Jin Feng from the University of Kansas will give a talk titled: A Hamilton-Jacobi theory for hydrodynamic limits of global action minimizing collective dynamics.

Abstract: We take a variational approach to understand hydrodynamic limit of (global)
action-mininizing Lagrangian collective dynamics, of weakly interacting particles. Through the study of limit theorems on Hamilton-Jacobi equation in space of probability measures, we derive a hydrodynamic limit effective Hamiltonian and the corresponding variational problem. We make extensive use of recent theories of optimal transport, first order analysis in Alexandrov metric spaces (for understanding the PDEs involved), and the hydrodynamic limit effective Hamiltonian and corresponding variational problem as well as the weak KAM theory in finite dimensions (for establishing micro-canonical ensemble).