Johannes Christensen: KMS spectra for group actions on compact spaces

Title: KMS spectra for group actions on compact spaces

Abstract: The crossed product construction associates a C*-algebra to a countable group acting by homeomorphisms on a compact space, in such a way that the C*-algebra encodes information about the group action. This construction has stimulated a mutually beneficial interplay between dynamical systems and operator algebras.

In this talk I will uncover a surprising relation between geometric group theoretic properties of a group G and the so called KMS spectra for certain diagonal 1-parameter groups on the crossed product C*-algebras of actions of G. The KMS spectrum for a 1-parameter group is the set of inverse temperatures for which there exists a KMS state, a concept originally studied in relation to quantum statistical mechanics, that now plays a prominent role in the theory of C*-algebras.

The results I will present in this talk are joint work with Stefaan Vaes.