Math
I was a graduate student in mathematics at MIT (advised by Henry Cohn and Yufei Zhao), so I often think about math. The kinds of math I like best are
- visual: with drawing, pictures, or things to play around with;
- surprising: where different areas of math collide; and
- accessible: I can explain it to most anyone.
The specific area I research is called combinatorial, discrete, and convex geometry, which is all about patterns and structure of geometric objects. It checks all the boxes: I can explain the problems to other people (even if they aren't a mathematician), but the solutions are surprising and satisfying, often relying on connections to other fields of math, such as graph theory, probability, topology, linear algebra, and optimization. As you can see in the picture, I am occasionally a serious mathematician. (But not too often.)
Papers
My papers can be found in reverse-chronological order on the arXiv.
Discrete and convex geometry
- At most 10 cylinders mutually touch: a Ramsey-theoretic approach (with J. Koizumi and S. Luo), submitted (2025).
- Quantitative selection theorems, submitted (2025).
- Fixed-strength spherical designs. SIAM Journal on Discrete Mathematics 40 (2026): 789-815. [arXiv]
- Closed curve covering and multiagent TSP ratios (with A. Dumitrescu). Utilitas Mathematica <126> (2026): 297-304. [arXiv]
- Hollow polytopes with many vertices (with S. Arun), to appear in Contributions to Discrete Mathematics.
- Improved Helly numbers of product sets (with S. Arun), to appear in Contributions to Discrete Mathematics.
- The prime grid contains aribitrarily large empty polygons. Advances in Geometry 25 (2025): 403-407. [arXiv]
- Piercing intersecting convex sets (with I. Bárány, D. Pálvölgyi, D. Varga). Linear Algebra and Its Applications 710 (2025): 405-417. [arXiv]
- Explicit bounds for the layer number of the grid (with N. Varadarajan), preprint (2023).
- A mélange of diameter Helly-type theorems (with P. Soberón). SIAM Journal on Discrete Mathematics 35 (2021): 1615–1627. [arXiv]
- Discrete quantitative Helly-type theorems with boxes. Advances in Applied Mathematics 129 (2021): 102217. [arXiv]
Combinatorics
- Exponential multivalued forbidden configurations (with A. Sali). Discrete Mathematics & Theoretical Computer Science 23 (2021).
- An inverse problem for the collapsing sum. Australasian Journal of Combinatorics 79 (2021): 183–192.
- A combinatorial interpretation of Gaussian blur. Minnesota Journal of Undergraduate Mathematics 5 (2020).
Dynamical systems
- Dynamics and entropy of S-graph shifts. Discrete and Continuous Dynamical Systems 42 (2022): 5637–5663. [arXiv]
Number theory
- An average of generalized Dedekind sums (with S. Gaston). Journal of Number Theory 212 (2020): 323–338. [arXiv]
Expository notes
- An introduction to graph limits. One-semester course on dense graph limits at the advanced senior undergraduate level.
- Survey of enumerative combinatorics. Notes from a one-semester topics course taught by Alex Postnikov.
- Algebraic topology. Notes from a one-semester course.
- Rational choice theory. A quick tour through some aspects of the theories of social choice and games.
- Proof of G.E. Andrew's theorem that the number of vertices in a lattice polytope \(P\) in \(\mathbb{R}^d\) is at most \(O_d\big(\operatorname{Vol}(P)^{\frac{d-1}{d+1}})\).
Book
- For my undergraduate thesis, I wrote a book whose goal is to share the experience of doing mathematics with a general audience. It isn't yet publicly available (contact me if you can help me make that happen!), but you can view an excerpt here.