中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人： 章博宇  博士 （University of Maryland）
题  目：Knots, links, and the ring structure in instanton homology
时  间：2023.08.07（星期一），09:00-11:00
地  点：腾讯会议 : 218-800-791
摘 要：In this talk, I will discuss the ring structure of the singular instanton Floer homology of S^1 times a punctured surface.  This ring structure gives all the universal relations of the module structures on instanton Floer homology groups.  The algebraic properties of this ring have yielded a large number of topological applications, including detection results on Khovanov homology and new results on the SU(2) representation varieties of link complements.  I will also discuss some of these topological applications.  The talk is based on joint works with Yi Xie.

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报告人： 章博宇  博士 （University of Maryland）
题  目：Compactness problems for generalized Seiberg-Witten equations
时  间：2023.08.09（星期三），09:00-11:00
地  点：腾讯会议 : 899-545-325
摘 要：In this talk, I will present several results about the compactness problems for generalized Seiberg-Witten equations.  I will talk about the role of Z/2 harmonic spinors in the study of generalized Seiberg-Witten equations, and present a regularity result for their zero loci.  I will also present an abstract compactness result for a family of generalized Seiberg-Witten equations in dimension three.  This talk is partially based on a joint work with Thomas Walpuski.