My research interests lie in the field of arithmetic geometry. Currently I am thinking about arithmetic properties of (supersingular) varieties and Drinfeld modules over finite fields and their moduli spaces, (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 geometry 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.

**18. Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms**, submitted, 2024 (ArXiV), with J. Bergström and S. Marseglia.

**17. Supersingular Ekedahl-Oort strata and Oort's conjecture**, 2024 (ArXiV), with C.-F. Yu.

**16. Uniqueness of indecomposable idempotents in algebras with involution**, submitted, 2024 (ArXiV), with A. Tamagawa and C.-F. Yu.

**15. A survey of local-global methods for Hilbert's tenth problem**, *Women in Numbers Europe IV*, Association for Women in Mathematics Series vol. 32, Springer, Cham, 2024 (ArXiV), with S. Anscombe, Z. Kisakürek, V. Mehmeti, M. Pagano, and L. Paladino.

**14. Isomorphism classes of Drinfeld modules over finite fields**, *Journal of Algebra*, 664, 381-410, 2024 (journal, ArXiV), with J. Katen and M. Papikian.

**13. When is a polarised abelian variety determined by its p-divisible group?**, submitted, 2022 (ArXiV), with T. Ibukiyama and C.-F. Yu.

**12. Polarizations of abelian varieties over finite fields via canonical liftings**, *IMRN*, 2021 (journal, ArXiV), with J. Bergström and S. Marseglia.

**11. Cubic function fields with prescribed ramification**, *International Journal of Number Theory*, 17(9), 2019 - 2053, 2021 (journal, ArXiV), with S. Marques and J. Sijsling.

**10. Mass formula and Oort's conjecture for supersingular abelian threefolds**, *Advances in Mathematics* 386, 107812, 2021 (journal, ArXiV), with F. Yobuko 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.

**7. Dynamical Belyi maps and arboreal Galois groups**, *manuscripta mathematica* 165(1), 1-34, 2021 (journal, ArXiV), 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 (journal, ArXiV), with R. Pries.

**5. Dynamical Belyi maps**, *Women in Numbers Europe 2*, Association for Women in Mathematics Series, Springer, 2018 (volume, 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 (journal, ArXiV).

**3. Large Galois images for Jacobian varieties of genus 3 curves**, *Acta Arithmetica*, 174(4), 339-366, 2016 (journal, 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, 851-871, 2017 (journal, ArXiV), with G. Cornelissen.

**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.

**4. Geometry and arithmetic of moduli spaces of abelian varieties in positive characteristic**, AWS 2024 lecture notes (available here)

**3. Time Management**, AMS Notices article (available here).

**2. Thinking Positive: Arithmetic Geometry in Characteristic p**, AMS Notices article (available here), with R. Bell, J. Hartmann, P. Srinivasan, and I. Vogt.

**1. Reconstruction of function fields**, notes (available here) for an anabelian geometry reading seminar talk at the Courant Institute, New York in Spring 2018.

**2. Women in Numbers Europe IV - Research Directions in Number Theory**, Association for Women in Mathematics Series vol. 32, Springer, Cham, 2024 (Springer website)

**1. Arithmetic, Geometry, Cryptography, and Coding Theory 2021**, Contemporary Mathematics vol. 779, AMS, 2022 (AMS website)

**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.