Orateur
Prof.
Alexander Goncharov
(Yale University)
Description
Given a bipartite graph G on a possibly punctured surface S, there is a (non-commutative) cluster Poisson variety X(G,S). It depends only on the equivalence class of G under certain elementary transformations. A threefold M which bounds the surface S with filled punctures gives rise to a Lagrangian in the generic symplectic fibers of X(G,S). I will explain that it carries a natural non-commutative cluster symplectic structure.
The construction requires a 3d generalization of bipartite surface graphs. The talk reflects joint work with Maxim Kontsevich.
