Groups and Operator Algebras seminar

Speaker: Gábor Szabó (KU Leuven)

Title: On equivariant Z-stability and its applications

Abstract: The Jiang-Su algebra Z is a touchstone object in the classification theory for C*-algebras, which most commonly manifests through the concept of Jiang-Su stability and thus gives rise to one of the central properties in the Toms-Winter conjecture. This property extends even to noncommutative dynamical systems: Given a countable discrete group G, we say that a G-action on a C*-algebra is equivariantly Z-stable, if it is cocycle conjugate to its tensor product with the trivial action on the Jiang-Su algebra. One can expect this to be of particular interest when the underlying C*-algebra is simple nuclear Z-stable and G is amenable. In this talk I present a dynamical counterpart to recent work of Castillejos et al: Under the aforementioned assumptions, equivariant Z-stability turns out to coincide with (the a priori weaker) equivariant uniform property Gamma, which in turn implies a dynamical version of the so-called tracial local-to-global principle. If time permits, I will outline potential applications towards the classification of group actions. This talk is based on joint work with Lise Wouters.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar