Yifeng Huang

Last modified on Feb 22, 2024

I am currently a postdoctoral fellow at the University of British Columbia. My mentors are Jim Bryan, Kalle Karu and Zinovy Reichstein. I will move to the University of Southern California in Aug 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 as of Nov 2023.

Photo of Yifeng

  • Email: huangyf αt math dot ubc ∂οt ca
  • Office: MATH 209
  • Pronunciation: ee-FENG or yee-FENG
  • Pronouns: he/him/his

Seminars

Preprints and Publications

  1. Commuting matrices via commuting endomorphisms, submitted. pdf
  2. A non-abelian variant of the classical Mordell-Lang conjecture, with Dragos Ghioca. submitted. pdf
  3. Generating series for torsion-free bundles over singular curves: rationality, duality and modularity, with Ruofan Jiang. pdf, arXiv page, slides in algebraic geometry, number theory, combinatorics
  4. The cokernel of a polynomial push-forward of a random integral matrix with concentrated residue, with G. Cheong. arXiv page
  5. Punctual Quot schemes and Cohen–Lenstra series of the cusp singularity, with Ruofan Jiang. arXiv page, poster
  6. Counting matrix points on certain varieties over finite fields, with Ken Ono and Hasan Saad, Contemp. Math., Amer. Math. Soc., accepted. arXiv page
  7. Spiral shifting operators from the enumeration of finite-index submodules of Fq[[T]]^d, with Ruofan Jiang. pdf, arXiv page
  8. Counting on the variety of modules over the quantum plane, Algebr. Comb. 5(3) (2022), 583–592. pdf, arXiv page, slides, video
  9. Mutually annihilating matrices, and a Cohen–Lenstra series for the nodal singularity, J. Algebra 619 (2023), 26–50. pdf, arXiv page, slides, poster
  10. 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
  11. Cohomology of configuration spaces on punctured varieties. pdf, arXiv page, slides
  12. 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
  13. Unit equations on quaternions, Q. J. Math. 71 (2020), 1521–1534. pdf, published version, arXiv page, slides
  14. 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 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). The paper by the undergraduate mentees has been submitted for publication. Come to JMM 2024 to listen to their talk!

Outreach

Contributed Talks (upcoming and past)

I often speak in seminars of several research groups at my own school.

Teaching

I am currently (Fall 2023) teaching matrix algebra (MATH 221) at UBC. If you are a student, check the Canvas page.

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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