Speaker
Description
Wave kinetic theory, also known as wave turbulence theory, is the kinetic description of systems with an asymptotically large number of weakly interacting waves. It is the wave analog of Boltzmann’s kinetic theory for particle systems, and plays a fundamental role in various fields of science. Over the last five years, in collaboration with Yu Deng (Chicago), we have developed a robust paradigm that put this theory on solid mathematical foundations, including the rigorous derivation of the corresponding kinetic equation, known as the "wave kinetic equation" (WKE). This culminated with providing a long time derivation of that equation, covering the full life span of its solutions. The latter result was the first of its kind, be it for particle or wave systems, and it provided the strategy to resolve the classical problem of deriving Boltzmann’s equation on long time intervals (done recently with Yu Deng and Xiao Ma). The aim of this minicourse is to give an overview of this progress.
