Research Interests

I am interested in number theory and algebraic geometry. So far I have worked on research topics related to abelian varieties over global or local fields, to consequences of the Birch and Swinnerton-Dyer conjecture, to the arithmetic of (elliptic, hyperelliptic, and modular) curves, and to integer dynamics.

Publications and Preprints

On a conjecture of Agashe. Trans. Amer. Math. Soc. 374 (2021), 7143-7160. ArXiv version.

Integer dynamics, with D. Lorenzini, A. Suresh, M. Suwama, and H. Wang. Int. J. Number Theory 18 (2022), no. 2, 397–415. ArXiv version.

Purely additive reduction of abelian varieties with torsion. J. Number Theory 239 (2022), 21–39. Arxiv version.

Tamagawa numbers of elliptic curves with torsion points. Arch. Math. (Basel) 119 (2022), no. 2, 155–165. ArXiv version.

A divisibility related to the Birch and Swinnerton-Dyer conjecture. J. Number Theory 245 (2023), 150–168. ArXiv version.

Torsion and twists of abelian varieties. Bull. London Math. Soc. 56 (2024), no 2, 589-601. ArXiv version.

Universal quadratic forms and Dedekind zeta functions, with V. Kala. Int. J. Number Theory 20 (2024), no. 7, 1833-1847. ArXiv version.

Reduction and isogenies of elliptic curves. Acta Arith. 215, No. 2, 179–192 (2024). ArXiv version.

Reduction types of CM curves. Pacific J. Math. 329-2 (2024), 233-257. ArXiv version.

An analogue of a conjecture of Rasmussen and Tamagawa for abelian varieties over function fields. Indag. Math. (N.S.) 35 (2024), no. 6, 1270–1281. ArXiv version.

Low rank specializations of elliptic surfaces. To appear in Bull. Aust. Math. Soc. ArXiv version.

Talks and expositions/notes

Here is a video of me giving a talk at the Shafarevich Seminar of the Steklov Mathematical Institute.

Here is a video of me giving a talk at the PAlmetto Joint Arithmetic, Modularity, and Analysis Series (PAJAMAS) conference.

Here are some notes I typed up while reading the paper “Degenerate fibers and stable reduction of curves” by M. Artin and G. Winters. I haven't edited them in a long time so please use at your own risk.

Here are my notes for a talk I gave at UGA following the paper "O-minimality and the André-Oort conjecture for C^n" by J. Pila. Beware of typos.