My research is in number theory and algebraic geometry. More specifically, I am interested in rational points and explicit methods in arithmetic geometry.

Publications

1. Local heights on hyperelliptic curves and quadratic Chabauty (with L. Alexander Betts, Juanita Duque-Rosero, and Pim Spelier), arXiv:2401.05228.
2. Towards a classification of isolated j-invariants (with Abbey Bourdon, Timo Keller, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, and Himanshu Shukla, and an appendix by Maarten Derickx and Mark van Hoeij), to appear in Mathematics of Computation.
3. Self-dual matroids from canonical curves (with Alheydis Geiger, Bernd Sturmfels, and Raluca Vlad), to appear in Experimental Mathematics.
4. Geometric quadratic Chabauty and p-adic heights (with Juanita Duque-Rosero and Pim Spelier), Special Issue in Honor of B. Edixhoven, Expositiones Mathematicae, 41, (2023), no. 3, 631–674.
5. Quadratic Chabauty and p-adic Gross-Zagier, Transactions of the American Mathematical Society, 376, (2023), no. 5, 3725-3760.
6. A geometric linear Chabauty comparison theorem (with Pim Spelier), Acta Arithmetica 202 (2022), no. 1, 67–88. 11G30 (11D45).
7. A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold (with Katrina Honigs, Alicia Lamarche, and Isabel Vogt, and an appendix by Nicolas Addington), Research in Number Theory 8 (2022), no. 1, Paper No. 12.
8. 38406501359372282063949 & all that: Monodromy of Fano Problems (with Borys Kadets), International Mathematics Research Notices (2020), rnaa275.
9. Chabauty-Coleman computations on rank 1 Picard curves (with Travis Morrison), Arithmetic Geometry, Number Theory, and Computation, Simons Symposia, Springer, 2021, 485-506.
10. Computing rational points on rank 0 genus 3 hyperelliptic curves (with María Inés de Frutos-Fernández), Arithmetic Geometry, Number Theory, and Computation, Simons Symposia, Springer, 2021, 449-460.

Here are some expository notes on the geometric quadratic Chabauty theory of Edixhoven and Lido.