**Title**: Cohomology of smooth abelian group actions and applications of exotic topological groups

**Speaker**: Kurt Vinhage (University of Chicago)

**Abstract**: We will discuss the cohomology of homogeneous partially hyperbolic abelian group actions and recently (re)discovered tools which combine group homology, Lie criteria for topological groups, and some exotic topological groups, namely the free product of Lie groups. We will also discuss how these tools may be used to obtain smooth rigidity results, as well as other possible applications, including in the rank one setting.