[Online] NCG seminar: Mikkel Munkholm

Mikkel Munkholm,

KL obstruction to quasidiagonality.

Abstract: The talk will cover an analysis of the KK-theory of the trace-kernel extension, leaning on the fairly recently developed techniques by Christopher Schafhauser and James Gabe. It will appeal to an audience with a keen eye on classification (of certain simple nuclear C∗-algebras) alongside the interplay between amenable traces and quasidiagonal traces. It will feature a biproduct of Christopher Schafhauser’s methods in his AF-embedding paper, whereby the KK - and KL-theory of the key extension, the trace-kernel extension, are shown to coincide. I will make an effort to emphasize on how uniqueness results are connected to said KK (and KL) biproduct and flag up the various key ingredients.

Keywords: KK/KL-theory, (tracial) ultrapowers, UCT, quasidiagonal and amenable traces, the trace-kernel extension, nuclear absorption.