Aaron Brown University of Chicago I will present the proof due to myself, D. Fisher, and S. Hurtado that (for n >= 3) every action of a cocompact lattice in Sl(n,R) on an (n-2)-dimensional manifold factors through the action of a finite group. If time, I will explain some modifications that are needed for actions by lattices in other higher-rank, R-split, simple Lie groups.