Title: Connections between commutators and weighted inequalities

Abstract: I will cover the Cauchy integral approach to the boundedness of commutators of Calderon-Zygmund operators and BMO functions.  I spoke about this approach and proved the basic commutator theorem of Coifman-Rochberg-Weiss in the fall of 2017.  In this talk I will go over some powerful extensions and a new converse to the theorem.