Larry Guth: Decoupling Theorems in Fourier Analysis

Abstract: In the last few years, Jean Bourgain and Ciprian Demeter have proven a variety of striking ``decoupling'' theorems in Fourier analysis.  I think this is an important development in the subject.  I don't know any applications to the theory of computation, but there are applications in partial differential equations and in number theory.  I will explain what decoupling theorems say and why I think they're important, I'll sketch an application in number theory, and I'll give a detailed sketch of the proof of the simplest decoupling theorem.