Cuntz semigroups

Abstract: The Cuntz semigroup is a geometric refinement of K-theory that plays an important role in the structure theory of C*-algebras. It is defined analogously to the Murray-von Neumann semigroup by using equivalence classes of positive elements instead of projections. Starting with the definition of the Cuntz semigroup of a C*-algebra, we will look at some of its classical applications. I will then talk about the recent breakthroughs in the structure theory of Cuntz semigroups and some of the consequences.

operator algebras

Audience: researchers in the topic

Comments: Assumed Knowledge: Basic C*-algebra theory, including comparison theory for projections.

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UK Virtual operator algebras seminar

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