Baby NCG seminar

SPEAKER: Andreas Hallbäck

TITLE: Classification of C*-algebras through descriptive set theory

ABSTRACT: This will be an overview of the descriptive set theoretic approach to classification problems. We will define Borel reducibility and discuss the Borel hierarchy of equivalence relations. Moreover we will discuss how to apply this to the classification of C*-algebras. In particular we will show how to parametrize C*-algebras as standard Borel spaces and explain how to view Kirchberg's exact embedding theorem and $A \otimes O_2$ theorem as Borel measurable maps between standard Borel spaces.