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.

[pre-talk at 1:20PM]