Speaker: Yu Deng (University of Chicago)

Title: The Hilbert sixth problem: particle and waves

Abstract:

A major component of the Hilbert sixth problem concerns the derivation of macroscopic equations of motion, and the associated kinetic equations, from microscopic first principles. In the classical setting of Boltzmann's kinetic theory, this corresponds to the derivation of the Boltzmann equation from particle systems governed by Newtonian dynamics; in the theory of wave turbulence, this corresponds to the derivation of the wave kinetic equation from nonlinear dispersive equations.

In this talk we present recent joint works with Zaher Hani and Xiao Ma, where we consider the hard sphere model in the particle setting, and the cubic nonlinear Schrödinger equation in the wave setting. In both cases we derive the corresponding kinetic equation up to arbitrarily long times, as long as the solution to this kinetic equation exists. This is a key step towards the resolution of the Hilbert sixth problem.

*Pre-reception held in 2-290 at 3:30pm. Note the exceptional date, time, and location