On some arithmetic statistics for matrices

3:00pm, Wednesday 5 Aug 2026

Abstract

In this talk we consider various questions of arithmetic statistics for matrices with elements of certain arithmetic structure, in particular, rational numbers of height at most H, parametrised by polynomials evaluated at integers of size at most H, or S-units. This questions include counting such matrices having a given determinant, rank, or characteristic polynomial, or being non-diagonalisable.