Algebra and Combinatorics Seminar
- When
- Friday, November 13, 20261:00 PM – 2:00 PM CSTAdd to calendarGoogle Calendar
- Where
- Founders Building (FO) 2.208800 W. Campbell Road, Richardson, Texas 75080-3021Open in Maps
- Hosted by
- Natural Sciences & Mathematics
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About
Speaker: Michael Shapiro (Michigan State University)
Title: Symplectic groupoid and cluster structure on the Teichmueller space of closed genus two surfaces.
Abstract: The symplectic groupoid of unipotent nxn upper-triangular matrices is formed by pairs (B, A) where B is a nondegenerate nxn matrix, A is a unipotent upper-triangular nxn matrix, and BAB^t is unipotent upper triangular. The symplectic groupoid is equipped with the natural symplectic form defined by Bondal, which induces a Poisson bracket on the space of upper triangular unipotent matrices studied by Bondal, Dubrovin-Ugaglia, and others. We compute the cluster structure compatible with the Poisson structure and discuss its connection with the Teichmueller space of genus g curves with one or two holes equipped with a Goldman Poisson bracket. As an unexpected byproduct, we obtain a cluster structure on the Teichmueller space of closed genus two curves unknown earlier. This is a joint project with L. Chekhov.