Polynomial equations for matrices over integers modulo a prime power and the cokernel of a random matrix

Abstract: Over a commutative ring of finite cardinality, how many $n \times n$ matrices satisfy a polynomial equation? In this talk, I will explain how to solve this question when the ring is given by integers modulo a prime power and the polynomial is square-free modulo the prime. Then I will discuss how this question is related to the distribution of the cokernel of a random matrix and the Cohen--Lenstra heuristics. This is joint work with Yunqi Liang and Michael Strand, as a result of a summer undergraduate research I mentored.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.