4/19/2005

Alexander Gorodnik
Caltech

Ergodic theory of semisimple lattices

Consider a measure-preserving action of a lattice (in semisimple Lie group) on a probability measure space. For such actions, we prove strong maximal inequality, mean and pointwise ergodic theorems. For lattices satisfying property (T), we get ergodic theorems with exponential rate of convergence. In the case of algebraic lattice actions that preserve finite measure, we show that all dense orbits are equidistributed. Our methods can be also applied to some infinite volume homogeneous spaces. This is joint work with Amos Nevo and Barak Weiss.