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George Mason University
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Geometry MMA Seminar: Moduli spaces of piecewise circular polygons and positivity

Sep 25, 2023, 10:30 - 11:30 AM

 

Speaker:  Jean-Philippe Burelle, University of Sherbrooke

Title:   Moduli spaces of piecewise circular polygons and positivity

Abstract:  A circular n-gon is a polygon in the 2-sphere with circular arcs as its edges, with the additional assumption that adjacent arcs are tangent at the vertices (allowing singularities). In joint work with R. Kirk, we define a moduli space parameterizing circular n-gons up to a natural action of the symplectic group Sp(4,R), and for n=2k we relate this moduli space to the space of k-tuples of pairwise transverse isotropic flags. Using this relation we describe a special connected component homeomorphic to a ball, corresponding to the positive component of Fock and Goncharov. 

 

Time: Monday, September 25, 2023 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106