The geometric median as well as the Fréchet mean of points in a Hadamard space are
important in both theory and applications. Surprisingly, no algorithms for their computation …

We study property (T) and the fixed-point property for actions on L p and other Banach
spaces. We show that property (T) holds when L 2 is replaced by L p (and even a …

We give a group theoretic characterization of geodesics with superlinear divergence in the
Cayley graph of a right-angled Artin group A Γ with connected defining graph. We use this to …

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 …

Kac–Moody groups over finite fields are finitely generated groups. Most of them can
naturally be viewed as irreducible lattices in products of two closed automorphism groups of …

Hadamard spaces have traditionally played important roles in geometry and geometric
group theory. More recently, they have additionally turned out to be a suitable framework for …

Suppose that X is a smooth quasiprojective variety over ℂ and ρ: π1 (X, x)→ SL (2, ℂ) is a
Zariski-dense representation with quasiunipotent monodromy at infinity. Then ρ factors …

In this paper we discuss some connections between measurable dynamics and rigidity
aspects of group representations and group actions. A new ergodic feature of familiar group …

In this survey article, we present some panorama of groups acting on metric spaces of non-
positive curvature. We introduce the main examples and their rigidity properties, we show …

We use the convexity of a certain function discovered by W. Kendall on small metric balls in
CAT (1)-spaces to show that any probability measure on a complete CAT (1)-space of small …