Title:  Matrix weights, the convex-set valued maximal operator, and Rubio de Francia extrapolation

Abstract:  In this series of talks (I project three), I want to talk about the theory of matrix weights:  its history and motivation, and some recent results by myself, Kabe Moen, and others.  The ultimate goal is to give an overview of my work with Marcin Bownik on a proof of Rubio de Francia extrapolation for matrix weights.  The proof requires the introduction of completely new techniques involving convex-set valued functions and the corresponding maximal operator.   No prior knowledge of matrix weights will be assumed, though some familiarity with scalar weighted norm inequalities will be helpful.   I hope to conclude the talks with some open problems.