Algebra/Topology Seminar

Speaker: Nir Gadish

Title: Computing top weight cohomology of M_{2,n} using configurations on graphs

Abstract: The moduli space of algebraic curves has hugely complicated and interesting cohomology. While in low dimensions the cohomology exhibits a form of (representation-) stability, near the top dimension very little is known. Tropical geometry gives access to some of this high dimensional cohomology, namely its top weight. In this talk I will briefly describe the moduli space of tropical curves with marked points, and how it relates to the top weight cohomology of the algebraic moduli space. Then we will discuss joint work with Bibby, Chan and Yun that reduces the calculation in genus 2 to configurations on a graph, as well as some new computations made possible by this reduction.