Yifeng Huang

Last modified on Aug 6, 2025

I am currently an Assistant Profesor (RTPC) at the University of Southern California.

I was a postdoctoral fellow at the University of British Columbia in academic years 2022-2024; my mentors were Jim Bryan, Kalle Karu and Zinovy Reichstein.

I received my PhD at the Department of Mathematics at the University of Michigan–Ann Arbor in Apr 2022. My thesis advisor is Michael Zieve and my co-advisor is Jeffrey Lagarias. I am interested in the interface of algebraic geometry, number theory and combinatorics. Among other things, I have worked on arithmetic statistics, moduli spaces, discrete random matrix theory, partitions, random permutations, Diophantine equations and arithmetic dynamics.

Here are my CV and my research statement as of Nov 2023.

Photo of Yifeng

  • Email: yifeng.huang αt usc ∂οt edu
    My previous email huangyf@math.ubc.ca is discontinued.
  • Office: KAP 438D
  • Pronunciation: ee-FENG or yee-FENG
  • Pronouns: he/him/his

Seminars

Preprints and Publications

  1. Cohen–Lenstra flag universality for random matrix products, with Hoi Nguyen and Roger Van Peski. arXiv page
  2. Coh zeta functions for inert quadratic orders, submitted. arXiv page, slides
  3. Hilbert Series for Configuration Spaces of Punctured Surfaces, with Eric Ramos. arXiv page.
  4. Low degree subvarieties of universal hypersurfaces, with Borys Kadets and Olivier Martin, submitted. arXiv page.
  5. A Mordell–Lang type problem for GLm, with J. Bell and D. Ghioca, Bull. Aust. Math. Soc. 111(3) (2025), 433–444. published version
  6. Cokernels of random matrix products and flag Cohen–Lenstra heuristic, Forum Math. 37(5) (2025), 1325–1332. arXiv page
  7. Commuting matrices via commuting endomorphisms, submitted. pdf, arXiv page
  8. A non-abelian variant of the classical Mordell-Lang conjecture, with Dragos Ghioca. submitted. pdf
  9. Motivic Coh and Quot zeta functions of singular curves, with Ruofan Jiang. pdf, arXiv page, slides in algebraic geometry, number theory, combinatorics, poster in a Ramanujan conference
  10. The cokernel of a polynomial push‑forward of a random integral matrix with concentrated residue, with G. Cheong, Math. Proc. Cambridge Philos. Soc. 178(2) (2025), 229–257. arXiv page
  11. Punctual Quot schemes and Cohen–Lenstra series of the cusp singularity, with Ruofan Jiang. arXiv page, poster
  12. Counting matrix points on certain varieties over finite fields, with Ken Ono and Hasan Saad, Contemp. Math. 818 (2025), 181–195. arXiv page
  13. Lattices in Fq[[T]]^d and spiral shifting operators, with Ruofan Jiang. Adv. Applied Math. 171 (2025), 102950. published version, arXiv preprint
  14. Counting on the variety of modules over the quantum plane, Algebr. Comb. 5(3) (2022), 583–592. pdf, arXiv page, slides, video
  15. Mutually annihilating matrices, and a Cohen–Lenstra series for the nodal singularity, J. Algebra 619 (2023), 26–50. pdf, arXiv page, slides, poster
  16. Continuously Increasing Subsequences of Random Multiset Permutations, with A. Clifton, B. Deb, S. Spiro and S. Yoo, European J. Combin. 110 (2023), 103708. pdf, arXiv page. Also published in Séminaire Lotharingien de Combinatoire 86B (2022) as proceedings of FPSAC 2022. proceedings webpage, extended abstract pdf, poster link
  17. Cohomology of configuration spaces on punctured varieties. pdf, arXiv page, slides
  18. Betti and Hodge numbers of configuration spaces of a punctured elliptic curve from its zeta functions, with G. Cheong, Trans. Amer. Math. Soc. 375(9) (2022), 6363–6383. pdf, arXiv page, slides, video
  19. Unit equations on quaternions, Q. J. Math. 71 (2020), 1521–1534. pdf, published version, arXiv page, slides
  20. Cohen–Lenstra distributions via random matrices over complete discrete valuation rings with finite residue fields, with G. Cheong, Illinois J. Math. 65(2) (2021), 385–415. pdf, published version, arXiv page

Invited Talks (upcoming and past)

Thesis

Topics on Polynomial Equations in Noncommutative Rings and Motivic Aspects of Moduli Spaces. thesis pdf, defense slides, defense video on Youtube

A thesis template (Rackham 2022) based on a Rackham 2021 template developed by Angus Chung and Eamon Quinlan-Gallego, with updates according to the changes of requirements of the Rackham Graduate School in 2022.

Mentoring

  • I am mentoring Kosuke Sato (undergraduate USC) on a project on truncations of flag Cohen–Lenstra measures.
  • I have co-mentored Danny Vargas (undergraduate Harvey Mudd, PhD student Berkeley since Fall 2025) on the paper Dynamical structure of AGM over finite fields with order congruent to 5 mod 8, accepted by Ramanujan journal. arXiv page
  • I was a mentor of a research group in the REU program in Number Theory at the University of Virginia, joint with Hasan Saad (Jun 5–Jul 14, 2023). They published Sato–Tate type distributions for matrix points on elliptic curves and some K3 surfaces, J. Number Theory. published version

Outreach

Contributed Talks (upcoming and past)

This list consists of my talks at local seminars.

Teaching

At USC, I am currently (Fall 2025) teaching Calculus (MATH 118) and Number Theory (MATH 430). I have taught Linear Algebra and Linear Differential Equations (MATH 225) and Applied Combinatorics (MATH 432).

At UBC, I previously taught Differential and Integral Calculus (MATH 100, 101), Linear Algebra (MATH 221), and Multivariable Calculus (MATH 200).

At the University of Michigan, I previously taught MATH 105: Data, Functions and Graphs, MATH 115: Calculus I, MATH 116: Calculus II and EECS 203: Discrete Mathematics.


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