Structure and classification of C*-dynamics

ended

We study group actions on C*-algebras from a structure and classification point of view, importing concepts from the Elliott classification program into the equivariant context. The challenge is to advance the structure theory for natural classes of actions of amenable groups on C*-algebras. In a similar vein, we shall consider flows on C*-algebras, which are the mathematical abstractions of time evolutions. The objectives of this proposal are: A: Establish an Ocneanu-type rigidity result for actions of amenable groups on strongly self-absorbing C*-algebras as well as the automatic tensorial absorption of such actions under natural conditions. B: Obtain an equivariant version of the KK-theoretic stable uniqueness theorem à la Lin-Dadarlat-Eilers. C: Study the rigid behavior of flows on Kirchberg algebras with the Rokhlin property, in order to solve a long-standing open problem set out by Kishimoto. We also consider other natural classes of flows without the Rokhlin property, the projected classification of which will solve open problems such as Robert's conjecture and part of the Toms-Winter conjecture. The solution to this challenge employs equivariant generalizations of important classical concepts like strong self-absorption, W*-bundles, KK-theory, and combines these with known concepts like Rokhlin dimension in an innovative way. The projected results are ground-breaking for the field of C*-algebras, and the methods to obtain them go well beyond the state-of-the-art. The projects are chosen to maximize the transfer of knowledge between the ER and the supervisor. Taking into account the excellent opportunities for professional training and public engagement provided by the University of Aberdeen as well as the other suggested activities described in the proposal, the MSC IF will have a substantial impact on the ER’s career, qualifying him for a permanent position at a research-driven institution after completing the fellowship.