Prime number theorems for polynomials from homogeneous dynamics

Katy Woo, Princeton University
Fine Hall 214

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits. 

The Bateman-Horn conjecture gives a prediction for how often an irreducible polynomial takes on prime values. In joint work with Giorgos Kotsovolis, we introduce a new class of polynomials for which we can prove the Bateman-Horn conjecture. In this talk, I will focus on the proof of Bateman-Horn for two examples -- the determinant polynomial on nxn matrices and the determinant polynomial on nxn symmetric matrices. A key tool in the proof is the input of homogeneous dynamics to count the number of integral points on level sets.