Operator Algebra seminar

Speaker:  Joachim Zacharias (Glasgow)

Title: Dimension theories for dynamical systems related to nuclear dimension

Abstract: In this talk which is based on collaboration with Ilan Hirshberg, Gabor Szabo, Jinchao Wu and Wilhelm Winter we will survey part of the developments surrounding Rokhlin dimension and other dimension concepts from coarse geometry in connection with nuclear dimension, a dimension concept for C*-algebras modelled on covering dimension for topological spaces. Nuclear dimension plays an important role in the classification programme. Unfortunately it is hard to estimate in general and in particular for crossed product C*-algebras. However, for automorphisms with the Rokhlin property one can find nice such nuclear dimension estimates. Motivated by that we introduced a dimensional invariant for dynamical systems which is modelled on a sort of equivariant covering dimension. Automorphisms with finite Rokhlin dimension allow nice estimates for their crossed products. Recently, the definition of Rokhlin dimension has been extended to much larger classes of groups and flows, and connections to other dimension concepts in coarse geometry have been found. Coarse geometric invariants feature in the nuclear dimension estimates for the corresponding crossed products. We close by pointing out some possible future development.