The main focus of my research is in number theory, group theory, and arithmetic geometry. In particular, I am interested in applying group theory to solve number theoretic questions, with a focus on the study of structures of maximal Galois groups of global fields with restricted ramifications and the relating arithmetic statistics, inverse Galois problem, and Galois cohomology.
The imaginary case of the nonabelian Cohen--Lenstra heuristics, with Ken Willyard
Number fields generated by points in linear systems on curves, with Irmak Balçik, Stephanie Chan, and Bianca Viray
submitted (2025), arXiv:2503.07846
On the distribution of class groups of abelian extensions, with an appendix by Peter Koymans,
submitted (2024), arXiv:2411.19318
On the p-rank of class groups of p-extensions,
International Mathematics Research Notices (2024), no. 6, 5274–5325. arXiv:2212.09888
Non-abelian Cohen--Lenstra Heuristics in the presence of roots of unity,
submitted (2022), arXiv:2202.09471
Tamely ramified covers of the projective line with alternating and symmetric monodromy, with Renee Bell, Jeremy Booher, and William Chen,
Algebra & Number Theory 16 (2022), no. 2, 393-446. arXiv: 2007.12299
Presentations of Galois groups of maximal extensions with restricted ramification,
Algebra & Number Theory, to appear, arXiv: 2005.07329
Generalized Bockstein maps and Massey products, with Yeuk Hay Joshua Lam, Romyar Sharifi, Preston Wake and Jiuya Wang,
Forum Math. Sigma 11 (2023), Paper No. e5, 41 pp. arXiv: 2004.11510
A predicted distribution for Galois groups of maximal unramified extensions, with Melanie Matchett Wood and David Zureick-Brown,
Inventiones Mathematicae, 237(2024), no.1, 49-116. arXiv: 1907.05002
The realizability problem with prescribed inertia conditions,
thesis (2019), part of it is available at arXiv: 1705.03184
On the level of modular curves that give rise to isolated j-invariant, with Abbey Bourdon, Özlem Ejder, Frances Odumodu, and Bianca Viray
Advances in Mathematics, 357 (2019), 106824, 33 pp. arXiv: 1808.04520
The free group on n generators modulo n+u random relations as n goes to infinity, with Melanie Matchett Wood
Journal für die reine und angewandte Mathematik (Crelle), 762 (2020), 123-166. arXiv: 1708.08509