Discrete Groups in Geometry and Analysis: Papers in Honor of G.D. Mostow on His Sixtieth Birthday

Description

In this volume commemorating the 60th birthday of G.D. Mostow, distinguished authors survey the important role discrete groups currently play in geometry and analysis. The dramatic phenomena first brought to light by Mostow's Strong Rigidity Theorem form the theme of three of the six papers. R. Zimmer discusses superrigidity for cocycles and its import for discrete group actions on manifolds; Y.-T. Siu surveys results on strong rigidity of Kahler manifolds; and J. Millson develops ideas of Thurston to construct and describe examples of groups (of infinite covolume!), acting on hyperbolic space, that have non-trivial deformations. The key role discrete groups play in algebraic geometry as the fundamental groups of moduli spaces is the premise of P. Deligne's article, which establishes very general theorems for the monodromy actions of such groups. J. Igusa and M. Mostow consider problems in analysis suggested by groups: Igusa's problem in distribution theory stems from the Siegel-Weil Formula, while Mostow's problem on function division is motivated by gauge field theory. The papers provide substantial discussions and show the vitality of this active area of current research. TABLE OF CONTENTS 1. Un Theoreme de Finitude Pour la Monodromie, 1 par P. Deligne. 2. Some Aspects of the Arithmetic Theory of Polynomials, 20 by Jun-ichi Igusa. 3. Deformation Spaces Associated to Compact Hyperbolic Manifolds, 48 by Dennis Johnson and John Millson. 4. On Division of Functions, Solution of Matrix Equations, and Problems in Differential Geometry and Physics, 107 by Mark Alan Mostow. 5. Strong Rigidity for Kahler Manifolds and the Construction 124 of Bounded Holomorphic Functions, by Yum-Tong Siu. 6. Lattices in Semisimple Groups and Invariant Geometric 152 Structures on Compact Manifolds, by Robert J. Zimmer.