Topology Seminar

Date: November 3, 2021

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Cheuk Yu Mak, University of Edinburgh

Title: Lagrangian Floer theory and a simplicity problem

Abstract: It is a classical and fundamental problem to study algebraic properties (e.g. simplicity, perfectness) of the automorphism group of an object. Building on the foundational works of Kirby, Thurston, Fathi and many others, there are a lot of studies for the automorphism group of compact (smooth) manifolds, possibly equipped with additional structures. When it comes to the simplicity of volume preserving homeomorphism groups, surprisingly, the higher dimensional cases are well-understood and the 2 dimensional case is more mysterious. In this talk, I will explain how to combine ideas from Lagrangian Floer theory and Hofer geometry to completely resolve this 40-year-old question. The technical heart of the proof is an extension of Calabi homomorphism, which answers a question of Ghys at his 2006 ICM talk on knots and dynamics. This is based on a joint work with Daniel Cristofaro-Gardiner, Vincent Humili`ere, Sobhan Seyfaddini and Ivan Smith.