I am interested in all sorts of problems in combinatorics and adjacent fields. Many of my recent projects have concerned arithmetic combinatorics and combinatorial number theory. I am also active in extremal and probabilistic combinatorics; dynamic algebraic combinatorics; and classical analysis.
All of my papers are available on the arXiv (but journal versions may be more up to date).
2025:
"The distribution of prime values of random polynomials" (with Katy Woo and Max Xu). Arxiv.
"Quantitative pyjama" (with James Leng). Arxiv.
"Statistics of Erdős-Rényi random numerical semigroups" (with Santiago Morales and Carl Schildkraut). Arxiv.
"On Graham's rearrangement conjecture over 𝔽₂ⁿ" (with Benjamin Bedert, Matija Bucic, Richard Montgomery, and Alp Müyesser). Arxiv.
"Finer control on relative sizes of iterated sumsets" (with Jacob Fox and Shengtong Zhang). Arxiv.
"Simultaneous generating sets for flags" (with Chayim Lowen and Federico Glaudo). Arxiv.
"The structure of Lonely Runner spectra" (with Vikram Giri). Arxiv.
2024:
"Relative sizes of iterated sumsets". Arxiv.
"Relative Lonely Runner Spectra" (with Vanshika Jain). Arxiv.
"Graham's rearrangement conjecture beyond the rectification barrier" (with Benjamin Bedert). ArXiv.
"Corners with polynomial side length" (with Borys Kuca and James Leng). ArXiv.
"Quantitative concatenation for polynomial box norms" (with Borys Kuca and James Leng). ArXiv.
"Rearranging small sets for distinct partial sums". ArXiv.
"Rainbow stackings of random edge-colorings" (with Noga Alon and Colin Defant). ArXiv.
"Bender-Knuth billiards in Coxeter groups" (with Grant Barkley, Colin Defant, Eliot Hodges, and Mitchell Lee). ArXiv.
2023:
"Ordering candidates via vantage points" (with Noga Alon, Colin Defant, and Daniel Zhu). ArXiv.
"Hermite-Hadamard inequalities for nearly-spherical domains" (with Mitchell Lee), unpublished note. ArXiv.
"Reconstructing a set from its subset sums: the 2-torsion-free case" (with Federico Glaudo). ArXiv.
"The Ungar games (with Colin Defant and Nathan Williams). ArXiv.
2022:
"Foot-sorting for socks" (with Colin Defant), The Electronic Journal of Combinatorics 31.3, #P3.5. ArXiv. Journal.
"Logarithmically larger deletion codes of all distances" (with Noga Alon, Gabriela Bourla, Ben Graham, and Xiaoyu He), IEEE Information Theory 70.1, p. 125-130. ArXiv. Journal.
"Extensions of hitomezashi patterns (with Colin Defant and Bridget Tenner), Discrete Mathematics 346.10, #113555. ArXiv. Journal.
"Counting dope matrices (with Noga Alon and Kevin O'Bryant), Journal of Algebra 620, p. 502-518. ArXiv. Journal.
"Loops and regions in Hitomezashi patterns" (with Colin Defant), Discrete Mathematics 347.1, #113693. ArXiv. Journal.
2021:
"The runsort permuton" (with Noga Alon and Colin Defant), Advances in Applied Mathematics 139. ArXiv. Journal.
2020:
"Typical and extremal aspects of friends-and-strangers graphs" (with Noga Alon and Colin Defant), Journal of Combinatorial Theory, Series B 158, p. 3-42. ArXiv. Journal.
"Friends and strangers walking on graphs" (with Colin Defant), Combinatorial Theory 1.6. ArXiv. Journal.
"The smoothest average: Dirichlet, Fejer, and Chebyshev" (with Stefan Steinerberger), Bulletin of the London Mathematical Society 53.6, p. 1801-1815. ArXiv. Journal.
"Inverse problems for minimal complements and maximal supplements" (with Noga Alon and Matt Larson), Journal of Number Theory 223, p. 307-324. ArXiv. Journal.
"Promotion sorting" (with Colin Defant), Order 40, p. 199-316. ArXiv. Journal.
"Generalized difference sets and autocorrelation integrals", Acta Arithmetica 199, p. 199-219. ArXiv. Journal.
2019:
"Barely lonely runners and very lonely runners: a refined approach to the Lonely Runner Problem", Combinatorial Theory 1.17. Based on my Yale College senior thesis (under the direction of Stefan Steinerberger). ArXiv. Journal.
"Supertrees" (with Colin Defant and Ashwin Sah), The Electronic Journal of Combinatorics 27.2 #P2.7. ArXiv. Journal.
"Linear extension numbers of n-element posets" (with Ashwin Sah), Order 38.1, p. 49-66 . ArXiv. Journal.
"The largest (k,l)-sum-free sets in compact abelian groups", Integers 20, #A57. ArXiv. Journal.
2018:
"Stack-sorting for words" (with Colin Defant), Australasian Journal of Combinatorics 77.1, p. 51-68. ArXiv. Journal.
"A stronger connection between the Erdos-Burgess and Davenport constants" (with Ashwin Sah), Journal of Number Theory 210, p. 373-388. ArXiv. Journal.
"On the number of simultaneous core partitions with d-distinct parts", Discrete Mathematics 342.12, #111592. ArXiv. Journal.
"Harborth constants for certain classes of metacyclic groups", Discrete Mathematics 342.5, p. 1492-1509. ArXiv. Journal.
"Refining the two-dimensional signed small ball inequality", Journal of Fourier Analysis and Applications 25.4, p. 1921-1926. ArXiv. Journal.
2017:
"Ulam sequences and Ulam sets" (with Stefan Steinerberger), Integers 18, #A80. ArXiv. Journal.
"Targeted High-School Math Competitions: Girls in Math at Yale" (with Elaine Hou), Early Career Series in the Notices of the American Mathematical Society (2020). Magazine.
Yale College senior thesis in Near Eastern Languages and Civilizations (under the direction of Kevin van Bladel): "The Eleventh-Century Number Theory of 'Abd al-Qahir al-Baghdadi's Completion of Reckoning" (2020). PDF.
"Bridging the Gap: A Survey of Arabic Mathematics in the Middle Ages" (2018). PDF.