##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Gilyoung Cheong

#### UC Irvine

## 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.

[pre-talk at 1:20PM]

### February 2, 2023

### 2:00 PM

APM 6402 and Zoom; see https://www.math.ucsd.edu/~nts

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