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.
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, accepted for publication in Women in Numbers Europe 4, Association for Women in Mathematics Series, Springer (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.
Arithmetic, Geometry, Cryptography, and Coding Theory 2021, Contemporary Mathematics vol. 779, AMS, 2022 (AMS website)
Hecke algebras, Galois representations, and abelian varieties (available here).
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