On the Euler characteristic of the commutative graph complex

I will present recent results on the asymptotic growth rate of the Euler characteristic of Kontsevich's commutative graph complex. These results imply the same asymptotic growth rate for the top-weight Euler characteristic of $\mathcal{M}_g$, the moduli space of curves, due to a theorem by Chan, Galatius and Payne. Further, the results establish the existence of large amounts of unexplained cohomology in this graph complex and many related cohomologies. I will explain role of this graph complex and the implications of the new results from the perspective of the cohomology of $\mathcal{M}_g$.