|Date: Friday, September 16, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Moduli spaces of tropical curves and representations of the symmetric group
Abstract: I will discuss the combinatorial construction of the moduli space of stable tropical curves with labeled marked points, as a generalized simplicial complex parametrizing marked weighted metric graphs, with special attention to the representations of the symmetric group in its rational homology, with the action induced by permuting the marked points. In genus 0 and 1, these representations grow factorially in the number of marked points, but carry a "secret filtration" whose graded pieces are representation stable.
Although I will present the complex in question as a moduli space for tropical curves, it has other natural interpretations, e.g. as topological quotients of Culler-Vogtmann Outer Space, Harvey's complex of curves on a punctured surface, and Hatcher's complex of sphere systems; and as the dual complex of the boundary divisor in the Deligne-Mumford moduli space of stable algebraic curves. Hence the properties of this space and its homology have interpretations in each of these contexts.
Based on joint work with Melody Chan and Soren Galatius.
Speaker: Sam Payne
Institution: Yale U.
Event Organizer: Thomas Lam