Algebraic Combinatorics - Michael Borinsky

Thursday, November 24, 2022 1:00 pm - 1:00 pm EST (GMT -05:00)

Title: Asymptotics of the Euler characteristic of Kontsevich's commutative graph complex

Speaker: Michael Borinsky
Affiliation: ETH, Zurich
Location: MC 5479 or contact Olya Mandelshtam for Zoom link

Abstract: I will present results on the asymptotic growth rate of the Euler characteristic of Kontsevich's commutative graph complex. By a work of Chan-Galatius-Payne, these results imply the same asymptotic growth rate for the top-weight Euler characteristic of M_g, the moduli 
space of curves, and establish the existence of large amounts of unexplained cohomology in this space. This asymptotic growth rate 
follows from new generating functions for the edge-alternating sum of graphs without odd automorphisms. I will give an overview on this 
interaction between topology and combinatorics and illustrate the combinatorial and analytical tools that were needed to obtain these 
generating functions.