Partially Hyperbolic Actions of Semisimple Lie Groups

Zimmer proposed the study of higher-rank semisimple group actions in the 1980's after showing certain rigidity results, especially about associated cocycles in the measurable category. In this talk, I will describe recent progress towards classifying such actions in the presence of uniformly expanding and contracting directions. Joint work with D. Damjanovic, R. Spatzier and D. Xu.