Are Austad: A new characterization of discrete groups yielding compact quantum metric spaces

Abstract: A compact quantum metric space (CQMS) is a non-commutative analogue of a compact metric space. We give an introduction to this concept, along with a novel approach on how to obtain CQMSs from discrete groups equipped with length functions. This will allow us to rephrase important results of Christ-Rieffel and Ozawa-Rieffel. Moreover, we will explain how the new approach relates to a problem concerning obtaining CQMSs from groups with rapid decay.