9321385 Zimmer Zimmer will investigate several questions concerning the actions of semisimple Lie groups and their discrete subgroups on manifolds. This will include the topological, geometric, and analytic features of the spaces on which these groups act, and the corresponding features of the actions themselves. He will also study application of these questions to ergodic theory and differential geometry. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces. ***
