New patterns in the cohomology of moduli spaces of curves
Complex curves (a.k.a. Riemann surfaces) of positive genus are not rigid objects, but may be deformed and vary in families. The space \(M_g\) is a \((3g-3)\)-dimensional complex variety, whose points are in bijection with isomorphism classes of compact complex curves of genus \(g\). My talk will survey some old and new patterns in its cohomology, or, equivalently, in the cohomology of the corresponding mapping class group. Time permitting, I will discuss recent joint work with Kupers and Randal-Williams (arXiv:1805.07187), and with Chan and Payne (arXiv:1805.10186).
Professor Soren Galatius, University of Copenhagen