The award will support a project that explores computational aspects of the Langlands program, a grand unifying framework - akin to the Standard Model in particle physics - that incorporates much of the progress in number theory as in the late 20th century, The Langlands program is not always completely precise in its predictions, however.
To address that shortcoming, Kedlaya will be leading a research program to develop new computational infrastructure for making and testing precise predictions in the context of the Langlands program at the Institute for Computational and Experimental Rearsarch in Mathematics in fall 2015. One guiding example will be the relationship between elliptic curves and modular forms which went into the proof of Fermat's Last Theorem in the 1990s, Kedlaya says.
Some of Kedlaya's earlier research was on the topic of counting solutions of certain polynomial equations, in a setting relevant to cryptographic systems based on elliptic curves. This project uses some of those ideas again, but for a new purpose, he says. "Some of the insight gained by interacting with computer scientists is thus being plowed back into pure mathematics."
—UC San Diego