Hamiltonian Virasoro actions on Teichmueller spaces

In this talk, we explain that (infinite dimensional) Teichmueller spaces associated to hyperbolic surfaces with absolute boundary carry Hamiltonian actions of the Virasoro algebra. If time permits, we will also state some open problems for surfaces with marked points. Our study is motivated on the one hand by the work of Saad–Shenker–Stanford on Jackiw–Teitelboim gravity, and on the other hand by the Meinrenken–Woodward theory of Hamiltonian loop group actions.

The talk is based on a joint work with Eckhard Meinrenken, see arXiv:2401.03029.