SMS scnews item created by Haotian Wu at Sat 22 Oct 2016 1654
Type: Seminar
Distribution: World
Expiry: 8 Nov 2016
Calendar1: 26 Oct 2016 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry & Topology: Fock and Goncharov Moduli Space and its Poisson Structure
Auth: haotianw@14-202-233-61.static.tpgi.com.au (hawu2800) in SMS-WASM

# Fock and Goncharov Moduli Space and its Poisson Structure

### Alex Casella (Sydney)

Wednesday 26 October 2016, 12:00–13:00 in Carslaw 535A.

Abstract: Vladimir Fock and Alexander Goncharov recently (2006) introduced a very convenient coordinate system to describe $T_{3}^{+}(S)$, the moduli space of framed convex projective structures with geodesic boundary on a surface $S$. Via such coordinate system, they defined a Poisson structure on $T_{3}^{+}(S)$ closely related to Goldman’s Poisson structure introduced in 1984. We analysed Fock and Goncharov’s parametrisation and gave a geometric proof of the equivalence between the two Poisson structures. I will introduce F&G’s coordinate system and Poisson structure, and outline our idea in the proof. This work is part of a joint project with R. Haraway, D. Tate and S. Tillmann.