Joint Colloquium: Aidan Sims -- Graphs, C*-algebras and equilibrium states

The theory of C*-algebras developed in response to the advent of quantum theory in the
early 1900’s, and have since developed into an interesting and active area of
mathematics.  When studying a physical system, we are interested in equilibrium states
of the system – those which remain steady with the passage of time.  In C*-algebraic
models, such equilibrium states are called KMS-states, and are characterised by a
simple-looking algebraic relation.  This relation makes perfectly good sense even for
C*-algebras that are not based on physical systems, and we are learning that the KMS
states of a C*-algebra tend to capture very interesting structural information.  I will
discuss an excellent example of this phenomenon in the context of the graph C*-algebras
that were introduced by Kumjian, Pask, Raeburn and Renault in the late 1990’s and have
since become a major research industry worldwide.  This is joint work with Astrid an
Huef, Marcelo Laca and Iain Raeburn.