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Stayan Devadoss

2010-01-26
14:00:00 - 15:30:00

Topology of Real Moduli Spaces

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Our story is motivated by the configuration space of particles on spheres. In the 1970s, Deligne and Mumford constructed a way to keep track of particle collisions in this space using Geometric Invariant Theory. In the 1980s, this (compactified) moduli space was remarkably used by Gromov and Witten as invariants arising from string field theory. In the 1990s, Kontsevich and Fukaya generalized these ideas when studying deformation quantization to include particles collisions on surfaces with boundary. This talk, using visual brushstrokes, focuses on the topology of real points of particle collisions. These real analogs can be understood from several viewpoints: from tiling of convex polytopes, to blowups of hyperplane arrangements, to underlying operad structures, to spaces of phylogenetic trees, and to open-closed string field theory.