Abstract: This talk concerns the geometric classification of smooth, locally free, codimension-one actions of higher-rank simple Lie groups $G$ on closed manifolds. Under a natural ergodic assumption, we prove a rigidity theorem giving a sharp dichotomy. Every such action is either:
-Equivariantly diffeomorphic to the suspension of an action of a parabolic subgroup of $G$. -Finitely and equivariantly covered by the standard action on $G/\Gamma\times S^1$, where $\Gamma\leq G$ is a uniform lattice.
This result is in the spirit of the Zimmer program.
