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 …

We introduce the nuclear dimension of a C∗-algebra; this is a noncommutative version of
topological covering dimension based on a modification of the earlier concept of …

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general
construction of many actions of groups on quasi-trees. The groups we can handle include …

This book offers to study locally compact groups from the point of view of appropriate metrics
that can be defined on them, in other words to study" Infinite groups as geometric objects" …

We present problems and results that combine graph-minors and coarse geometry. For
example, we ask whether every geodesic metric space (or graph) without a fat $ H $ minor is …

We develop a dynamical version of some of the theory surrounding the Toms–Winter
conjecture for simple separable nuclear C*-algebras and study its connections to the C …

We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete
groups on locally compact spaces, and more generally for locally compact étale groupoids …

A long-standing open problem in the theory of hyperfinite equivalence relations asks
whether the orbit equivalence relation generated by a Borel action of a countable amenable …

The main topic of the book is amenable groups, ie, groups on which there exist invariant
finitely additive measures. It was discovered that the existence or non-existence of …

We prove that all hierarchically hyperbolic groups have finite asymptotic dimension. One
application of this result is to obtain the sharpest known bound on the asymptotic dimension …