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SUMMARY:Confined Subgroups of Semisimple Lie Groups
DTSTART:20231204T130000Z
DTEND:20231204T141500Z
DTSTAMP:20240222T004900Z
UID:indico-event-11022@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Mikołaj Frączyk (Jagiellonian University\, Krakow)
\n\nLet G be a semisimple Lie group\, e.g. G = SL(n\,R). A subgroup Γ of
G is called confined if there is a bounded neighborhood of the identity t
hat contains a non-trivial element of every conjugate of Γ. For example\
, any normal subgroup of a co-compact lattice is confined. In joint work w
ith Tsachik Gelander\, we proved that when G has higher rank (e.g. G = SL(
n\,R) with n>2)\, a discrete subgroup of G is confined if and only if it i
s a lattice\, which can be seen as an extension of Margulis' Normal Subgro
up Theorem. The proof consists of two independent steps that I hope to exp
lain in my talk: 1) the passage from discrete subgroups to stationary rand
om subgroups and 2) the classification of discrete stationary random subgr
oups in higher rank. If time permits\, I will also discuss some open quest
ions related to this work.\n\nhttps://indico.math.cnrs.fr/event/11022/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/11022/
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