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

I am particularly interested in uniformity questions for torsion groups of elliptic curves and abelian varieties. I am also interested in Galois representations of elliptic curves, as well as sporadic points on modular curves.

Here are slides (~20 minutes) for a recent talk on my results for bounds on torsion groups from geometric isogeny classes of elliptic curves. Here are slides (~50 minutes) for an earlier version of my talk.

Preprints

9. Polynomial bounds on torsion from a fixed geometric isogeny class. Submitted. Copy.
10. Growth of torsion groups of elliptic curves upon base change from number fields. Submitted. Copy.

Accepted and/or Published

7. Typically bounding torsion on elliptic curves isogenous to rational -invariant. Accepted to Proc. Amer. Math. Soc. Copy.
8. Computational study of non-unitary partitions, with A. P. Akande, Summer Haag, Maurice D. Hendon, Neelima Pulagam, Robert Schneider and Andrew. V. Sills. Accepted to J. Ramanujan Math. Soc. Copy.
9. Typically bounding torsion on elliptic curves with rational -invariant. J. Number Theory 238 (2022). Journal. Copy.
10. 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 .
11. Chevalley-Warning at the boundary, with Pete L. Clark and Frederick Saia. Expo. Math. 39 (2021). Journal. Copy.
12. 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.
13. 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. Copy.

Here is my github.