Recent Developments in Calderon-Zygmund theory

Abstract: The famous $A_2$ conjecture about the linear growth of the $A_2$ characteristic constant $[w]_{A_2}$ in weighted norm inequalities for Calder \'{o}n-Zygmund operators has been resolved recently  by T. Hytonen. It took considerable amount of time and efforts of a rather large group of mathematicians in order to have a better understanding of the problem. In the first part of the talk we will discuss various works in this direction and would highlight the most relevant papers in the context. Then, we would introduce the notion of multi-frequency Calder\'{o}n-Zygmund operators and discuss the proof of $A_2$ conjecture in this context with the sharp dependence of the operator norm on the number of frequencies involved. (This is a joint work with Dr. Senthil Raani K S).