My main research interests lie in the areas of arithmetic dynamics and algebraic number theory. Generally speaking, arithmetic dynamics is the study of the dynamics of rational maps defined over fields of arithmetic interest, like number fields and p-adic fields. Much of my work has involved studying properties of certain algebraic curves known as dynamical modular curves, which parametrize maps together with points exhibiting certain behaviors under iteration by those maps. I'm also interested in rational dynamics on the Berkovich projective line.
