Mumford's conjecture: a topological outlook

Ulrike Tillmann

Twenty-five years ago, Mumford defined certain canonical classes in the cohomology of the moduli space of Riemann surfaces, and asked whether these generate the rational cohomology in low dimensions (relative to the genus of the underlying curve). This conjecture has been proved by Madsen and Weiss. In this colloquium-style lecture, I will explain some of the main ideas that went into another proof subsequently given in joint work with Galatius, Madsen, and Weiss.