘要：We first introduce the definitions of weighted simplicial homology and cohomology of an orbifold. Then we show how to generalize the cup product in the usual cohomology theory to the weighted simplicial cohomology. Moreover, we discover that there is a natural duality

relation between the weighted simplicial homology and cohomology for a compact orbifold, which generalizes the Poincare-Lefschetz duality of compact manifolds.

张影（苏州大学）

题目：Length minima for an infinite family of filling closed curves on a one-holed torus

摘要：We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves,  $ a^2 b^n $ ($ n \ge 3 $), on a complete one-holed hyperbolic torus in its relative Teichmüller space, where $a, b$ are simple closed curves on the one-holed torus which intersect exactly once transversely. This provides concrete examples for the problem to minimize the geodesic length of a fixed filling closed curve on a complete hyperbolic surface of finite type in its relative Teichmüller space. This is joint work with Zhongzi Wang. 

赵学志（首都师范大学）

题目：不动点类理论的扩展及其应用

摘要：不动点类理论能得到比不动点存性更强的结论，给出映射同伦类中不动点个数的下界估计，其核心方法是不动点的分类。我们介绍一下，近期的一些扩展。一方面是对同伦加以限制，如：正则性、等变，另一方面是对不动点概念进行推广。特别地，我们介绍扩展不动点类理论的一些关联应用：纽结浸入圆盘的自交点集，曲面上曲线几何相交数，Heegaard-Floer 同调中的Whitney圆盘等。