# Group actions, groupoids, and their $$C^{*}$$-algebras

Becky Armstrong
University of Sydney
10 July 2017, 3-4pm, Carslaw 375, University of Sydney

## Abstract

$$C^{*}$$-algebras were first introduced in order to model physical observables in quantum mechanics, but are now studied more abstractly in pure mathematics. Much of the current research of $$C^{*}$$-algebraists involves constructing interesting classes of $$C^{*}$$-algebras from various mathematical objects---such as groups, groupoids, and directed graphs---and studying their properties. Groupoid $$C^{*}$$-algebras were introduced by Renault in 1980, and provide a unifying model for $$C^{*}$$-algebras associated to groups, group actions, and graphs. In this talk, I will define topological groupoids and examine Renault's construction of groupoid $$C^{*}$$-algebras. I will discuss several examples of groupoids, including group actions and graph groupoids, and will conclude with a brief description of my PhD research.