Higher rank lattices, for instance, SLnZ with n greater than 2, are expected to be rigid in many cases. In this talk, we will discuss about actions on manifolds by higher rank lattices under the dynamical assumption (existence of positive (topological) entropy element). We will focus on, how, under certain assumptions, one can obtain information about the action group. We will also see that how one can obtain ‘’homogeneous'' structure of the manifold from the dynamics.
The talk is based on a joint work with Aaron Brown.