中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：王慰 （上海海洋大学）

题  目：An invitation to the topology of diffeomorphism groups of high dimensional manifolds 1

时  间：2024.09.03（星期二）9:30-10:30

地  点：数学院南楼N820

摘  要：Let M be a compact smooth manifold. The diffeomorphism group Diff(M) of M is an important object in algebraic and geometric topology. In this talk, we will introduce two different models of Diff(M) and some general properties of Diff(M). 

题  目：An invitation to the topology of diffeomorphism groups of high dimensional manifolds 2

时  间：2024.09.03（星期二）10:30-11:30

地  点：数学院南楼N820

摘  要：We will review some classical methods of computing homotopy groups of diffeomorphism groups. We will end this talk by discussing our recent progress on the fundamental groups of diffeomorphism groups of certain high dimensional manifolds. 

题  目：An invitation to the topology of diffeomorphism groups of high dimensional manifolds 3

时  间：2024.09.04（星期三）09:30-10:30

地  点：数学院南楼N820

摘  要：In this talk, we will first focus on discussing some relations between diffeomorphism groups and embedding spaces. We will also survey some finiteness properties of diffeomorphism groups and some properties of Miller-Morita-Mumford classes of manifold bundles. 

题  目：An invitation to the topology of diffeomorphism groups of high dimensional manifolds 4

时  间：2024.09.04（星期三）10:30-11:30

地  点：数学院南楼N820

摘  要：We will discuss our recent progress on mapping class groups and block diffeomorphism groups of certain high dimensional manifolds.