Professor A. Sims obtained a Bachelor of Mathematics and a Bachelor of Computer Science at the University of Newcastle, Australia, in 2000. He completed his Bachelor of Mathematics with Honors (Class I, University Medal) in 2001. Afterwards, he obtained his Ph.D. in Mathematics at the same university in 2004. He is currently working as a Professor of Quantum Mathematics at the University of New South Wales and is currently the President of the Australian Mathematical Society. He received the Australian Mathematical Society Medal in 2016 and became a Fellow of the Australian Academy of Science in 2025. Professor A. Sims specializes in C*-algebras.

A directed graph is a network of points connected by directed edges, and they are used, among other things, to describe symbolic dynamics. In the late 1990’s, Kumjian, Pask, Raeburn and Renault developed an appropriate notion of a representation of a directed graph $E$ by bounded linear operators on Hilbert space so that the resulting $C^{*}$-algebra encodes the symbolic dynamics described by the graph. This led to an explosion of research—one that continues today—into the extent to which properties of the $C^{*}$-algebra can be read off from the graph and vice-versa. I will give an overview of the theory of graph $C^{*}$-algebras—from the basics to the major areas of current work.