Zoom link:  https://princeton.zoom.us/j/91248028438

By work of Harer, the Betti cohomology of the moduli space of smooth, complex curves of genus g > 1 vanishes in degrees above 4g - 5. In my talk, I give a new perspective on this result which relies on p-adic geometry. The approach also yields statements about moduli of stable curves and curves of compact type that are not covered by Harer's methods.