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SUMMARY:Rigidity of Higher-rank Lattice Actions
DTSTART:20231113T130000Z
DTEND:20231113T141500Z
DTSTAMP:20241104T123500Z
UID:indico-event-10820@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Vincent Pecastaing (Université Côte d'Azur)\n\nLat
tices in semi-simple Lie groups of rank at least 2 — e.g. SL(n\,Z) for n
>2 — form a class of discrete groups known for having remarkable linear
rigidity properties. Notably\, their finite dimensional representations ar
e determined by those of the ambient Lie group they live in — e.g. SL(n\
,R) in the case of SL(n\,Z). This is Margulis' super-rigidity theorem (197
4). Motivated by an ergodic version of this theorem\, an ambitious program
initiated by Gromov and Zimmer in the 1980s aims to understand "non-linea
r representations" of such lattices into diffeomorphism groups of closed m
anifolds\, or in other words\, the differentiable actions of such lattices
on closed manifolds.I will first discuss the history and geometric origin
s of this program. I will then focus on rigidity results about actions of
lattices which preserve non-unimodular geometric structures\, such as conf
ormal or projective structures\, and will mention open directions. The pro
ofs build on recent advances on Zimmer's conjectures\, especially an invar
iance principle which provides existence of finite invariant measures in v
arious dynamical contexts.\n\nhttps://indico.math.cnrs.fr/event/10820/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/10820/
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