Workshop on Pattern Formation

The focus of the workshop was to present latest results and open problems related to partial differential equation models (PDE) whose solutions exhibit complex spatio-temporal dynamics. A fundamental technique to understand these dynamics is to identify essential features which act as the basic building blocks of the solution to the PDE. Using these basic components, a complex PDE system can often be effectively described by a finite dimensional dynamical system of interacting particles. This reduced system of coupled ordinary differential equations (ODEs) is usually more amenable for the study of the existence, stability and dynamics of the different configurations supported by the system. This procedure is continually used with great success in many physical systems. The workshop focussed on bringing together researchers who use these finite dimensional reductions in a wide range of areas of application, including the study of vortex dynamics in Bose-Einstein condensates, in models of swarming behavior, and in the study of  first passage time problems in the presence of localized traps.