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SUMMARY:Non-differentiability of limit sets in anti-de Sitter geometry
DTSTART;VALUE=DATE-TIME:20190130T153000Z
DTEND;VALUE=DATE-TIME:20190130T164500Z
DTSTAMP;VALUE=DATE-TIME:20190921T193410Z
UID:indico-event-4257@indico.math.cnrs.fr
DESCRIPTION:\n The study of Anosov representations deals with discrete sub
groups of Lie groups that have a nice limit set\, meaning that they share
the dynamical properties of limit sets in hyperbolic geometry. However\, t
he geometry of these limits sets is different: while limit sets in hyperbo
lic geometry have a fractal nature (e.g. non-integer Hausdorff dimension)\
, some Anosov groups have a more regular limit set (e.g. $C^1$ for Hitchin
representations).\n My talk will focus on quasi-Fuchsian subgroups of SO(
n\,2)\, and show that the situation is intermediate: their limit sets are
Lipschitz submanifolds\, but not $C^1$. I will discuss the two main steps
of the proof. The first one classifies the possible Zariski closures of su
ch groups. The second uses anti-de Sitter geometry in order to determine t
he limit cone of such a group with a $C^1$ limit set.\n Based on joint wor
k with Olivier Glorieux.\n\n\nhttps://indico.math.cnrs.fr/event/4257/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4257/
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