Actions of non-abelian groups and measure rigidity

Abstract: Measure rigidity theorems (especially Ratner’s theorem) have played a big role in dynamics, with many applications outside the field. Traditionally problems of this type have
been considered in the context of homogeneous dynamics and other systems with a lot of structure. In this talk I will discuss a circle of ideas which suggests that, under some conditions, some measure rigidity theorems may hold for general smooth actions of non- abelian groups.