My research interests lie in the fields of arithmetic geometry and algebraic number theory. Currently I am thinking about arithmetic properties of (supersingular) varieties and Drinfeld modules over finite fields, (local-global principles for) rational points on varieties, anabelian geometry, and Galois representations.
Previously I also worked on (dynamical) Belyi maps, adelic algebraic groups, automorphic representations, and Galois representations attached to abelian varieties.
Keywords: Arithmetic of varieties over finite fields, local-global principles, rational points, Galois representations, algebraic groups, anabelian geometry, arithmetic curves, zeta functions, Neukirch-Uchida theory, abelian varieties.
13. The Gauss problem for central leaves (submitted, 2022, ArXiV), with T. Ibukiyama and C.-F. Yu.
9. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (Arithmetic geometry, number theory, and computation, 259-276, Simons Symposia, Springer, 2021, volume, ArXiV), with E. Costa, R. Donepudi, R. Fernando, C. Springer, and M. West.
8. A comparison between obstructions to local-global principles over semiglobal fields (Abelian Varieties and Number Theory, 135-146, Contemporary Mathematics vol. 767, AMS, 2021, volume, ArXiV), with D. Harbater, J. Hartmann, and F. Pop.
1. Galois representations and symplectic Galois groups over Q (Women in Numbers Europe, Association for Women in Mathematics Series, Springer, 2015, volume, ArXiV), with S. Arias-de-Reyna, C. Armana, M. Rebolledo, L. Thomas, and N. Vila.
Hecke algebras, Galois representations, and abelian varieties (available here).
If you would like an updated version with fewer typos/mistakes, please send me an email.
Arithmetic, Geometry, Cryptography, and Coding Theory 2021, Contemporary Mathematics vol. 779, AMS, 2022 (AMS website)
Time Management, AMS Notices article (available here).
Thinking Positive: Arithmetic Geometry in Characteristic p, AMS Notices article (available here), with R. Bell, J. Hartmann, P. Srinivasan, and I. Vogt.
Reconstruction of function fields, notes (available here) for an anabelian geometry reading seminar talk at the Courant Institute, New York in Spring 2018.