Groups and Operator Algebras Seminar

Speaker: Damian Osajda (University of Copenhagen)

Title: Locally elliptic actions on nonpositively curved spaces.

Abstract: For a finitely generated group Kazhdan’s property (T) is equivalent to the property that every isometric action on the Hilbert space is elliptic, that is, it fixes a point. The Hilbert space is a nonpositively curved (more precisely, CAT(0)) space of infinite dimension. There are striking differences between this case and the case of finitely dimensional nonpositively curved spaces. For example, conjecturally, every action of a finitely generated torsion group (i.e., every element has finite order) on the latter spaces is elliptic, whereas such torsion groups, even infinite Burnside groups, can act properly on the Hilbert space. I will present recent developments around related questions. This is based on joint works with Karol Duda, Thomas Haettel, Sergey Norin, and Piotr Przytycki.