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 Tata Institute of Fundamental Research 1998; 386 pp; hardcover ISBN-10: 81-7319-235-9 ISBN-13: 978-81-7319-235-7 List Price: US$40 Member Price: US$32 Order Code: TIFR/1 This volume presents the proceedings from an international colloquium on Lie groups and ergodic theory held at the Tata Institute of Fundamental Research (TIFR) in Mumbai, India. Designated a Golden Jubilee event at the Institute, this was one of the quadrennial colloquia of the School of Mathematics. There were 24 talks given by participants in Lie groups, ergodic theory and related fields. Leading mathematicians from around the world attended. Recent developments were presented and a session was devoted to discussion and problems for future research. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. Readership Graduate students and research mathematicians working in topological groups, Lie groups, and related fields. Table of Contents M. Babillot and F. Ledrappier -- Geodesic paths and horocycle flow on Abelian covers J. R. Choksi and M. G. Nadkarni -- On the question of transformations with simple Lebesgue spectrum S. G. Dani and C. R. E. Raja -- Asymptotics of measures under group automorphisms and an application to factor sets A. Eskin and B. Farb -- Quasi-flats in $$\mathbb{H}^2\times\mathbb{H}^2$$ H. Furstenberg -- Stiffness of group actions D. Y. Kleinbock -- Bounded orbits conjecture and diophantine approximation A. Lubotzky and R. J. Zimmer -- A canonical arithmetic quotient for simple Lie group actions S. Mozes -- On the congruence subgroup problem for tree lattices H. Oh -- Arithmetic properties of some Zariski dense discrete subgroups M. Ratner -- On the $$p$$-adic and $$S$$-arithmetic generalizations of Raghunathan's conjectures K. Schmidt -- On the cohomology of algebraic $$\mathbb{Z}^d$$-actions with values in compact Lie groups N. A. Shah -- Invariant measures and orbit closures on homogeneous spaces Y. Shalom -- Random ergodic theorems, invariant means and unitary representation G. A. Soifer -- Structure of infinite index maximal subgroups of $${\mathrm SL}_n(Z)$$ A. N. Starkov -- Dynamics of non-unipotent homogeneous flows W. A. Veech -- Geometric realizations of hyperelliptic curves, II D. Witte -- Cocycle superrigidity for ergodic actions of non-semi-simple Lie groups