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publications
[1] Gaussian universality of p-adic random matrix products via corners Electronic Journal of Probability, 2024. [arXiv] [journal]
[2] Non-Archimedean GUE corners and Hecke modules, joint with Roger Van Peski Preprint, 2024. [arXiv]
[3] Gaussian Universality of Products Over Split Reductive Groups and the Satake Isomorphism Selecta Mathematica, 2025. [arXiv] [journal]
[4] Groups with pairings, Hall Modules, and Hall-Littlewood Polynomials, joint with Roger Van Peski International Mathematics Research Notices, 2025. [arXiv] [journal]
[5] The Szemeredi-Trotter theorem over arbitrary field of characteristic zero Preprint, 2025. [arXiv]
[6] Universality of rational canonical form for random matrices over a finite field Preprint, 2025. [arXiv]
[7] High-low method and p-adic Furstenberg set over the plane, joint with Kevin Ren Preprint, 2025. [arXiv]
[8] Eigenvalues of p-adic random matrices, joint with Roger Van Peski Preprint, 2026. [arXiv]
[9] Quantative universality for cokernels of matrices with symmetries Preprint, 2026. [arXiv]
[10] The k-cycle shuffling with repeated cards Preprint, 2026. [arXiv]
[11] The Cutoff Profile for Random Transpositions on Repeated Cards in the Full Range of Parameters Preprint, 2026. [arXiv]
[12] Eigenvalue Distribution of p-adic Random Matrices Among Algebraic Extensions, with an Analogue for p-adic Random Polynomials Preprint, 2026. [arXiv]
[13] p-adic Sum-Product, Projections, and Furstenberg Sets Preprint, 2026. [arXiv]
[14] Hitting time mixing for random k-cycles, joint with Chen Shang, Jiyue Zeng, and Xinyi Zhang Preprint, 2026. [arXiv]
[15] The Resultant Distribution Method: Universality for p-adic Random Matrices and Polynomials Preprint, 2026. [arXiv]
[16] Sharp Threshold for Universality of Rational Canonical Forms over a Finite Field Preprint, 2026. [arXiv]
talks
Student Seminars at Columbia
Published:
I have organized and participated in several student seminars at Columbia, including: student probability seminar, since Spring 2024; student seminar on the work of Manjul Bhargava, Fall 2023, including number field asymptotics and Selmer groups; Automorphic Forms Student Seminar**, spring 2023, based on Daniel Bump’s Automorphic Forms and Representations.
Non-Archimedean GUE corners and Hecke modules
Published:
Random non-archimedean matrices play an important role in Cohen-Lenstra heuristics, whose singular numbers provide information for the distribution of ideal class groups for quadratic extension and Tate-Shafarevich groups of elliptic curves. In this talk, I will provide our result on the distribution of singular numbers for random alternating and Hermitian non-archimedean matrices, based on our new application of Hecke algebra.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
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Teaching experience 2
Workshop, University 1, Department, 2015
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