Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

In this talk, I will discuss about smooth higher rank lattice actions on manifolds with positive entropy. From dynamical information, we can detect information on groups and manifolds. For instance, when lattices in $SL(n,\mathbb R)$ act on an n-dimensional manifold with positive entropy, we can see that the lattice is abstractly commensurable with $SL(n,\mathbb Z)$.

This is joint work with Aaron Brown.