Rigidity in Dynamics and Geometry Contributions from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences Cambridge, United Kingdom, 5 January – 7 July 2000

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan­ uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.

Quasi-Conformal Geometry and Hyperbolic Geometry.- On and Around the Bounded Cohomology of SL2.- Densité d’orbites d’actions de groupes linéaires et propriétés d’équidistribution de marches aléatoires.- Exceptional Sets in Dynamical Systems and Diophantine Approximation.- An Introduction to Cocycle Super-Rigidity.- Rigid Geometric Structures and Representations of Fundamental Groups.- Coarse-Geometric Perspective on Negatively Curved Manifolds and Groups.- On Orbit Equivalence of Measure Preserving Actions.- The Margulis Invariant of Isometric Actions on Minkowski (2+l)-Space.- Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group.- Appendix: Diophantine Approximation on Hyperbolic Surfaces.- Bounded Cohomology, Boundary Maps, and Rigidity of Representations into Homeo+(S1) and SU(1, n).- SAT Actions and Ergodic Properties of the Horosphere Foliation.- Nonexpanding Maps, Busemann Functions, and Multiplicative Ergodic Theory.- The Phase Space of k-Surfaces.- Schottky Subgroups of Mapping Class Groups and the Geometry of Surface-by-Free Groups.- Actions of Semisimple Lie Groups with Stationary Measure.- On the Cohomology of Anosov Actions.- Harmonic Analysis and Hecke Operators.- Lp-Cohomology and Pinching.- Classical and Non-Linearity Properties of Kac-Moody Lattices.- Actions of Maximal Tori on Homogeneous Spaces.- Dynamics on Parameter Spaces: Submanifold and Fractal Subset Questions.- Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups.- Square Tiled Surfaces and Teichmüller Volumes of the Moduli Spaces of Abelian Differentials.- On Property (T) for Discrete Groups.