# Manjul Bhargava

Affiliation: Princeton University

Email: bhargava@math.princeton.edu

Title Of Talk: Squarefree values of polynomial discriminants

Abstract: The question as to whether a positive proportion of monic integer polynomials of degree $n$ have squarefree discriminant is an old one; an exact formula for the density was conjectured by Lenstra. (The interest in polynomials $f$ with squarefree discriminant comes from the fact that in such cases it is immediate to construct the ring of integers in the $\mathbb Q$-algebra $\mathbb Q[x]/f(x)$.)

In this talk, we will describe recent work with Arul Shankar and Xiaoheng Wang that allows us to determine the probability that a random monic integer polynomial has squarefree discriminant - thus proving the conjecture of Lenstra.