几何拓扑讨论班2022年7月4日-7月15日
地点：东7一层报告厅
Previous Seminars:
7月15日（星期五）报告安排 | ||
时间 | 报告人 | 题目摘要 |
10:00 | 林剑锋 (清华大学) | In this talk, we will sketch an argument that if two lens space become diffeomorphic after taking product with a circle, then themselves must be diffeomorphic. This follows from a result by Atiyah-Bott and Milnor. |
10:45 -11:30 |
| 题目：流形上有限循环群的自由作用。 摘要：我将简单介绍高连通流形上有限循环群的自由作用的分类及应用。 |
11:30 |
| 王晁和王中子的一个等变嵌入构造。 |
12:10 -12:30 | 王枫（浙江大学） | Title: On the log-concavity of chromatic polynomial of graphs Abstract: |
| 时间： | 7月14日（星期四），14:00 |
| 主讲人： | 苏阳 (中国科学院） |
| 题目： | A brief introduction to the topological classification of 4-manifolds and related topics II |
| 摘要： | I will give a brief introduction to the topological classification of 4-manifolds (simply-connceted, finite and infinite cyclic fundamental group) and the computation of the pseudo isotopy classes of diffeomorphisms. |
| 时间： | 7月14日（星期四），10:00 |
| 主讲人： | 林剑锋 (清华大学) |
| 题目： | The geography and botany problem of simply-connected smooth 4-manifolds II |
| 摘要： | Since the ground breaking work of Donaldson in the 1980s, gauge theory has been a powerful tool to understand smooth structures on 4-manifolds. In this talk, we will discuss some of the important developments in the past 40 years. The focus will be the following two questions: (1) Which simply-connected topological 4-manifolds admit an (irreducible) smooth structure? (2) Which simply-connected smooth 4-manifolds admit exotic smooth structures? This talk will not assume any prior knowledge about gauge theory or 4-dimensional topology. |
| 时间： | 7月13日（星期三），14:00 |
| 主讲人： | 林剑锋 (清华大学) |
| 题目： | The geography and botany problem of simply-connected smooth 4-manifolds |
| 摘要： | Since the ground breaking work of Donaldson in the 1980s, gauge theory has been a powerful tool to understand smooth structures on 4-manifolds. In this talk, we will discuss some of the important developments in the past 40 years. The focus will be the following two questions: (1) Which simply-connected topological 4-manifolds admit an (irreducible) smooth structure? (2) Which simply-connected smooth 4-manifolds admit exotic smooth structures? This talk will not assume any prior knowledge about gauge theory or 4-dimensional topology. |
| 时间： | 7月13日（星期三），10:00 |
| 主讲人： | 苏阳 (中国科学院） |
| 题目： | A brief introduction to the topological classification of 4-manifolds and related topics |
| 摘要： | I will give a brief introduction to the topological classification of 4-manifolds (simply-connceted, finite and infinite cyclic fundamental group) and the computation of the pseudo isotopy classes of diffeomorphisms. |
| 时间： | 7月12日（星期一），14:00 |
| 主讲人： | 杨文元 (北京大学) |
| 题目： | Group actions on hyperbolic spaces II |
| 摘要： | In last 30 years, studying groups via interesting actions on hyperbolic spaces has been proven fruitful in the field of Geometric Group Theory. In this talk, I will explain how this approach works in two exmples -- solving Burnside's problem and finiteness of asymptotic dimension of mapping class groups. These are based on the rotating family theory ( Delzant-Gromov, Coulon, Dahmani-Guirardell-Osin), and the projection complex machinary (Bestvina-Bromberg-Fujiwara). |
| 时间： | 7月11日（星期一），14:00 |
| 主讲人： | 王晁（华东师范大学） |
| 题目： | On cobordism of automorphisms of surfaces |
| 摘要： | I will give a brief introduction of the cobordism group of automorphisms of closed oriented surfaces and some related results. |
| 时间： | 7月11日（星期一），10:00 |
| 主讲人： | 杨文元 (北京大学) |
| 题目： | Group actions on hyperbolic spaces |
| 摘要： | In last 30 years, studying groups via interesting actions on hyperbolic spaces has been proven fruitful in the field of Geometric Group Theory. In this talk, I will explain how this approach works in two exmples -- solving Burnside's problem and finiteness of asymptotic dimension of mapping class groups. These are based on the rotating family theory ( Delzant-Gromov, Coulon, Dahmani-Guirardell-Osin), and the projection complex machinary (Bestvina-Bromberg-Fujiwara). |
