Multiscale interacting particle systems

In this talk we will consider SDE systems that are multiscale in time, in the regime of interest for stochastic averaging theory. When applying averaging methods a key assumption is that the dynamics for the fast scale is ergodic, i.e. that it has a unique equilibrium (invariant measure). If the fast scale has multiple invariant measures (which is a rather common occurrence in many scenarios, for example for McKean-Vlasov SDEs) then truly very little is known. In particular both averaging and homogenization theory are currently not very equipped to help tackle this problem. In this talk we will present situations in which this scenario occurs, with particular reference to multiscale interacting particle systems, summarise recent progress and point out gaps in current theory.