It was announced on March 22 2011 that Jonathan Pila is to receive a Clay Research Award 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.
The award will be presented at the 2011 Clay Research Conference, to be held May 16-17 at Harvard University in Science Center Lecture Hall A.