Tutte colloquium-Michael Borinsky

Title:Constraining moduli space cohomology by counting graphs

Abstract: In 1992, Kontsevich defined complexes spanned by graphs. These 
complexes are increasingly prominent in algebraic topology, geometric 
group theory and mathematical physics. For instance, a 2021 theorem by 
Chan-Galatius and Payne implies that the top-weight cohomology of the 
moduli space of curves of genus g is equal to the homology of a specific 
graph complex. I will present a new theorem on the asymptotic growth 
rate of the Euler characteristic of this graph complex and explain its 
implication on the cohomology of the moduli space of curves. The proof 
involves solving a specific graph counting problem.