Parabolic equations and ergodicity

This year's lecture focused on the long-time behavior of solutions to parabolic equations and on the ergodicity of diffusion processes. These issues have been addressed by a large number of authors, especially from the stochastic point of view, and our aim is to establish a general and systematic theory that will enable us to synthesize (and generalize) all previous contributions. In addition, the methods introduced also allow us to tackle non-linear problems.