Operator algebras seminar

Speaker: Clemens Borys (University of Copenhagen)

Title: The Furstenberg Boundary of a Groupoid

Abstract: The recent successes in the characterizations of C*-simplicity of discrete groups and their crossed products by compact spaces have largely been enabled by a new description of an old tool: The Furstenberg boundary of the group, recast as Hamana's equivariant injective envelope of the action in question. By providing a new method of induction for the action of a (locally compact Hausdorff) étale groupoid with compact unit space, we construct groupoid-equivariant injective envelopes in the appropriate category. This yields a notion of Furstenberg boundary of such groupoids, for which we discuss possible applications to groupoid C*-simplicity.