# Seminars & Events for Graduate Student Seminar

##### Cohen-Lenstra Heuristics

The class group of a number field, in colloquial terms, measures the failure of unique factorization in its ring of integers. Despite its central role in number theory, information about its structure, and even its size, mostly remain mysteries. In this talk, we will discuss conjectures on the asymptotics of the structure of class groups (the Cohen-Lenstra heuristics) as well as a more general notion of "categorical randomness" which has led to several other conjectures.

##### The Polynomial Method in Harmonic Analysis

We'll discuss incidence problems in harmonic analysis. I'll focus on recent progress which interestingly comes from algebra and topology. In particular, we'll examine Dvir's proof of the Kakeya conjecture over finite fields, Guth's endpoint estimate for the multilinear Kakeya function which used tools from algebraic topology and the joints problem.