Most of my research concerns curves and abelian varieties in positive characteristic. A leading question is the following: if C is a (specified type of) curve in characteristic p, then what are the possibilities for its p-torsion group scheme Jac(C)[p]? In other words, how does the (open) Torelli locus intersect the Ekedahl-Oort stratification? Of particular interest to me are Artin-Schreier covers, which admit an automorphism of degree p.
A related research direction I'm interested in is the interaction between the Ekedahl-Oort stratification and the Newton stratification on Shimura varieties of PEL type. There are many interesting unanswered questions in this area, for instance which Ekedahl-Oort strata of certain unitary Shimura varieties intersect the supersingular locus.
I am also interested in arithmetic statistics and rational points on curves in characteristic 0.
8. Traverso's isogeny conjecture for some unitary p-divisible groups, preprint, 2025. Joint with Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson and Sandra Nair. (ArXiV)
7. Heuristics for (ir)reducibility of p-rank strata of the moduli space of hyperelliptic curves, preprint, 2025. Joint with Thomas Bouchet, Erik Davis, Zachary Porat and Benjamin York. (ArXiV)
6. The p-rank stratification of the moduli space of double covers of a fixed elliptic curve, preprint, 2025. Joint with Kevin Chang, Dusan Dragutinovic, Yuxin Lin, Natalia Pacheco-Tallaj and Deepesh Singhal. (ArXiV)
5. Ekedahl-Oort strata and the supersingular locus in the GU(q-2,2) Shimura variety, preprint, 2024. Joint with Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson and Sandra Nair. (ArXiV)
4. a-Numbers of cyclic degree p^2 covers of the projective line , Journal of Number Theory, 279, 78-116, 2026. Joint with Huy Dang. (Journal ) (ArXiV)
3. Powers of the Cartier Operator on Artin-Schreier covers, International Journal of Number Theory, 20(7), 1901-1941, 2024. (Journal) (ArXiV)
2. Doubly isogenous genus-2 curves with D4-action, Mathematics of Computation, 93, 347-381, 2024. Joint with Vishal Arul, Jeremy Booher, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries and Caleb Springer. (Journal) (ArXiV)
1. A parametrized set of explicit elements of Ш(E/Q), Integers, 22(A108), 2022. Joint with Jaap Top. (Journal) (ArXiV)
p-Torsion of Abelian Varieties in Characteristic p, 2023, PhD thesis at the University of Warwick, supervised by Damiano Testa. (Link)
Descent by a Rational 3-Isogeny on Elliptic Curves, 2019, MSc thesis at the University of Groningen, supervised by Jaap Top. (Link)
Matijasevic’s Theorem: Diophantine descriptions of recursively enumerable sets, 2017, BSc thesis at the University of Groningen, supervised by Jaap Top. (Link)