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]