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.