Some of the most central and nuanced constructions in operator algebras are tensor products. Universal facts from the purely algebraic setting become powerful properties that hold for only certain classes of operator algebras, and some of the deepest questions and most powerful techniques in the field can be captured or characterized in the language of tensor products. One of the chief players in the evolution of our understanding of the depth and power of C*-tensor products is Eberhard Kirchberg. In this seminar, we will explore the nuances of the theory and delve into Kirchberg's remarkable insights into the structure of tensor products and how the language of tensor products can create a bridge connecting seemingly distant problems in operator algebras and related areas.
T. Ceccherini-Silberstein, M. Coornaert
Cellular automata and groups.
Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2010. xx+439 pp.
V. Capraro M. Lupini,
Introduction to sofic and hyperlinear groups and Connes' embedding conjecture.
With an appendix by Vladimir Pestov. Lecture Notes in Mathematics, 2136. Springer, Cham, 2015. viii+151 pp.
Das Seminar richtet sich an Studierende ab dem 5. Semester und eignet sich als Einstieg in eine Bachelorarbeit.
It is also appropriate for Masters students and can be used to fulfil an Specialisation Supplement and Research Skills Module (Ma-E) (Ergänzungsmodul (E-Modul)) or a Specialisation Module (Ma-S2, Ma-S3 or Ma-S5) (Spezialisierungsmodul (S-Modul)).