Speaker: Johannes Christensen (KU Leuven)

Title: KMS spectra for group actions on compact spaces

Time/Date: 4:45-6:15pm, June 22 (Tue.), 2021

Room: Online

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.

In this talk I will introduce the audience to KMS states and the basic setup for studying KMS states on crossed products. 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.

I will present results which illustrates that the possible KMS spectra depend heavily on the acting group G: when G has subexponential growth, only the subsets {0}, [0,+∞), (-∞,0] and R arise as KMS spectrum; for general amenable groups all closed subsets of R containing zero can arise and are concretely realized for certain wreath product groups; while for arbitrary countable groups, any closed subset of R may appear and is concretely realized for the free group with infinitely many generators.

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