Research

My broad research interests are number theory, arithmetic geometry, and algebraic geometry.

My specific research interests are rational points on varieties, non-Archimedean geometry, hyperbolicity, explicit methods in arithmetic geometry, Galois representations associated to elliptic curves, and p-adic Hodge theory.

Preprints:

18. Connections between K-Stability and Vojta's Conjecture (with Yueqiao Wu), arXiv (submitted)

17. Boundedness of hyperbolic varieties, arXiv (submitted)

16. The conjugate uniformization via 1-motives (with Sean Howe and Peter Wear), arXiv (submitted)

15. Non-Archimedean entire curves in projective varieties dominating an elliptic curve, arXiv (submitted)

14. Irrational points on hyperelliptic curves (with Joseph Gunther) arXiv, video (submitted)

Publications

13. Integral points on varieties with infinite étale fundamental group (with Niven Achenjang)

International Mathematics Research Notices (arXiv, journal)

12. Towards a classification of entanglements of Galois representations attached to elliptic curves (with Harris B. Daniels and Álvaro Lozano-Robledo)

Revista Matemática Iberoamericana 39 (2023), no. 3, 803–844 (arXiv, code, journal)

11. Ramification of p-power torsion points of formal groups (with Adrian Iovita and Alexandru Zaharescu)

Annales mathématiques du Québec (2023) (arXiv, journal)

10. A non-Archimedean analogue of Campana's notion of special (with Giovanni Rosso)

Algebraic Geometry 10 (3) (2023) 262--297 (arXiv, journal)

9. On p-adic uniformization for abelian varieties with good reduction (with Adrian Iovita and Alexandru Zaharescu)

Compositio Mathematica (2022), 158(7), 1449-1476 (arXiv, journal)

8. A group theoretic perspective on entanglements of division fields (with Harris B. Daniels)

Transcations of the AMS, Series B, (9), 827 - 858 (arXiv, code, journal)

7. Sporadic Cubic Torsion (with Maarten Derickx, Anastassia Etropolski, Mark van Hoeij, and David Zureick-Brown)

Algebra and Number Theory (2021) vol. 15, no. 7, pp. 1837–1864 (arXiv, journal, code, video)

6. Non-Archimedean entire curves in closed subvarieties of semi-abelian varieties

Mathematische Annalen (2021) 379, 1003–1010 (arXiv, journal)

5. Composite images of Galois for elliptic curves over Q & Entanglement fields

Mathematics of Computation (2019) vol. 88, no. 319, pp. 2389–2421 (arXiv, journal, code)

4. Chip-firing groups of iterated cones (with Morgan V. Brown and David Zureick-Brown)

Linear Algebra and its Applications (2018) vol. 556, pp. 46–54 (arXiv, journal)

3. The twisting Sato--Tate group of the curve y^2 = x^8 - 14x^4 + 1 (with Sonny Arora, Victoria Cantoral-Farfán, Aaron Landesman, and Davide Lombardo)

Math Z. (2018) vol. 290, issue 3-4, pp. 991-1022 (arXiv, journal)

2. Selmer groups of twists of elliptic curves over K with K-rational torsion points

Research in Number Theory (2016), no. 1, vol. 2 (arXiv, journal, code)

1. On the least prime congruent to 1 modulo n

Involve, A Journal of Mathematics (2015), no. 8, pp. 357-359 (PDF, journal)