Yifeng Huang

Last modified on Oct 6, 2026

I am currently a Postdoctoral Research/Teaching Fellow at Emory. I am on the tenure-track job market as of Fall 2026.

I was an Assistant Professor (RTPC) at University of Southern California (2024-2026) and a Postdoctoral Research Fellow at the University of British Columbia (2022-2024).

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.

Photo of Yifeng

  • Email: yifeng.huang αt emory ∂οt edu
    My previous email yifeng.huang@usc.edu is discontinued.
  • Office: MSC E425
  • Pronunciation: ee-FENG or yee-FENG
  • Pronouns: he/him/his

Preprints and Publications

  1. Flag Quot and Coh zeta functions, with Ruofan Jiang, Contemp. Math., accepted.
  2. Rogers–Ramanujan identities from the geometry of X^a=Y^b, with Kenny Lau and Ken Ono. arXiv page, submitted.
  3. Quot scheme of points on torus knot singularities, with Ruofan Jiang and Alexei Oblomkov. arXiv page
  4. Algebraic geometric framework of Rogers–Ramanujan identities, with Kenny Lau, Ken Ono, and Peter Paule, submitted. arXiv page
  5. A quadratic form generalization of rational dinv, Res. Math. Sci. 13 (2026), Article 44. arXiv page, slides
  6. Multiple Rogers–Ramanujan type identities for inert quadratic orders, with Shane Chern, submitted. arXiv page
  7. Matrix points on varieties, with Asvin G, Ruofan Jiang, and Yifan Wei, submitted. arXiv page
  8. Cohen–Lenstra flag universality for random matrix products, with Hoi Nguyen and Roger Van Peski, submitted. arXiv page, slides
  9. Coh zeta functions for inert quadratic orders, submitted. arXiv page, slides
  10. Hilbert Series for Configuration Spaces of Punctured Surfaces, with Eric Ramos, submitted. arXiv page.
  11. Low degree subvarieties of universal hypersurfaces, with Borys Kadets and Olivier Martin, J. Reine Angew. Math. 2026(833) (2026), 317–337. arXiv page.
  12. A Mordell–Lang type problem for GLm, with J. Bell and D. Ghioca, Bull. Aust. Math. Soc. 111(3) (2025), 433–444. published version
  13. Cokernels of random matrix products and flag Cohen–Lenstra heuristic, Forum Math. 37(5) (2025), 1325–1332. arXiv page
  14. Commuting matrices via commuting endomorphisms, Linear Algebra Appl., accepted. pdf, arXiv page
  15. A non-abelian variant of the classical Mordell-Lang conjecture, with Dragos Ghioca, Manuscripta Math. 176, Paper No. 71 (2025). pdf
  16. 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
  17. 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
  18. Punctual Quot schemes and Cohen–Lenstra series of the cusp singularity, with Ruofan Jiang. arXiv page, poster
  19. Counting matrix points on certain varieties over finite fields, with Ken Ono and Hasan Saad, Contemp. Math. 818 (2025), 181–195. arXiv page
  20. Lattices in Fq[[T]]^d and spiral shifting operators, with Ruofan Jiang. Adv. in Appl. Math. 171 (2025), 102950. published version, arXiv preprint
  21. Counting on the variety of modules over the quantum plane, Algebr. Comb. 5(3) (2022), 583–592. pdf, arXiv page, slides, video
  22. Mutually annihilating matrices, and a Cohen–Lenstra series for the nodal singularity, J. Algebra 619 (2023), 26–50. pdf, arXiv page, slides, poster
  23. 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
  24. From the Greene–Wu Convolution to Gradient Estimation over Riemannian Manifolds, with Tianyu Wang and Didong Li. arXiv page
  25. Cohomology of configuration spaces on punctured varieties. pdf, arXiv page, slides
  26. 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
  27. Unit equations on quaternions, Q. J. Math. 71 (2020), 1521–1534. pdf, published version, arXiv page, slides
  28. 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

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.

Teaching

At Emory, I am currently (Fall 2026) teaching Linear Algebra (MATH 221).

At USC, I have taught Calculus (MATH 118), Linear Algebra and Linear Differential Equations (MATH 225), Number Theory (MATH 430), 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.

