Date/Time
Date(s) - 05/04/2024
3:30 pm - 4:30 pm

Location: HH 305

Speaker: François Labourie (Université Côte d’Azur)

Title: Poisson algebra, combinatorics and representations of surface groups 

Abstract:
In this talk, I will start by recalling what a Poisson algebra is by first concentrating on the basic example of the algebra of polynomials in 2 variables. I will then briefly recall the relationship of Poisson algebras with Hamiltonian and Quantum Dynamics.  Then I will explain a beautiful combinatorial construction due to Bill Goldman giving the structure of a Lie algebra on the vector space formally generated by loops on a surface $S$. The motivation underlying Goldman’s construction is motivated by the Poisson algebra of regular functions on the character variety of $\pi_1(S)$ in a Lie group $G$. From that I will move to the deformation space of Anosov representations of $\pi_1(S)$ in a non-compact Lie group $G$ and show that there are more natural functions than regular ones (think of length or cross-ratio functions on Teichmüller space) and show that their Poisson Structure can also be described by a combinatorial object called « Ghost Bracket ». This is a joint work with Martin Bridgeman.

The first part of the talk will be elementary, the second part also but some knowledge of the hyperbolic plane will make it easier to understand.

Please see recording for this talk, here

Coffee and cookies will be served in HH 216 at 3pm – All are welcome.