Broadly speaking, I am interested in number theory and arithmetic geometry.
I am particularly interested in uniformity problems 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.
- 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
- 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 isogenous to rational -invariant. Proc. Amer. Math. Soc 151 (2023). Journal. 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.