Two applications of the Lagrangian Floer theory of symmetric products

Speaker： Dr.  Cheuk Yu Mak（University of Edinburgh, UK）
Title：Two applications of the Lagrangian Floer theory of symmetric products
Time&Venue：2022.03.01，16:00-18:00  Tencent Meeting：534-468-554
Abstract：In this talk, we will describe two applications arising from studying Lagrangian Floer theory of symmetric products. The first one resolves a simplicity problem of the volume preserving homeomorphism groups of surfaces from the 70s, and it is a joint work with Daniel Cristofaro-Gardiner, Vincent Humili`ere, Sobhan Seyfaddini and Ivan Smith. We will then explain the difficulties in generalizing it to higher dimensions. A partial progress is obtained in a joint work with Ivan Smith, where we discover a new Lagrangian linking phenomenon, resolving a 20 years old question of Polterovich.