In the last years, there has been important progress in the mathematical understanding of effective theories for interacting quantum gases and classical fluids. Notable examples are Gross-Pitaevskii theory for Bose-Einstein condensates, and the Boltzmann equation for rarefied gases. With respect to the fundamental microscopic laws of motion, effective theories involve a much smaller number of degrees of freedom and are usually nonlinear, due to an averaging mechanism taking place at a mesoscopic/macroscopic scale. From the point of view of physics, the emergent nonlinearity is often responsible for interesting collective phenomena, turbulence in fluids being one of the most striking. The workshop will focus on the analysis of effective evolution equations for many particle systems, with a particular emphasis on the emergence of turbulence from nonlinear dynamics, and on the rigorous derivation of effective theories starting from the fundamental laws of microscopic motion.
Application for this event is currently open.