The focus will be on the interaction of experts in diverse directions working on nonlinear partial differential equations, and other applied sciences. Our primary goal is to expose a limited number of postdoctoral fellows and advanced graduate students to current problems associated with nonlinear partial differential equations, and to highlight some of the recent mathematical advances in Navier-Stokes equations, nonlinear diffusion and kinetic equations, Einstein vacuum equations, De Giorgi conjecture, spikes and higher dimensional concentration phenomena, reaction-diffusion systems and localized behavior in mathematical biology, etc.