Speaker: Leonid Chekhov (Steklov Mathematical Institute and Michigan State University)

Title: Symplectic groupoid: geometry, networks, and moduli spaces of closed Riemann surfaces

Date and time:  25.06.2025, 17:00 (GMT +03:00)

Abstract: I will describe the Bondal's symplectic groupoid: a set of pairs (B,A) with A unipotent upper-triangular matrices and B an element of GL(n) being such that the matrix B A B^T is itself unipotent upper triangular. Since works of J.Nelson, T.Regge, B.Dubrovin,  and M.Ugaglia it was known that entries of A can be identified with geodesic functions on a Riemann surface with holes; these entries then enjoy a closed Poisson algebra (reflection equation) expressible in the r-matrix form. In our recent work with M.Shapiro, we solved the symplectic groupoid in terms of planar networks; we used this solution to construct a complete set of geodesic functions for a closed Riemann surface of genus 2; all geodesic functions are elements of the upper cluster algebra whereas Dehn twists are described by cluster mutations. This is a joint work with M.Shapiro.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com