Classifiability of transformation group C*-algebras.

Eusebio Gardella (Göteborgs Universitet)

Wednesday 8th February, 2023 16:00-17:00 Maths 116


Given a topological dynamical system, there is  a standard way to associate a C*-algebra to it, namely the crossed product (also known as the transformation group C*-algebra). Crossed products have provided both new examples of interesting C*-algebras, as well as new ways
to study already known ones (such as the irrational rotation algebra). Given the tremendous recent success of the classification program for simple, nuclear C*-algebras, it becomes an imperative task to determine, in dynamical terms, when a crossed product belongs to the classifiable 
class. I will give an overview of the state of the art, highlighting the surprising differences between the cases of amenable and nonamenable groups. The results on nonamenable groups are joint work with Shirly Geffen, Julian Kranz and Petr Naryshkin.

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