The distribution of cubic character sums

In this talk, we will discuss the distribution of the maximum of cubic character sums. First, we will show that the distribution of large cubic character sums behaves very differently from those in the family of non-principal characters modulo a large prime and the family of quadratic characters. Secondly, we will show a surprising structure result of cubic characters with large character sums. We will begin with some background on character sums and then briefly outline the proofs. The proofs use the pretentious theory of character sums, the large sieve, and the method of moments, among other things. This is joint work with Youness Lamzouri.