# Gilyoung Cheong

# I am a Visiting Assistant Professor in the Department of Mathematics at the University of California--Irvine. My mentor is Nathan Kaplan.

email: gilyounc at uci dot edu

I obtained my PhD at the University of Michigan. My advisors were Michael Zieve and Mircea Mustaţă.

# Research

My research deals with many combinatorial and probabilistic phenomena of various algebraic objects. The problems I deal with often include diverse fields in mathematics such as algebraic geometry, combinatorics, number theory, and probability theory.

# Papers

The distribution of the cokernel of a polynomial evaluated at a random integral matrix, with Myungjun Yu, submitted, arxiv preprint

Polynomial equations for matrices over integers modulo a prime power and the cokernel of a random matrix, with Yunqi Liang and Michael Strand, submitted, arxiv preprint

Pólya enumeration theorems in algebraic geometry, Mathematical Research Letters 29 (2022) p.1347-1376, old arxiv preprint.

Jordan--Landau theorem for matrices over finite fields, with Jungin Lee, Hayan Nam, and Myungjun Yu, Linear Algebra and its Applications 655 (2022) p.100-128, old arxiv preprint

Betti and Hodge numbers of configuration spaces of a punctured elliptic curve from its zeta functions, with Yifeng Huang, Transactions of the American Mathematical Society 375 (2022), p.6363-6383, old arxiv preprint.

Generalizations of results of Friedman and Washington on cokernels of random p-adic matrices, with Nathan Kaplan, Journal of Algebra 604 (2022), p.636-663, old arxiv preprint.

Cohen-Lenstra distributions via random matrices over complete discrete valuation rings with finite residue fields, with Yifeng Huang, Illinois Journal of Mathematics 65 (2021) p.385-415, old arxiv preprint.

Weighted distribution of points on cyclic covers of the projective line over finite fields, Finite Fields and Their Applications 57 (2019), p.29-46. old arxiv preprint

The distribution of points on superelliptic curves over finite fields, with Melanie Matchett Wood and Azeem Zaman, Proceedings of the American Mathematical Society 143 (2015) p.1365-1375. old arxiv preprint.

# Research Mentoring

MIT PRIMES (2023): Counting nilpotent matrices modulo prime power and its relation to the distribution of the Smith normal form of powers of matrices

University of California--Irvine (September 2022): Counting solutions to a polynomial equation over a finite matrix algebra

University of California--Irvine (July - August 2022): Cokernels of p-adic integral random matrices -- a paper in result

# Thesis

Cycle indices in arithmetic geometry, University of Michigan (2021)

# Talks

University of California--Irvine, "Probability/Combinatorics Seminar" (April 5, 2023)

Caremont McKenna College, "Number Theory Seminar" (March 28, 2023)

University of California--San Diego, "Number Theory Seminar" (February 2, 2023)

Yonsei University, "BK Number Theory Seminar" (August 30, 2022)

Chonnam National University, "Number Theory Seminar" (August 25, 2022)

Korean Institute of Advanced Study, "Number Theory Seminar" (August 4, 2022)

University of California--Los Angeles, "Number Theory Seminar" (November 15, 2021)

UNIST, "Number Theory Seminar" (October 6, 2021)

PAlmetto Joint Arithmetic, Modularity, and Analysis Series (December 5, 2020)

University of Michigan--Ann Arbor, "RTG: Number Theory Seminar" (August 5, 2020)

University of Waterloo, "Algebraic Combinatorics Seminar" (July 30, 2020)

Korean Institute of Advanced Study, "Three W's Seminar" (May 11, 2020)

University of Michigan--Ann Arbor, "Combinatorics Seminar" (September 6, 2019)

University of California--Irvine, "Number Theory Seminar" (March 7, 2019)