Group actions on manifolds, rigidity and local rigidity

[MPI-Oberseminar currently in-person only]

One classical approach to study manifolds and groups is studying their interactions. The basic question whether a certain group can act on a certain manifold was looked at, and is the main theme of Zimmer's program. Depending on the context of the manifolds, the class of groups, and the types of actions, many results have been found over the last several decades. The talk will give an overview from old results, even before Zimmer proposed his program, to recent developments. We then focus on some recent local rigidity phenomena discovered in the settings of actions with low regularity.