Pure Mathematics Colloquium - C*-simplicity of groupoids

Dates

Tuesday, April 19, 2022 - 14:00 to 15:00

Speaker: Sam Se-Jin Kim (University of Glasgow)

Title: C*-simplicity of groupoids

Abstract: Groupoids are a generalization of groups where mutliplication is only partially defined. This minor change in definition allows much broader objects to be defined through groupoids. For example, invertible dynamical systems and equivalence relations may be modelled through groupoids. This talk, in joint work with Matthew Kennedy, Xin Li, Sven Raum, and Dan Ursu, concerns a certain property of groupoids called C*-simplicity. We will define C*-simplicity, which is a purely representation theoretic notion, and describe its equivalence to certain properties intrinsic to the groupoid. Along the way, we will connect these notions to the theory of groups, where it is demonstrated that C*-simplicity is a notion that is far from a finiteness property for groups called amenability.