"Ergodicity in infinite dimensions:
Degenerately forced Stochastic Partial Differential equations" Jonathan Mattingly, Duke University I will discuss a body of work which has emerged over the last number of year to treat the ergodic theory of one class of Markov processes on infinite dimensional phase spaces. In particular, I will discuss the idea of an Asymptotically Strong Feller Diffusion. Using some estimates from Malliavin calculus, we can apply the results to a class of dissipative partial differential equations forced by only a few brownian motions. This class includes the 2D Navier-Stokes equation and reaction diffusion equations. This is an inherently nonlinear phenomenon which uses the nonlinearity to move the randomness about phase space. I will also describe how the theory give spectral gaps in a Wasserstein metric for the Markov semigroups. The discussion will center on phenomenon which are infinite dimensional in nature.