The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

This paper compiles basic components of the construction of random groups and of the
proof of their properties announced in [G10]. Justification of each step, as well as the …

THE NON-LINEAR GEOMETRY OF BANACH SPACES AFTER NIGEL KALTON 1. Introduction.
Four articles among Nigel Kalton’s last papers ar Page 1 ROCKY MOUNTAIN JOURNAL OF …

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 …

arXiv:math/0402405v1 [math.KT] 25 Feb 2004 Page 1 arXiv:math/0402405v1 [math.KT] 25
Feb 2004 The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory Wolfgang …

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 …

Since persistence diagrams do not admit an inner product structure, a map into a Hilbert
space is needed in order to use kernel methods. It is natural to ask if such maps necessarily …

In this note we will study a connection between the conjecture that C∗ r (Γ) is exact and the
Novikov conjecture for Γ. The main result states that if the inclusion of the reduced C∗ …

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 …