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.
Papers:
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,
submitted (2020), 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 to appear, 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