## Number Theory Seminar

### Tuesday, November 6th, 2018

**Time:** 10:00-11:00 a.m. **Place:** Jeffery Hall 422

**Speaker:** Brad Rodgers (Queen's University)

**Title:** Integers in short intervals representable as sums of two squares.

**Abstract:** Consider the set S of integers that can be represented as a sum of two squares. How are the elements of S distributed? In particular, how many elements fall into a random "short interval". (The definition of short interval will be given in the talk.) For very short intervals elements of S seem to be laid down at random, but I will discuss evidence that this ceases to be the case for longer short intervals. In particular, I will discuss a function field analogue of this problem and a connection to z-measures, an object first investigated in the context of asymptotic representation theory. This is joint work with O. Gorodetsky.