My research lies at the intersection of arithmetic dynamics and arithmetic geometry, two fields concerned with the interplay between algebraic structures and number theory. Arithmetic dynamics extends ideas from classical Diophantine geometry to the iteration of rational maps. Just as Diophantine geometry studies rational points on curves and higher-dimensional varieties, arithmetic dynamics studies orbit structures of dynamical systems defined over number fields and function fields.
Much of my work is motivated by dynamical analogues of central conjectures in arithmetic geometry, such as the Torsion Conjecture and Lehmer’s problem, in the setting of polynomial and rational maps. I study problems related to canonical heights, the distribution of preperiodic points, and the growth of iterated Galois groups. These problems connect to broader conjectures in number theory, including the abc-Conjecture, and often require blending arithmetic methods with techniques from complex dynamics and algebraic geometry.
I am also interested in the arithmetic of abelian varieties, particularly height bounds and torsion phenomena. A recurring theme in my work is the pursuit of effective and/or uniform statements: not only proving that certain arithmetic phenomena occur finitely often, but also establishing uniform bounds that reveal the underlying arithmetic structure of dynamical systems.
