PhD Defense: Clemens Borys

Title: Groups, Actions, and C*-algebras

Abstract: I will discuss my work on simplicity of etale groupoids and its applications, as well as the greater context of these results within the theory of Operator Algebras. As a PhD defense, this talk will in large part be accessible to a general audience.

Simplicity, that is, the absence of ideals, is an important concept in understanding the structure and classification of C*-algebras, but for a given C*-algebra it may be hard to decide whether it is simple. In recent years, much progress has been made on describing the ideals of certain C*-algebras constructed from discrete groups and simplicity can completely be described in group-theoretic terms, linking them to so-called recurrent subgroups. I provide a generalization of these results to Hausdorff etale groupoids, which is surprisingly analogous in the right language, but covers a much wider class of C*-algebras. These methods leverage the theory of injective envelopes, adapted to groupoids via a new induction functor, which will be introduced during the talk. Finally, we briefly look at examples and applications.

Advisors: Mikael Rørdam and Magdalena Musat

Assessment committee: Søren Eilers (chair), Carla Farsi (University of Colorado, Boulder) and Sven Raum (Stockholm University). The two external members participate via video link.

Moderator: Asger Tornquist

Zoom link: https://ucph-ku.zoom.us/j/66002708960?.

Meeting ID: 660 0270 8960
Passcode: 463322