Yifeng Huang

I got my PhD at the Department of Mathematics at the University of Michigan–Ann Arbor in Apr 2022. My thesis advisor is Michael Zieve. I am interested in a variety of concrete problems in algebraic geometry, number theory and combinatorics. I have also worked on arithmetic dynamics. I will move to University of British Columbia, Vancouver in August 2022.

Here is my CV and my research statement.

Photo of Yifeng

  • Email: huangyf αt umich ∂οt edu
  • Office: None
  • Pronunciation: ee-FENG or yee-FENG
  • Pronouns: he/him/his

Thesis

Topics on Polynomial Equations in Noncommutative Rings and Motivic Aspects of Moduli Spaces. thesis pdf, defense slides, defense video (to be expired Aug 2022)

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.

Publications

  1. Counting on the variety of modules over the quantum plane, Algebr. Comb. (2022), to appear. pdf, arXiv page, slides, video
  2. Betti and Hodge numbers of configuration spaces of a punctured elliptic curve from its zeta functions, with G. Cheong, Trans. Amer. Math. Soc. (2022), to appear. pdf, arXiv page, slides, video
  3. Unit equations on quaternions, Q. J. Math. 71 (2020), 1521–1534. pdf, published version, arXiv page
  4. 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

Preprints

  1. Continuously Increasing Subsequences of Random Multiset Permutations, with A. Clifton, B. Deb, S. Spiro and S. Yoo, submitted. pdf, arXiv page
  2. Mutually annihilating matrices, and a Cohen–Lenstra series for the nodal singularity, submitted. pdf, arXiv page, slides
  3. Cohomology of configuration spaces on punctured varieties. pdf, arXiv page, slides

Research Talks (upcoming and past)

Posters

Teaching

I have previously taught MATH 105: Data, Functions and Graphs, MATH 115: Calculus I, MATH 116: Calculus II and EECS 203: Discrete Mathematics.

Non-research writings

  • Handwritten notes on mass formulae predicting the distribution of number field discriminants, following a paper by Manjul Bhargava, for the final presentation of a topic course on arithmetic statistics in Winter 2020. It contains an attempt to explain a subtle mismatch in the quadratic case.
  • Expository notes on quadratic forms and quadratic fields.
  • Notes on elliptic curves with complex multiplication, attempting to fix a gap in Silverman's Advanced Topics in the arithmetic of elliptic curves, Theorem II.4.1.
  • Notes on abelian varieties, written as final projects of the algebraic geometry course in Winter 2016 and the abelian variety course in Fall 2017.
  • Two introductory notes on Chern classes. via Schubert calculus, via differential geometry

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