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 is in enumerative and probabilistic phenomena in algebra and number theory. More specifically, I am interested in
discrete random integral matrices (especially p-adic matrices),
random algebraic curves over finite fields, and
connections between arithmetic, combinatorics, and topology.
A substantial part of my research involves some explicit counting, which suits for various undergraduate research projects. So far, there has been a publication that came out of mentoring undergraduate research, and there are many more potential projects. Lately, I have been also interested in Data Science and Machine Learning algorithms.
Papers
The cokernel of a polynomial push-forward of a random integral matrix with concentrated residue, with Yifeng Huang, submitted, arxiv preprint
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, Linear Algebra and its Applications 677 (2023) p.1-30.
Pólya enumeration theorems in algebraic geometry, Mathematical Research Letters 29 (2022) p.1347-1376.
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.
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.
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.
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.
Weighted distribution of points on cyclic covers of the projective line over finite fields, Finite Fields and Their Applications 57 (2019), p.29-46.
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.
Research Mentoring
MIT PRIMES (2023): Counting symmetric matrices with concentrated residue modulo prime power
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
Thesis
Cycle indices in arithmetic geometry, University of Michigan (2021)
Talks
Southern California Discrete Mathematics Symposium 2023 at CSULA (Nov 5, 2023)
International Workshop in Analytic Number Theory at Seoul National University / UNIST (Aug 24, 2023)
Summer School on Arithmetic Statistics at Korea Institute of Advanced Study (Aug 16 - 17, 2023)
University of California--Irvine, "Probability/Combinatorics Seminar" (Apr 5, 2023)
Claremont McKenna College, "Number Theory Seminar" (Mar 28, 2023)
University of California--San Diego, "Number Theory Seminar" (Feb 2, 2023)
Yonsei University, "BK Number Theory Seminar" (Aug 30, 2022)
Chonnam National University, "Number Theory Seminar" (Aug 25, 2022)
Korean Institute of Advanced Study, "Number Theory Seminar" (Aug 4, 2022)
University of California--Los Angeles, "Number Theory Seminar" (Nov 15, 2021)
UNIST, "Number Theory Seminar" (Oct 6, 2021)
PAlmetto Joint Arithmetic, Modularity, and Analysis Series (Dec 5, 2020)
University of Michigan--Ann Arbor, "RTG: Number Theory Seminar" (Aug 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" (Sep 6, 2019)
University of California--Irvine, "Number Theory Seminar" (Mar 7, 2019)