Jonathan Pila

The 2011 Clay Research Award has been made to Jonathan Pila for his resolution of the André-Oort Conjecture in the case of products of modular curves.

This work gives the first unconditional proof of fundamental cases of these general conjectures beyond the original theorem of André concerning the product of two such curves. The foundational techniques that Pila developed to achieve this breakthrough range from results in real analytic geometry, which give sharp upper bounds for the number of rational points of bounded height on certain analytic sets, to the use of O-minimal structures in mathematical logic.