Prime number theorems for polynomials from homogeneous dynamics
Prime number theorems for polynomials from homogeneous dynamics

Katy Woo, Princeton University
Fine Hall 214
Meeting ID: 920 2195 5230
Passcode: The threedigit integer that is the cube of the sum of its digits.
The BatemanHorn 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 BatemanHorn conjecture. In this talk, I will focus on the proof of BatemanHorn 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.