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.

08.12.22 18.04.24

Seminar on Algebra and Combinatorics

Universität Leipzig Augusteum - A314

Mirke Olschewski

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