Groups and Operator Algebras Seminar

Speaker: Tim de Laat (WWU Münster)

Title: Actions of higher rank groups on uniformly convex Banach spaces

Abstract: Fixed point properties for isometric group actions on Banach spaces are fundamental rigidity properties with various applications. After an introduction to this topic, I will explain that all isometric actions of higher rank semisimple Lie groups and their lattices on arbitrary uniformly convex Banach spaces have a fixed point. This vastly generalizes a recent breakthrough of Oppenheim. Combined with earlier work of Lafforgue and of Liao on strong Banach property (T) for non-Archimedean higher rank semisimple groups, this confirms a long-standing conjecture of Bader, Furman, Gelander and Monod. As an application, we deduce that box space expanders constructed from higher rank lattices are superexpanders. This talk is based on joint work with Mikael de la Salle.

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