Research

Hilbert’s Tenth Problem and the Inverse Galois Problem (with Francesca Balestrieri and Alexandra Shlapentokh)

Computing endomorphism rings of supersingular elliptic curves and connections to pathfinding in isogeny graphs (with Kirsten Eisentraeger, Sean Hallgren, Christopher Leonardi, and Travis Morrison)

Everywhere local solubility for hypersurfaces in products of projective spaces (with Tom Fisher and Wei Ho)

Cycles in the supersingular -isogeny graph and corresponding endomorphisms (with Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisentraeger, and Travis Morrison)

Effective Chabauty for symmetric powers of curves

A heuristic for boundedness of ranks of elliptic curves (with Bjorn Poonen, John Voight, and Melanie Matchett Wood)

As Easy as : Hilbert’s Tenth Problem for Subrings of the Rationals and Number Fields (with Kirsten Eisentraeger, Russell Miller, and Alexandra Shlapentokh)

Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields (with Lisa Berger, Chris Hall, René Pannekoek, Rachel Pries, Shahed Sharif, Alice Silverberg, and Doug Ulmer)

Insufficiency of the Brauer-Manin obstruction for Enriques surfaces (with Francesca Balestrieri, Jennifer Berg, Michelle Manes, and Bianca Viray)

Faithful realizability of tropical curves (with Man-Wai Cheung, Lorenzo Fantini, and Martin Ulirsch)

Comparing arithmetic intersection formulas for denominators of Igusa class polynomials (with Jacqueline Anderson, Jennifer Balakrishnan, Kristin Lauter, and Bianca Viray)

A universal first order formula defining the ring of integers in a number field