In this talk, I will discuss the uniform trace norms on a C*-algebras and the resulting completions. These completions generalise the theory of tracial von Neumann algebras and W* bundles and arose from work on the structure and classification of amenable C*-algebras. After outlining the basic theory, I will move on to discuss property gamma, CPoU, amenability and classification in this context. 

 

This talk is based on joint work with  Carrión, Castillejos, Gabe, Schafhauser, Tikuisis and White.

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