Greg Faurot
The Ohio State University
Title
Regularity of Graph C*-Algebras
Abstract
The study of C*-algebras is frequently referred to as "noncommutative topology," as Gelfand duality shows that any (unital) commutative C*-algebras arises as the algebra of continuous functions on a compact Hausdorff space. As a result, many techniques and properties used to study C*-algebras are generalized from topology. One such example is nuclear dimension, which is a noncommutative analogue of covering dimension. In this talk, we will discuss bounds on the nuclear dimension of graph C*-algebras, whose properties are closely related to their underlying graph structure. We will also discuss the related regularity property of $\mathcal{Z}$-stability and its application to graph C*-algebras. Portions of this work is joint with Samuel Evington and Christopher Schafhauser.