Starting from the foundations, the author presents an almost entirely self-contained treatment
of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which …

In this paper and its companion [31], we introduce new techniques and results in an attempt
to extend rigidity theory beyond the scope of linear groups. Amongst our main tools is the …

LET M be a compact manifold of negative curvature. In [7], R. Spatzier studies the ergodic
theoretic properties of the action of xl (M) on the geometric boundary of the universal cover …

This paper is a survey on the Zimmer program. In its broadest form, this program seeks an
understanding of actions of large groups on compact manifolds. The goals of this survey are …

The author obtains some classification result for the mapping class groups of compact
orientable surfaces in terms of measure equivalence. In particular, the mapping class groups …

Let G denote a semisimple group, Γ a discrete subgroup, B= G/P the Poisson boundary.
Regarding invariants of discrete subgroups we prove, in particular, the following:(1) For any …

We prove amenability for a broad class of equivalence relations which have trees
associated to the equivalence classes. The proof makes crucial use of percolation on trees …

We study the properties of rigid geometric structures and their relation with those of finite
type. The main result proves that for a noncompact simple Lie group G acting analytically on …

Let M be a connected compact pseudoRiemannian manifold acted upon topologically
transitively and isometrically by a connected noncompact simple Lie group G. If m₀, n₀ are …

We present a new approach to the amenability of groupoids (both in the measure theoretical
and the topological setups) based on using Markov operators. We introduce the notion of an …