Groups and Operator Algebras Seminar

Speaker: Giorgio Mangioni (Heriot-Watt University)

Title: From C*-algebras to geometric inverse semigroup theory

Abstract: In the same way as groups abstract the notion of symmetries of an object, inverse semigroups abstract the idea of partial symmetries (think of bijections between subsets of a given set). In this talk we will first motivate their study, in relation to the classification of certain C*-algebras. Next, we will adopt the perspective of a geometric (semi)group theorist and consider actions of inverse semigroups on metric spaces. This investigation will culminate in a Milnor-Schwarz-like theorem: every "nice" action gives rises to a distance function on the semigroup, which is quasi-isometric to the distance on the metric space. The latter result is joint work with Francesco Tesolin.