Speaker: Professor Philip Gressman

Abstract:  I will attempt to give a brief overview of a family of fundamental questions in harmonic analysis which include Radon-like operators and Fourier restriction. In both cases, these can be understood as natural operators (both linear and multilinear) that can be associated to submanifolds of Euclidean space. The underlying problem from a harmonic analysis perspective is to determine which standard function spaces best capture the properties of these operators. Recently a host of ideas from other areas of mathematics have been shown to be useful in approaching this problem, and in this talk I hope to give a few concrete examples both of operators of interest and of interesting ideas from other branches of mathematics which have proved to be useful in this setting.