Large scale geometry is the study of geometric objects viewed from a great distance. The
idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of …

Embeddings of discrete metric spaces into Banach spaces recently became an important
tool in computer science and topology. The purpose of the book is to present some of the …

We introduce the notion of cotype of a metric space, and prove that for Banach spaces it
coincides with the classical notion of Rademacher cotype. This yields a concrete version of …

The coarse geometric Novikov conjecture provides an algorithm to determine when the
higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this …

We present geometric conditions on a metric space (Y, dY) ensuring that, almost surely, any
isometric action on Y by Gromov's expander-based random group has a common fixed …

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to
satisfy a spectral calculus inequality that establishes their decay along Cesàro averages …

EXAMPLES OF RANDOM GROUPS 1. Introduction In the late 1950’s, working on the uniform
classification of metric spaces, Smirnov Page 1 EXAMPLES OF RANDOM GROUPS G …

In this paper, we prove that the Strong Novikov Conjecture for a residually finite group is
essentially equivalent to the Coarse Geometric Novikov Conjecture for a certain metric …

An important problem in higher dimensional topology is the Novikov conjecture on the
homotopy invariance of higher signature. The Novikov conjecture is a consequence of the …

Motivated by a question of Vincent Lafforgue, we study the Banach spaces $ X $ satisfying
the following property: there is a function $\varepsilon\to\Delta _X (\varepsilon) $ tending to …