Title: Cotlar’s Inequality Abstract: We will go over Cotlar’s classic inequality concerning the maximal truncation operator of a Calderon-Zygmund operator.  We will also cover some recent results for operators that satisfy a stronger Cotlar inequality.

Abstract:  In this talk I will give an over-view of the Stieltjes integral and  review some of the many definitions that appear in the literature.  I will talk about the strengths and weaknesses of each, particularly in relationship to the classical Darboux and Riemann integrals.  I will conclude with a discussion of a new definition

Title: Calderon-Zygmund theory for nonlinear partial differential equations and applications Abstract: In this talk, we will discuss several recent developments on regularity theory estimates in Sobolev spaces for solutions of several classes of elliptic and parabolic nonlinear PDEs. Some classes of considered equations may be singular and degenerate. Important ideas and techniques will be highlighted. Connections and applications of the results