Number Theory and Topology
The theory of automorphic forms sits at the interface between analysis, geometry, topology, and number theory, and leads to deep connections and interrelations between these areas. In this talk I will explain some of these connections (without presuming prior knowledge of, or dwelling very much on, the automorphic theory that lurks in the background).
More particularly, I will explain some applications of ideas coming from number theory and automorphic forms to the study of the growth of mod p Betti numbers in certain towers of 3-manifolds. This is joint work with Frank Calegari.
Professor Matthew Emerton, University of Chicago