Speaker: David Kerr (Texas A&M Univ.)

Title: Dimension, comparison, and almost finiteness

Time/Date: 4:45-6:15, Monday, June 26, 2017.

Room: 118

Abstract: I will explain how one can develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C^*-algebras. In particular, I will introduce a notion of almost finiteness for group actions on compact spaces as an analogue of both hyperfiniteness in the measure-preserving setting and of Z-stability in the C^*-algebra setting. This generalizes Matui's concept of the same name from the zero-dimensional context and is related to dynamical comparison in the same way that Z-stability is related to strict comparison in the Toms-Winter context. For free minimal actions of countably infinite groups on compact metrizable spaces the property of almost finiteness implies that the crossed product is Z-stable, which leads to new examples of classifiable crossed products.