Recent developments on dimension theory for dynamical systems and the nuclear dimension for crossed products

Jianchao Wu  (Universitaet Muenster)

9:30 am to 10:30 am, July 30th, 2015   Science Building A1510

Abstract:

Nuclear dimension is a dimension concept for (nuclear) C*-algebras that generalizes the notion of covering dimension for topological spaces. It has played an important role in the classification program of simple separable unital nuclear C*-algebras. An important problem currently under active research is the behavior of nuclear dimension under taking crossed products. To this end, various dimensions of dynamical nature have recently been developed, including Rokhlin dimension, amenability dimension, etc. Roughly speaking, these dimensions measure the complexity of the topological or C*-dynamical system that gives rise to a given crossed product. We will survey these concepts and discuss their connections to each other as well as applications.

The talk is based on joint works with Ilan Hirshberg, Gabor Szabo, Wilhelm Winter and Joachim Zacharias.

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