Research
Research Interests
Algebraic Number Theory and Arithmetic Geometry, with a focus on elliptic curves, modular curves, and Galois representations attached to abelian varieties.
Publications
ℓ-primary Torsion in Elliptic Curves over ℚWith Álvaro Lozano-Robledo and Enrique González-Jiménez.
In preparation
Classification of Isogeny-Torsion Graphs in Quadratic FieldsWith Rakvi.
In preparation
Elliptic Curve Rank Growth in Multi-Quadratic ExtensionsWith Álvaro Lozano-Robledo. Preprint: arXiv:2610.31925
Preprint, October 2026
An Elliptic Curve of Rank ≥ 34 and Root Number −1 over a Quadratic FieldWith Álvaro Lozano-Robledo. Preprint: hexagon:2610.00280
Preprint, October 2026
More About My Research
Background & Introduction to Elliptic Curves
An introduction to elliptic curves, from the basic definitions onward.
Motivating Questions
The questions behind my past and current research projects.
Applications of Research
Where elliptic curves show up: cryptography, isogeny-based post-quantum schemes, Fermat’s Last Theorem, and even string theory.
A full list of my talks is on my CV, and software built around my research is on the Projects page.