Abstract:

Abstract: The dark matter problem in the moduli space of curves is a question about the nature of its unstable cohomology: Huge amounts of unstable cohomology are known to exist due to an Euler characteristic computation by Harer and Zagier. However, there are almost no constructions for unstable classes. A theorem of Chan, Galatius and Payne uses Kontsevich's commutative graph complex to shed new light on this dark matter problem. I will explain how the asymptotic behaviour of the Euler characteristic of this graph complex gives new insights into the limits of Chan, Galatius and Payne's construction and provides a new dark matter problem for commutative graph homology.