Title: Cluster algebras and Poisson structures
Speaker: Michael Shapiro (Michigan State University)
Abstract: In the first talk we give an elementary overview of hyperbolic approach to cluster algebra theory. Starting from the special coordinates on the configuration space of n points on $RP^1$ we define similar coordinates for the Teichmuller space $T_{g,s}$ of (decorated) Riemann surfaces of genus $g$ with $s$ punctures, discuss (compatible) Weil-Petersson Poisson bracket (pre-symplectic form) and then generalize the construction to two dual versions of (generalized) cluster algebras of Fomin and Zelevinsky together with the compatible Poisson bracket (pre-symplectic form).
The talk is based on papers by Fock-Goncharov, Fomin-Zelevinsky, Gekhtman-S.-Vainshtein, Fomin-S.-Thurston, and S.-Chekhov.
Seminar URL: https://people.math.osu.edu/anderson.2804/gcis/