Reductions, constraints and generalizations on KP systems

In this talk, we will review a series of our studies on all kinds of reductions, constraints and generalizations on the Kadomtsev-Petviashvili (KP) hierarchy, including Gelfand-Dickey hierarchy, constrained KP hierarchy, B type KP hiearchy, C type KP hierarchy, universal character hierarchies, noncommutative KP type integrable systems, multicomponent KP type integrable systems, dispersionless KP type integrable systems, discrete KP type integrable hierarchies, supersymmetric KP type hierarchies and so on. These studies contains their symmetries, Darboux transformations, tau functions and so on.