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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, March 11, 2021 - 3:30pm

Claudia Yun

Brown

Location

University of Pennsylvania

on zoom

zoom link sent to CAGE mailing list the day before or day of the talk

Fix non-negative integers g  and n such that 2g-2+n>0, the tropical moduli space \Delta_{g,n} is a topological space that parametrizes isomorphism classes of n-marked stable tropical curves of genus g with total edge length 1. These spaces are important because their reduced rational homology is identified equivariantly with the top weight cohomology of the algebraic moduli spaces M_{g,n}, with respect to the S_n-action of permuting marked points. In this talk, we focus on the genus 2 case and compute the characters of \tilde{H}_i(\Delta_{2,n};\Q) as S_n-representations, for n up to 8. To carry out the computations, we use a cellular chain complex for symmetric \Delta-complexes, a technique developed by Chan, Galatius, and Payne. The computation is done in SageMath.