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.
9. The Ekedahl-Oort and Newton stratification of the GU(3,2) Shimura variety, preprint, 2025. Joint with Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson and Sandra Nair. (ArXiV)
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 in the GU(q-2,2) Shimura variety, preprint, 2024 (adapted significantly in 2025). 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)