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email: gilyoung at lumetec dot com / gcheong at ucla dot edu
Research
Research
My current research interest is in machine learning (ML) and deep learning (DL) in fiber optic sensing technologies. I am interested in bringing in various mathematical tools into practical ML/DL algorithms that are designed for specific industrial tasks.
Previously, I worked on diverse topics in mathematics, including:
discrete random integral matrices (especially p-adic matrices),
random algebraic curves over finite fields, and
connections between arithmetic, combinatorics, and topology.
Papers
Papers
The distribution of the cokernel of a polynomial evaluated at a random integral matrix, with Myungjun Yu, to appear in the American Journal of Mathematics, arxiv preprint
The cokernel of a polynomial push-forward of a random integral matrix with concentrated residue, with Yifeng Huang, Mathematical Proceedings of the Cambridge Philosophical Society 178 (2) (2025) p.229-257, 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
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
Thesis
Cycle indices in arithmetic geometry, University of Michigan (2021)
Talks
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)
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