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**

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

**Accepted and/or Published**

**Typically bounding torsion on elliptic curves isogenous to rational -invariant.**Accepted to*Proc. Amer. Math. Soc.*Copy.**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.**Typically bounding torsion on elliptic curves with rational -invariant.***J. Number Theory*238 (2022). Journal. Copy.**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 .

**Chevalley-Warning at the boundary****,**with Pete L. Clark and Frederick Saia.*Expo. Math.*39 (2021). Journal. Copy.**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.**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.