| 时间： | 7月9日（星期六），10:00 |
| 主讲人： | 马继明（复旦大学） |
| 题目： | Some results on hyperbolic geometry |
| 摘要： | In this talk, I will first survey some examples and results on hyperbolic 3-manifolds, and then I will talk about similar questions on higher dimensional hyperbolic manifolds, in particular, on the existence of hyperbolic Coxeter polytopes. This will involve joint work with Fangting Zheng. |
| 时间： | 7月8日（星期五），14:00 |
| 主讲人： | 李友林（上海交通大学） |
| 题目： | Contact structures on 3-manifold |
| 摘要： | In this talk, I will survey the main ingredients of the 3-dimensional contact topology: convex surfaces, Legendrian and transverse knots, contact surgery, open book decompositions and symplectic fillings. |
| 时间： | 7月8日（星期五），10:00 |
| 主讲人： | 李友林（上海交通大学） |
| 题目： | Contact structures on 3-manifolds |
| 摘要： | In this talk, I will survey the main ingredients of the 3-dimensional contact topology: convex surfaces, Legendrian and transverse knots, contact surgery, open book decompositions and symplectic fillings. |
| 时间： | 7月7日（星期四），14:00 |
| 主讲人： | 张影（苏州大学） |
| 题目： | Convexity of length functions on Teichmuller space |
| 摘要： | We talk about the convexity of length functions on Teichmuller space as given by Bestvina-Bromberg-Fujiwara-Souto in their paper Shearing coordinates and convexity of length functions on Teichmuller space (Amer. J. Math., 2013). |
| 时间： | 7月7日（星期四），10:00 |
| 主讲人： | 余斌 （同济大学） |
| 题目： | Dehn-Fried-Goodman surgeries of Anosov flows on 3-manifolds |
| 摘要： | Dehn-Fried-Goodman (abbreviated as DFG) surgery is a type of `dynamical’ Dehn surgery, which is used to construct new Anosov flow from old one. DFG surgery plays an important role in the study of Anosov flows on 3-manifolds. In this talk, we will introduce some results and questions related to DFG surgeries of Anosov flows on 3-manifolds. |
| 时间： | 7月6日（星期三），14:00 |
| 主讲人： | 余斌（同济大学） |
| 题目： | Veering triangulations, Branched surfaces and Pseudo-Anosov flows-I |
| 摘要： | In this talk, we will introduce the main idea of building an ideal triangulation (veering triangulation) of a mapping torus of a pseudo-Anosov map punctured along the singular fibers, due to Agol 2011. |
| 时间： | 7月5日（星期二），14:00 |
| 主讲人： | 马继明（复旦大学） |
| 题目： | Complex hyperbolic geometry |
| 摘要： | Complex hyperbolic geometry is a cousin of real hyperbolic geometry, but we know very few about it. We will survey some questions in this area and talk about some methods to show a group acts discretely on complex hyperbolic space. |
| 时间： | 7月5日（星期二），10:00 |
| 主讲人： | 汪世达 |
| 题目： | Topological and Smooth Knot Concordance II |
| 摘要： | A cobordism between knots is called a concordance if its genus is zero. We will review some related notions and survey a few classical results in this area by Fox-Milnor, Levine and Casson-Gordon. Then the difference between smooth and topological categories will be discussed. We will also introduce concordance problems about algebraic knots. |
| 时间： | 7月4日（星期一），14:00 |
| 主讲人： | 汪世达 |
| 题目： | Topological and Smooth Knot Concordance I |
| 摘要： | A cobordism between knots is called a concordance if its genus is zero. We will review some related notions and survey a few classical results in this area by Fox-Milnor, Levine and Casson-Gordon. Then the difference between smooth and topological categories will be discussed. We will also introduce concordance problems about algebraic knots. |
In this talk, we will sketch an argument that if two lens space become diffeomorphic after taking product with a circle, then themselves must be diffeomorphic. This follows from a result by Atiyah-Bott and Milnor. 流形上有限循环群的自由作用。
