This volume is a collection of papers related to lectures delivered in an international colloquium held at the Tata Institute of Fundamental Research, Mumbai, in January 1996. The colloquium, which was designated a Golden Jubilee event of the Institute, was aimed at bringing into focus various recent developments in ergodic theory, related to Lie groups and discrete subgroups. Experts from all over the world spoke at the meeting, on different aspects of the topic.

Geodesic Paths and Horocycle Flow on Abelian Covers / On the Question of Transformations with Simple Lebesgue / Asymptotics of Measures under Group Automorphisms and an Application to Factor Sets / Quasi-flats in H2 x H2 Stiffness of Group Actions / Bounded Orbits Conjecture and Diophantine Approximation / A Canonical Arithmetic Quotient for Simple Lie Group Actions / On the Congruence Subgroup Problem for Tree Lattices / Arithmetic Properties of Some Zariski Dense Discrete Subgroups / On the p-adic and S-arithmetic Generalizations of Raghunathan’s Conjectures / On the Cohomology of Algebraic Zd-actions with Values in Compact Lie Groups / Invariant Measures and Orbit Closures on Homogeneous Spaces / Random Ergodic Theorems, Invariant Means and Unitary Representation / Structure of Infinite Index Maximal Subgroups of SLn (Z) / Dynamics of Non-unipotent Homogeneous Flows / Geometric Realizations of Hyperelliptic Curves, II / Cocylcle Superrigidity for Ergodic Actions of Non-semi-simple Lie Groups.

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