Actions of higher rank groups on uniformly convex Banach spaces

  • Tim de Laat (University of Münster)
Raum P801 Universität Leipzig (Leipzig)


I will explain that all affine isometric actions of higher rank simple Lie groups and their lattices on arbitrary uniformly convex Banach spaces have a fixed point. This vastly generalises a recent breakthrough of Oppenheim. Combined with earlier work of Lafforgue and of Liao on strong Banach property (T) for non-Archimedean higher rank simple groups, this confirms a long-standing conjecture of Bader, Furman, Gelander and Monod. As a consequence, we deduce that box space expanders constructed from higher rank lattices are superexpanders.

This is joint work with Mikael de la Salle.

12/8/22 1/25/24

Seminar on Algebra and Combinatorics

Universität Leipzig Seminargebäude 213

Mirke Olschewski

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