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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, January 11, 2024}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Izhar Oppenheim 
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  (BGU)
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will talk about
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{\Large\bfseries Banach Fixed Point Properties of Higher Rank Groups\par}
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\textsc{Abstract:}
A classical Theorem of Delorme-Guichardet states that a group G has property (T) if and only if every continuous affine isometric action of G on a Hilbert space has a fixed point.

There was a conjecture (attributed to Margulis) that for simple higher rank algebraic groups, this result has the following far reaching generalization: For a simple higher rank algebraic group with a finite center G, every continuous affine isometric action of G on a uniformly convex space has a fixed point.

This conjecture was recently settled by the joint works of V. Lafforgue, Liao for the non-Archimedean case, and myself, and de Laat and de la Salle in the real case.

In my lecture, I will discuss the history of the conjecture mentioned above and a further generalization of its solution beyond algebraic groups (namely, for higher rank universal lattices and Steinberg groups).








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