Mentoring

  • I was a Postdoctoral Mentor in the Caltech SURF program (2026).
  • I mentored Kosuke Sato (undergraduate USC) through MATH 490 (Directed Reading) in Spring 2025 and continue to mentor his project on truncations of flag Cohen–Lenstra measures.
  • I have co-advised Danny Vargas (undergraduate Harvey Mudd, PhD student Berkeley since Fall 2025) on the undergraduate thesis and the paper Dynamical structure of AGM over finite fields with order congruent to 5 mod 8, Ramanujan J. published version
  • 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

Organizing

Outreach

Invited Talks (upcoming and past)

  • Algebra & Number Theory Seminar, Louisiana State University (Oct 27, 2026)
  • AMS Fall Southeastern Sectional, Special Session on Representation Theory with Applications in Geometry, Algebra and Mathematical Physics, Kennesaw State University (Oct 11, 2026)
  • AMS Fall Southeastern Sectional, Special Session on Connections between q-Series, Partitions and Modular Forms, Kennesaw State University (Oct 11, 2026)
  • SIAM Annual Meeting (AN26), Minisymposium on Special Functions with Applications in Number Theory and Combinatorics, Cleveland (Jul 2026)
  • Mini-course on Cohen-Lenstra-type heuristics for random matrices, Ohio State (May 2026)
  • Mathematics Colloquium, California State University, Northridge (May 4, 2026)
  • AMS Spring Eastern Sectional, Special Session on Configuration Spaces and Applications, Boston College (Mar 2026)
  • AMS Fall Virtual Eastern Sectional, Special Session on Representations of p-adic Groups and Noncommutative Geometry (Oct 25, 2025)
  • Number Theory Seminar, UC Irvine (Oct 9, 2025)
  • The Third Joint SIAM/CAIMS Annual Meetings (AN25), Special Session on Hypergeometric Series and Their Applications, Montréal (Aug 1, 2025)
  • Algebra and Geometry Seminar, HKUST (Jun 18, 2025)
  • Algebra Seminar, UCSD (Mar 10, 2025)
  • (20 minute talk) AMS Joint Mathematics Meeting, Special Session on Quaternions, Seattle (Jan 2025)
  • Valley Geometry Seminar, UMass Amherst (Oct 11, 2024)
  • ANTC Seminar, Claremont McKenna (Oct 8, 2024)
  • Algebra Seminar, Virginia Tech (Nov 10, 2023)
  • Combinatorics Seminar, UCSD (Oct 10, 2023)
  • (8 min lightning talk) Southern California Number Theory Day, UC Irvine (Oct 7, 2023)
  • Algebraic Geometry Seminar, UCSD (Oct 6, 2023)
  • Algebra and Algebraic Geometry Seminar, University of Washington (Apr 18, 2023)
  • Number Theory and Algebraic Geometry Seminar, Simon Fraser University (Mar 2, 2023)
  • Algebra Seminar, Virginia Tech (Feb 24, 2023)
  • (20 min talk) AMS Joint Mathematics Meeting, Special Session on Quaternions, Boston (Jan 4-6, 2023)
  • (20 min talk) AMS Joint Mathematics Meeting, Special Session on the Combinatorics and Geometry of Jordan Type and Lefschetz Properties, Boston (Jan 4-6, 2023)
  • Algebra Seminar, Virginia Tech (Nov 15, 2022)
  • Algebra Seminar, University of Virginia (Nov 9, 2022)
  • (20 min talk) AMS Eastern Sectional Meeting, Special Session on Young Voices in Combinatorics, Amherst (Oct 1-2, 2022)
  • Number Theory Seminar, University of California, Irvine (Sep 27, 2022)
  • Combinatorics Seminar, University of Southern California (Sep 26, 2022)
  • Graduate Algebra and Representation Theory Seminar, Rutgers University (May 2, 2022)
  • NYC Noncommutative Geometry Seminar, St Johns University - New York City (Dec 1, 2021)
  • Algebra Seminar, University of Waterloo (Nov 25, 2020)
  • Discrete Mathematics Seminar, UBC (Nov 24, 2020)
  • Algebra and Algebraic Geometry Seminar, UBC (Nov 06, 2020).
  • Rutgers Algebra Seminar, Rutgers University (Sep 23, 2020).
  • UMN Combinatorics and Commutative Algebra Seminar, University of Minnesota (Sep 18, 2020).

Contributed Talks to local seminars

  • Combinatorics Seminar, USC (May 6, 2026)
  • Combinatorics Seminar, USC (Nov 10, 2025)
  • Topology Seminar, USC (Oct 20, 2025)
  • USC/Caltech Joint Algebra and Geometry Seminar, Caltech (Oct 2, 2025)
  • Algebra Seminar, USC (Sep 8, 2025)
  • Number Theory Seminar, Caltech (Mar 6, 2025)
  • Combinatorics Seminar, USC (Sep 23, 2024)
  • Algebraic Geometry Seminar, UBC (Nov 6, 2023)
  • Number Theory Seminar, UBC (Sep 14, 2023)
  • Discrete Mathematics Seminar, UBC (Jan 17, 2023)
  • Algebraic Geometry Seminar, UBC (Jan 16, 2023)
  • Number Theory Seminar, UBC (Nov 30, 2022)
  • RTG Seminar on Number Theory, University of Michigan (Sep 27, 2021)
  • RTG Seminar on Number Theory, University of Michigan (Jul 29, 2020).

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