Title: The action of Hamiltonian homeomorphisms on surfaces and its applications

Abstract: The famous Gromov-Eliashberg Theorem, that the group of symplectic diffeomorphisms is $C^0$-closed in the full group of diffeomorphisms, makes us interested in defining a symplectic homeomorphism as a homeomorphism which is a $C^0$-limit of symplectic diffeomorphisms. This becomes a central theme of what is now called “$C^0$-symplectic topology”. On dimension 2, we can generalise the classical action function to the case of Hamiltonian homeomorphisms. Through studying the properties of the generalised action function, we may generalise several classical results from the smooth world to the $C^0$ world, e.g., the $C^0$-Schwarz's theorem, the existence of three actions of a non-trivial Hamiltonian homeomorphism which is a strengthening of the $C^0$-Arnold Conjecture on surfaces. Moreover, we answer a variant of a question posed by Buhovsky-Humiliere-Seyfaddini on dimension 2.

报告人简介：王俭，南开大学数学学院副教授。博士毕业于清华大学&巴黎第十三大学，曾在南开大学陈省身数学研究所、德国马普所、巴西IMPA做博士后。主要从事曲面动力系统以及辛动力系统的研究，目前在GAFA，Adv in Math, TAMS, AIHP C, IMRN等国际知名数学期刊发表论文多篇。

时间：2021年12月16日（周四）16:00-17:00

地点：中心校区知新楼B座924报告厅

邀请人：胡锡俊  况闻天