Index theory studies the solutions to differential equations on geometric spaces, their
relation to the underlying geometry and topology, and applications to physics. If the space of …

Ideal structure and pure infiniteness of ample groupoid C∗-algebras Page 1 Ergod. Th. &
Dynam. Sys. (2020), 40, 34–63 doi:10.1017/etds.2018.39 c Cambridge University Press, 2018 …

We investigate the rigidity of the ℓ p analog of Roe‐type algebras. In particular, we show that
if p∈[1,∞)∖{2}, then an isometric isomorphism between the ℓ p uniform Roe algebras of two …

In this paper we study structural and uniqueness questions for Cartan subalgebras of
uniform Roe algebras. We characterise when an inclusion BA of C-algebras is isomorphic to …

The goal of this paper is to study when uniform Roe algebras have certain C∗‐algebraic
properties in terms of the underlying space: in particular, we study properties like having …

In this article we analyze the notions of amenability and paradoxical decomposition from an
algebraic perspective. We consider this dichotomy for locally finite extended metric spaces …

Recently, Ludewig and Thiang introduced a notion of a uniformly localized Wannier basis
with localization centers in an arbitrary uniformly discrete subset D in a complete …

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-
local algebra associated to a metric space of bounded geometry. In the process, we …

Very recently, Špakula and Tikuisis provide a new characterisation of (uniform) Roe
algebras via quasi-locality when the underlying metric spaces have straight finite …

We prove that a minimal second countable ample groupoid has dynamical comparison if
and only if its type semigroup is almost unperforated. Moreover, we investigate to what …