Project supervised by Prof. Jacqui Ramagge, and Dr. Nathan Brownlowe

There are now characterisations of the equilibrium states of many different classes of C*-algebras, including those associated to right LCM semigroups, self-similar actions,

and higher-rank graphs. The PhD project will investigate a unifying construction of these C*-algebras using categories. We will then construct natural dynamics for these C*-algebras and will characterise the resulting equilibrium states.