# New patterns in the cohomology of moduli spaces of curves

## Seminar/Forum

Evan Williams
Peter Hall
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).