Admissible KMS bundles on classifiable C$^*$-algebras

Named after mathematical physicists Kubo, Martin, and Schwinger, KMS states are a special class of states on any C$^*$-algebra admitting a continuous action of the real numbers. Unlike in the case of von Neumann algebras, where each modular flow has a unique KMS state, the collection of KMS states for a given flow on a C$^*$-algebra can be quite intricate. In this talk, I will explain what abstract properties these simplices have and show how one can realise such a simplex on various classes of simple C$^*$-algebras.