I am an arithmetic geometer, which means that I study problems in number theory through the lens of algebraic geometry. Most recently, I have been interested in problems relating to rational points on curves, Galois representations attached to elliptic curves, and densities of primes for which families of elliptic curves have certain arithmetic properties over finite fields. I am also interested in making undergraduate mathematics research more accessible.
Publications and Preprints
Density of Primes for Isomorphic Group Structures in Isogeny Classes of Elliptic Curves, with John Cullinan and Nathan Kaplan. In preparation.
Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny. Submitted.
Rational Points on a Family of Genus 3 Hyperelliptic Curves. Journal of Number Theory, Volume 286, 2026, Pages 67-90.
The Probability of Non-Isomorphic Group Structures of Isogenous Elliptic Curves in Finite Field Extensions, II, with J. Cullinan, S. Dobson, L. Frey, A. Hamakiotes, N. Kaplan, J. Mello, G. Scullard. Journal of Number Theory, Volume 266, 2025, Pages 131-165.
Online Talks
Rational Points on a Family of Genus 3 Hyperelliptic Curves, Lathisms Lecture Series: Café con Leche.