Most of my research concerns curves and abelian varieties in positive characteristic. A leading question is the following: if C is a (smooth) 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.
6. The p-rank stratification of the moduli space of double covers of a fixed elliptic curve (joint with Dusan Dragutinovic, Yuxin Lin, Natalia Pacheco-Tallaj and Deepesh Singhal), preprint.
5. Ekedahl-Oort strata and the supersingular locus in the GU(q-2,2) Shimura variety (joint with Emerald Anne, Deewang Bhamidipati, Maria Fox, Heidi Goodson and Sandra Nair), preprint.
4. a-numbers of cyclic degree p^2 covers of the projective line (joint with Huy Dang), preprint.
3. Powers of the Cartier Operator on Artin-Schreier Covers, published in International Journal of Number Theory.
2. Doubly Isogenous Genus-2 Curves with D4-Action, (joint with Vishal Arul, Jeremy Booher, Everett Howe, Wanlin Li, Vlad Matei, Rachel Pries and Caleb Springer), published in Mathematics of Computation.
1. A parametrized set of explicit elements of Ш(E/Q), (joint with Jaap Top), published in Integers.
p-Torsion of Abelian Varieties in Characteristic p, 2023, PhD thesis at the University of Warwick, supervised by Damiano Testa.
Descent by a Rational 3-Isogeny on Elliptic Curves, 2019, MSc thesis at the University of Groningen, supervised by Jaap Top.
Matijasevic’s Theorem: Diophantine descriptions of recursively enumerable sets, 2017, BSc thesis at the University of Groningen, supervised by Jaap Top.