An indispensable tool for studying C*-algebras is through its double dual (which is a von Neumann algebra). For instance, it follows from Connes’ groundbreaking work on injective von Neumann algebras that a C*-algebra is nuclear exactly when its double dual is injective. Unfortunately, it is quite difficult to extract sufficient information from the double dual. In recent work, Schafhauser proved a new technique for extracting information from the von Neumann algebras induced by a tracial state on a nuclear C*-algebra. This has many interesting consequences, and in particular has been used to give a new proof that simple nuclear well-behaved C*-algebras are classified by their K-theory and traces. This is joint work with José Carrión, Chris Schafhauser, Aaron Tikuisis, and Stuart White.

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