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.

** 11. Cubic function fields with prescribed ramification** (submitted, 2020, ArXiV), with S. Marques and J. Sijsling.

** 10. Mass formula and Oort's conjecture for supersingular abelian threefolds** (submitted, 2020, ArXiV), with F. Yobuko and C.-F. Yu.

** 9. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves** (submitted, 2020, 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** (to appear in *Abelian Varieties and Number Theory*, Contemporary Mathematics, AMS, ArXiV), with D. Harbater, J. Hartmann, and F. Pop.

** 7. Dynamical Belyi maps and arboreal Galois groups** (*Manuscripta Mathematica* (2020), pdf), with I. Bouw and O. Ejder.

** 6. Fully maximal and fully minimal abelian varieties** (*Journal of Pure and Applied Algebra*, 223(7), 3031-3056, 2019, ArXiV), with R. Pries.

**5. Dynamical Belyi maps** (*Women in Numbers Europe 2*, Association for Women in Mathematics Series, Springer, 2018, ArXiV), with J. Anderson, I. Bouw, O. Ejder, N. Girgin, and M. Manes.

**4. Hecke algebras for GLn over local fields** (*Archiv der Mathematik*, 107(4), 341-353, 2016, ArXiV).

**3. Large Galois images for Jacobian varieties of genus 3 curves** (*Acta Arithmetica*, 174(4), 339-366, 2016, ArXiV), with S. Arias-de-Reyna, C. Armana, M. Rebolledo, L. Thomas, and N. Vila.

**2. Hecke algebra isomorphisms and adelic points on algebraic groups** (*Documenta Mathematica* 22 (2017), 851--871, 2017, pdf), with G. Cornelissen.

**1. Galois representations and symplectic Galois groups over Q** (*Women in Numbers Europe*, Association for Women in Mathematics Series, Springer, 2015, 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.

**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.