2024苏州拓扑学会议——学术报告
(西交利物浦大学与苏州大学联合举办)
会议地点：西交利物浦大学数学楼MA405教室
报告题目：Heegaard presentation length for 3-Manifold groups
报告人：刘毅（北京大学）
时间：2024-10-26（星期六）09:25-10:15
摘要：The Heegaard presentation length of an orientable closed 3-manifold refers to the minimal presentation length among all finite presentations of the fundamental group which arise from Heegaard splittings. I will discuss basic properties of this quantity, and mention some applications where this new concept is involved.
报告题目：On 4-dimensional Dehn twists and Milnor fibrations
报告人：林剑锋（清华大学）
时间：2024-10-26（星期六）10:40-11:30
摘要：Milnor fibration of a singularity is an important object in algebraic geometry. In complex dimension 3, such fibration gives an open book decomposition of 𝑆5. And the monodromy represents an element in the mapping class group of the Milnor fiber. In this talk, I will discuss a recent work that shows this monodromy is usually of infinite order when the Milnor fibration has a 𝐶∗ action. The proof makes uses of recent advances in equivariant monopole Floer theory. A large part of the talk will be used to discuss the motivation (simultaneous resolution of ADE singularities by Atiyah, Brieskorn and Wahl). No prior knowledge about algebraic geometry or gauge theory will be assumed. (Based on a joint with Hokuto Konno, Anubhav Mukherjee and Juan Munoz Echaniz).
报告题目：On contact solid tori in contact 3-manifolds
报告人：李友林（上海交通大学）
时间：2024-10-26（星期六）14:00-14:50
摘要：Contact knotted solid tori in contact 3-manifolds are closely related to Legendrian knots. In this talk, I will present several recent results concerning contact solid tori in contact 3-manifolds，involving contact width and Legendrian large cables. This is joint work with John Etnyre and Bulent Tosun.
报告题目：A lower bound of the crossing number of composite knots
报告人：王晁（华东师范大学）
时间：2024-10-26（星期六）15:00-15:50
摘要：Let 𝑐(𝐾) denote the crossing number of a knot 𝐾 and let 𝐾1#𝐾2 denote the connected sum of two oriented knots 𝐾1 and 𝐾2. It is a very old unsolved question that whether 𝑐(𝐾1#𝐾2)=𝑐(𝐾1)+𝑐(𝐾2). We show that 𝑐(𝐾1#𝐾2)>(1/16)(𝑐(𝐾1)+𝑐(𝐾2)). This is a joint work with Ruifeng Qiu.
报告题目：Exponential volumes of moduli spaces of hyperbolic surfaces
报告人：孙哲（中国科学技术大学）
时间：2024-10-26（星期六）16:10-17:00
摘要：Mirzakhani found a remarkable recursive formula for the volumes of the moduli spaces of the hyperbolic surfaces with geodesic boundary, and the recursive formula plays very important role in several areas of mathematics: topological recursion, random hyperbolic surfaces etc. We consider some more general moduli spaces 𝑀𝑆(𝐾,𝐿) where the hyperbolic surfaces would have crown ends and horocycle decorations at each ideal points. But the volume of the space 𝑀𝑆(𝐾,𝐿) is infinite when S has the crown ends. To fix this problem, we introduce the exponential volume form given by the volume form multiplied by the exponent of a canonical function on 𝑀𝑆(𝐾,𝐿). We show that the exponential volume is finite. And we prove the recursion formulas for the exponential volumes, generalizing Mirzakhani's recursions for the volumes of moduli spaces of hyperbolic surfaces. We expect the exponential volumes are relevant to the open string theory. This is a joint work with Alexander Goncharov.
报告题目：Kervaire不变量问题和同伦球面的分类
报告人：王国祯（复旦大学）
时间：2024-10-26（星期六）17:10-18:00
摘要：流形的分类是拓扑学中的核心问题。对于同伦球面的分类，可以划归为三个问题：h配边的分类，标架流形的配边分类，以及手术操作的障碍理论。对于5维及以上的球面，h-配边定理由Smale解决；标架配边分类等价于球面稳定同伦群的计算；而Milnor和Kervaire的工作指出手术的障碍来自于中间维数的符号差以及Kervaire不变量。我们将介绍最新的关于球面稳定同伦群的一些工作，这使得我们可以对于5至90维球面上的微分结构进行分类，并且彻底的解决关于Kervaire不变量在哪些维数非平凡的问题。
报告题目：Thurston的“几何剖分猜想”
报告人：葛化彬（中国人民大学）
时间：2024-10-27（星期日）10:10-11:00
摘要：Thurston“几何剖分猜想”认为每个体积有限的带 cusp 三维双曲流形都可以几何剖分为双曲理想四面体。此猜想对理解三维双曲流形的几何结构起奠基性作用，是双曲几何与三维拓扑领域遗留的重要问题之一。本报告将介绍用组合Ricci流工具研究“几何剖分猜想”的主要想法和部分结果。报告将围绕三维双曲多面体度量的刚性、存在性与几何剖分、三维双曲流形的多面体剖分、角度结构、三维组合Ricci流等相关内容展开。
报告题目：圆丛间的映射
报告人：王诗宬（北京大学）
时间：2024-10-27（星期日）11:10-12:00
摘要：Circle bundles over surfaces are primary examples of fiber bundles, and cover six of eight geometries in Thurston's picture of 3-manifolds, and many inspiring phenomena arise from them. The non-zero degree maps between circle bundles over surfaces often are well-behaved. We will talk about maps between 𝑆1-bundles over 𝑛-manifolds, including motivations, methods, results and application.
欢迎参加！