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…
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