I mainly work in the areas of arithmetic dynamics, diophantine geometry, and algebraic number theory. I'm interested in both theoretical and computational aspects of these subjects; in fact most of my work is a blend of theory and computation. At present I'm mostly focused on finding a way to prove certain special cases of a uniform boundedness conjecture in dynamics.
With Nicole Sutherland. Submitted.
An implementation of the main algorithm is included in Magma via the intrinsic function HilbertIrreducibilityCurves.