Recent progress in the Zimmer program

Abstract

This paper can be viewed as a sequel to the author's long survey on the Zimmer program \cite{F11} published in 2011. The sequel focuses on recent rapid progress on certain aspects of the program particularly concerning rigidity of Anosov actions and Zimmer's conjecture that there are no actions in low dimensions. Some emphasis is put on the surprising connections between these two different sets of developments and also on the key connections and ideas for future research that arise from these works taken together.