Broadly speaking, I am interested in number theory and arithmetic geometry.

I am particularly interested in uniformity results for torsion groups and Galois representations of elliptic curves. I am also interested in sporadic points on modular curves.

Here are slides for my 2026 JMM talk.

Preprints

15. The possible adelic indices for elliptic curves admitting a rational cyclic isogeny, with Kate Finnerty, Jacob Mayle and Rakvi. arXiv.
16. Uniform bounds on the level of cyclotomic division fields of elliptic curves, with Sam Allen. arXiv.
17. Counting points on some genus zero Shimura curves, with Tristan Philips, Frederick Saia, Tim Santens and John Yin. arXiv.
18. A uniform bound on the smallest surjective prime of an elliptic curve, with Jacob Mayle and Jeremy Rouse. arXiv. Code.

Accepted and/or Published

11. Uniform polynomial bounds on torsion from rational geometric isogeny classes, with Abbey Bourdon. Accepted to Math. Res. Lett. arXiv.
    Here are slides from a 20-minute talk, and here are slides from a 50-minute talk talk. Here are slides from a 5-minute talk.
12. New isogenies of elliptic curves over number fields. Int. J. Number Theory 21 (2025). Journal. arXiv.
    • Here are slides from a talk for an older version (~20 minutes).
13. Polynomial bounds on torsion from a fixed geometric isogeny class of elliptic curves. J. Théor. Nombres Bordeaux 36 (2024). Journal. arXiv.
14. Growth of torsion groups of elliptic curves upon base change from number fields. Ramanujan J. 63 (2024). Journal. arXiv.
    • Here are slides from a talk (~20 minutes).
15. Computational study of non-unitary partitions, with A. P. Akande, Summer Haag, Maurice D. Hendon, Neelima Pulagam, Robert Schneider and Andrew. V. Sills. J. Ramanujan Math. Soc. 38 (2023). Journal. arXiv.
16. Typically bounding torsion on elliptic curves isogenous to rational -invariant. Proc. Amer. Math. Soc 151 (2023). Journal. arXiv.
17. Typically bounding torsion on elliptic curves with rational -invariant. J. Number Theory 238 (2022). Journal. arXiv.
18. The least degree of a CM point on a modular curve, with Pete L. Clark, Paul Pollack and Frederick Saia. J. Lond. Math. Soc. (2) 105 (2022). Journal. Copy.
    • Least CM degrees & code. For example, here are 1,000,000 least degrees for CM points on the modular curves .
19. Chevalley-Warning at the boundary, with Pete L. Clark and Frederick Saia. Expo. Math. 39 (2021). Journal. Copy.
20. Faltings heights of CM elliptic curves and special gamma values, with Adrian Barquero-Sanchez, Lindsay Cadwallader, Olivia Cannon and Riad Masri. Res. Number Theory 3 (2017). Journal. Copy.
21. The density of primes dividing a particular non-linear recurrence sequence, with Alexi Block Gorman, Heesu Hwang, Noam Kantor, Sarah Parsons and Jeremy Rouse. Acta Arith. 175 (2016).  Journal. arXiv.

Here is my github.