Title: Automorphic forms and the partition function
Abstract: The partition function p(n) counts the number of ways to break a positive integer into parts. Its values are the coefficients of a modular form of weight -1/2, and this opens the door to study properties of p(n) using the theory of automorphic forms. There are two branches to this study; the analytic side involves Maass forms and spectral theory and the arithmetic side involves holomorphic modular forms and Galois representations. In all cases the study can be viewed as a "testing ground"for more general theorems about modular forms. I will discuss a number of results which have been proved with various collaborators (most of whom have an Illinois connection) in the last few years.