My research is in arithmetic geometry, the branch of mathematics that explores the interplay between number theory and algebraic geometry. I am particularly interested in Galois representations of elliptic curves and, more generally, abelian varieties. Much of my research is grounded in computations, primarily involving Magma, Sage, and the LMFDB.
Preprints and Publications
An Effective Open Image Theorem for Products of Principally Polarized Abelian Varieties
Joint with Tian Wang
Submitted (2022; updated 2023)
On the Effective Version of Serre’s Open Image Theorem
Joint with Tian Wang
Bull. London Math. Soc. Vol. 56 (2024), no. 4, 1399--1416.
Serre Curves Relative to Obstructions Modulo 2
Joint with Rakvi
LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics
Computing Nonsurjective Primes Associated to Galois Representations of Genus 2 Curves
Joint with Barinder Singh Banwait, Armand Brumer, Hyun Jong Kim, Zev Klagsbrun, Padmavathi Srinivasan, and Isabel Vogt
LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics
Rigidity in Elliptic Curve Local-Global Principles
Acta Arith. Vol. 211 (2023), no. 3, 265--288.
A Bound for the Image Conductor of a Principally Polarized Abelian Variety with Open Galois Image
Proc. Amer. Math. Soc. Ser. B Vol. 9 (2022), 272--285.
Joint with Neelima Borade
J. Integer Seq. Vol. 24 (2021), no. 7, Art. 21.7.4, 14 pp.
The Asymptotic Distribution of a Hybrid Arithmetic Function
Joint with Sarah Manski and Nate Zbacnick
Integers Vol. 15 (2015), Paper No. A28, 16 pp.