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 to other areas will be discussed or briefly mentioned. In particular, a solution to an open question on the existence and uniqueness of smooth global-time solutions of a system of nonlinear parabolic equations called cross-diffusion equations will be given.