Young Mathematicians in C*-Algebras

The University of Copenhagen

August 17-21, 2015

Stuart White (Glasgow):

Interactions between von Neumann algebras and C*-algebras

Recent developments in the structure of simple nuclear C*-algebras have shown remarkable parallels with the structure of injective factors. Indeed key regularity properties of simple nuclear C*-algebras can be viewed as 'coloured versions' of properties of von Neumann algebras. During the talks, I'll explore the connections between von Neumann algebras and C*-algebras with the aim of making the previous sentence precise. I'll show how von Neumann type techniques are currently being used in the structure theory of simple nuclear C*-algebras, including how the structure of Connes proof that injective II1 factors are hyperfinite gives an architecture for obtaining covering dimension estimates for C*-algebras, and how the different flavours of central sequence algebras enter into the picture.

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