Speaker: Anton Alexeev (Université de Genève)

Time:  Oct 14, 10:00-11:30 am

Location: No. 6, Teaching Building 六教 6A103

Title: Teichmüller spaces for surfaces with boundary, and Virasoro algebra

Abstract:

Teichmüller spaces associated to closed oriented surfaces carry Weil-Petersen symplectic structures which admit many descriptions. In particular, by the results of Goldman and Hitchin, these Teichmüller spaces are connected components of moduli spaces of flat connections which carry Atiyah-Bott symplectic forms, and they admit explicit Fenchel-Nielsen Darboux coordinates.

In this talk, we consider infinite dimensional  Teichmüller spaces associated to oriented surfaces with absolute boundary. We show that similarly to their finite dimensional counterparts they carry canonical symplectic forms. Suprizingly, they also carry Hamiltonian actions of the Virasoro algebra.

This work is motivated by recent works on Jackiw-Teitelboim 2-dimensional gravity, and by the study of moduli of flat connections for surfaces with boundary. The talk is based on a joint work with E. Meinrenken, see arXiv:2401.03029,  and on a work in progress with R. Dalipi and S. Shatashvili.