Title: Ergodic results for the stochastic nonlinear damped Schroedinger equation

Abstract: We study the nonlinear stochastic Schrödinger equation with linear damping. We prove the existence of invariant measures in the case of two dimensional compact Riemannian manifolds without boundary and compact smooth domains of R^2 with either Dirichlet or Neumann boundary conditions. We prove the uniqueness of the invariant measure in R^d, d=2,3 when the damping coefficient is sufficiently large.

The talk is based on joint works with B. Ferrario and Z. Brzeźniak.