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.
- Counting on the variety of modules over the quantum plane, Algebr. Comb. (2022), to appear. pdf, arXiv page, slides, video
- 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
- Unit equations on quaternions, Q. J. Math. 71 (2020), 1521–1534. pdf, published version, arXiv page
- 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
- Continuously Increasing Subsequences of Random Multiset Permutations, with A. Clifton, B. Deb, S. Spiro and S. Yoo, submitted. pdf, arXiv page
- Mutually annihilating matrices, and a Cohen–Lenstra series for the nodal singularity, submitted. pdf, arXiv page, slides
- Cohomology of configuration spaces on punctured varieties. pdf, arXiv page, slides
Research Talks (upcoming and past)
- Graduate Algebra and Representation Theory Seminar, Rutgers University (May 2, 2022)
- NYC Noncommutative Geometry Seminar, St Johns University - New York City (Dec 1, 2021)
- RTG Seminar on Number Theory, University of Michigan (Sep 27, 2021)
- Graduate Online Combinatorics Colloquium (GOCC), virtual (May 12, 2021)
- Graduate Student Combinatorics Conference (GSCC 2021), virtual (Apr 25, 2021)
- Algebra Seminar, University of Waterloo (Nov 25, 2020)
- Discrete Mathematics Seminar, University of British Columbia (Nov 24, 2020)
- Algebra and Algebraic Geometry Seminar, University of British Columbia (Nov 06, 2020).
- Student Combinatorics, University of Michigan (Sep 29, 2020).
- Rutgers Algebra Seminar, Rutgers University (Sep 23, 2020).
- UMN Combinatorics and Commutative Algebra Seminar, University of Minnesota (Sep 18, 2020).
- RTG Seminar on Number Theory, University of Michigan (Jul 29, 2020).
- 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