[2] His dissertation was entitled "Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields".

This work began with an early paper with Enrico Bombieri, and developed through collaborations with Alex Wilkie and Umberto Zannier.

The techniques obtained have led to advances in Diophantine problems, including Pila's unconditional proof of the André–Oort conjecture for powers of the modular curve.

The approach he and his collaborators have developed, which combines analytic ideas with model theory, is entirely new and shows great promise for further applications.

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