Abstract: Over many decades fully nonlinear PDEs, especially the Monge-Ampere equation played a central role in the study of complex manifolds. Most previous works focused on problems that can be expressed as equations involving real (1, 1) forms. As many important questions, especially those involving higher cohomology classes, in algebraic and complex geometry involve real (p; p) forms for p > 1, we develop a nonlinear PDE theory involving (p,p) forms on Hermitian manifolds. In this talk, I will discuss the basic setup and explain some of the main challenges in working with such equations. The existence of solutions is shown for a large class of these equations. This is a joint work with Bo Guan.