a1 Mathematical Sciences Research Institute, 2223 Fulton Street, Berkeley, CA 94720, USA
A conference on the interaction of ergodic theory, differential geometry and the theory of Lie Groups was held at the Mathematical Sciences Research Institute from May 24 to June 1, 1984. This is a report of the problem session organized by A. Katok and R. Zimmer and held on May 25, 1984 dealing with the topics in the title. Another problem session was centred on the rigidity of manifolds of non-positive curvature and related topics concerning their geodesic flows. This is reported on by K. Burns and A. Karok separately .
(Received December 26 1984)
(Revised February 15 1984)