An infinity-structure in Morse theory

Abstract 

In the light of Morse homology initiated by Witten and Floer, we construct two infinity-categories. One comes out of the Morse-Samle pairs and their higher homotopies, and the other strict one concerns the chain complexes of the Morse functions. Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters, we also build up a weak infinity-functor between them. The talk is based on the joint work with with Chenxi WANG.

About the speaker 

孙善忠，首都师范大学数学科学学院教授，博士生导师，2001年博士毕业于南开大学陈省身数学研究所。研究兴趣在于与物理相关之数学问题诸如天体力学中的多体问题等哈密顿系统、辛拓扑中的Fukaya范畴、半经典迹公式、形变量子化以及Resurgence理论。相关工作发表在ARMA、CMP、Adv. Math.等著名期刊。