Ralf Spatzier will carry out research on the interface of geometry and dynamical systems. A central theme of this project is the study of rigidity. He will study rigidity properties of spaces of nonpositive curvature and actions of semisimple groups and their lattices. This involves problems from geometry as well as ergodic theory and group theory. The problems fall into three categories: spaces of higher rank, rank one manifolds and rigidity of group actions.
