Arithmetic groups in action

12.07.2023, 14:45 - 17:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium

Holger Kammeyer (Heinrich Heine University), Roman Sauer (Karlsruher Institut für Technologie)

14:45 Holger Kammeyer (Heinrich Heine University)

15:30 Tea and Coffee Break

16:00 Roman Sauer (Karlsruher Institut für Technologie)

Holger Kammeyer (Heinrich Heine University): Can one recover arithmetic groups from permutation actions?

Abstract:It is a mathematical paradigm that groups should be studied by their actions. The easiest way a group can act is by permutations on a finite set. But how much can we learn about a group from such finite actions? Might it be possible to recover the group up to isomorphism? These are deep and wide open questions even in the important case of certain matrix groups known as arithmetic groups. The purpose of the talk is to shed some light on the problem and to report on recent progress in joint work with Ryan Spitler.

Roman Sauer (Karlsruher Institut für Technologie): Higher fixed point properties of arithmetic groups.

Abstract:Property T of a group G is a fixed point property of actions of G on Hilbert spaces. It was introduced by Kazhdan in the 1960's in a most influential 3-page paper.
We study and prove a higher analog of property T for arithmetic groups which is formulated in cohomological terms. Earlier related results often relied on deep analytic and number-theoretic results. Our novel method is based on results of geometric group theory such as isoperimetric inequalities in groups. Joint work with Uri Bader.

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