Yu Deng

A Clay Research Award is made to Yu Deng (Chicago) and Zaher Hani (Michigan) in recognition of their remarkable derivation of the Boltzmann equation for long times, starting from a system of hard spheres. 

The question of deriving macroscopic laws rigorously from microscopic models goes back at least to Hilbert’s 6th problem stated in 1900, and remains a deep and essentially unsolved problem in mathematical physics. Yu Deng and Zaher Hani, together with their co-author Xiao Ma, have solved part of the problem by deriving the Boltzmann equation describing intermediate, mesoscopic scales, starting from a microscopic system of hard spheres, for large times which may even diverge with the number of particles, as long as the regular solution of the equation exists.

The result involves an exceptional mastery in combinatorics and in designing algorithms in extremely intricate models, and is a breakthrough in the field, 50 years after Lanford’s seminal result for short times, and more than 150 years after Boltzmann’s long-debated theory.