From configurations on graphs to high dimensional cohomology of moduli spaces M_{2,n}

The moduli spaces of algebraic curves with marked points have 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 quotient. In joint work with Bibby, Chan, Yun and Hainaut we relate the top weight cohomology of the moduli space of genus 2 curves with marked points with that of a configuration space on a graph, opening the door to extensive new calculations and qualitative analyses.