The $S_n$-equivariant rational homology of the tropical moduli spaces $\Delta_{2,n}$

Abstract: The tropical moduli space $\Delta_{g,n}$ is a topological space that parametrizes isomorphism classes of $n$-marked stable tropical curves of genus with total volume 1. Its reduced rational homology has a natural structure of $S_n$-representations induced by permuting markings. In this talk, we focus on $\Delta_{2,n}$ and compute the characters of these $S_n$-representations for $n$ up to 8. We use the fact that $\Delta_{2,n}$ is a symmetric $\Delta$-complex, a concept introduced by Chan, Glatius, and Payne. The computation is done in SageMath.

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.