Tuesday, September 30, 2014, 4:00 p.m., Samantha Xu (University of Illinois - Urbana-Champaign) Invariant Gibbs Measures and Hamiltonian PDEs Abstract: Liouville's Theorem says that the flow of a Hamiltonian ODE preserves Lebesgue measure, and a corresponding Gibbs measure as well. This notion can be generalized to infinite dimensional systems for various Hamiltonian PDEs. In this talk, we will discuss the role of randomization on initial datum, methods of constructing an invariant Gibbs measure, and some recent results.