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SUMMARY:Characterizations of Kleinian Groups
DTSTART;VALUE=DATE-TIME:20200203T133000Z
DTEND;VALUE=DATE-TIME:20200203T144500Z
DTSTAMP;VALUE=DATE-TIME:20200227T122100Z
UID:indico-event-5539@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Haissinsky (Aix-Marseille Université)\nIn low
dimension\, it is expected that topological properties determine a natura
l geometry. In this spirit\, several characterizations are conjectured for
Kleinian groups\, i.e. discrete subgroups of PSL(2\,C). We will survey di
fferent methods that lead to their topological and dynamical characterizat
ions\, and point out their limits and the difficulties encountered in obta
ining a complete answer.\nhttps://indico.math.cnrs.fr/event/5539/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/5539/
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SUMMARY:Cyclically Reduced Elements in Coxeter Groups
DTSTART;VALUE=DATE-TIME:20200203T153000Z
DTEND;VALUE=DATE-TIME:20200203T164500Z
DTSTAMP;VALUE=DATE-TIME:20200227T122100Z
UID:indico-event-5540@indico.math.cnrs.fr
DESCRIPTION:Speakers: Timothée Marquis (Université Catholique de Louvain
)\nLet W be a Coxeter group. We provide a precise description of the conju
gacy classes in W\, yielding an analogue of Matsumoto's theorem for the co
njugacy problem in arbitrary Coxeter groups. This extends to all Coxeter g
roups an important result on finite Coxeter groups by M. Geck and G. Pfeif
fer from 1993. In particular\, we describe the cyclically reduced elements
of W\, thereby proving a conjecture of A. Cohen from 1994.\nhttps://indic
o.math.cnrs.fr/event/5540/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/5540/
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SUMMARY:Local Rigidity of Diagonally Embedded Triangle Groups
DTSTART;VALUE=DATE-TIME:20200302T133000Z
DTEND;VALUE=DATE-TIME:20200302T144500Z
DTSTAMP;VALUE=DATE-TIME:20200227T122100Z
UID:indico-event-5701@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-Philippe Burelle (Université de Sherbrooke)\nR
ecent work of Alessandrini-Lee-Schaffhauser generalized the theory of high
er Teichmüller spaces to the setting of orbifold surfaces. In particular\
, these authors proved that\, as in the torsion-free surface case\, there
is a "Hitchin component" of representations into PGL(n\,R) which is homeom
orphic to a ball. They explicitly compute the dimension of Hitchin compone
nts for triangle groups\, and find that this dimension is positive except
for a finite number of low-dimensional examples where the representations
are rigid. In contrast with these results and with the torsion-free surfac
e group case\, we show that the composition of the geometric representatio
n of a hyperbolic triangle group with a diagonal embedding into PGL(2n\,R)
or PSp(2n\,R) is always locally rigid.\nhttps://indico.math.cnrs.fr/event
/5701/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/5701/
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SUMMARY:Spherical Functions on Hyperbolic Groups and Property RD (Rapid De
cay)
DTSTART;VALUE=DATE-TIME:20200302T153000Z
DTEND;VALUE=DATE-TIME:20200302T164500Z
DTSTAMP;VALUE=DATE-TIME:20200227T122100Z
UID:indico-event-5702@indico.math.cnrs.fr
DESCRIPTION:Speakers: Adrien Boyer (IMJ-PRG)\n\n We investigate properties
of some spherical fonctions defined on hyperbolic groups using boundary r
epresentations on the Gromov boundary endowed with the Patterson-Sullivan
measure class. We prove sharp decay estimates for spherical functions as w
ell as spectral inequalities associated with boundary representations. Thi
s point of view on the boundary allows us to view the so-called property R
D (Rapid Decay\, also called Haagerup's inequality) as a particular case o
f a more general behavior of spherical functions on hyperbolic groups. The
n I will explain how these representations are related to the so-called "c
omplementary series". The problem of the unitarization of such representat
ions will be at the heart of the discussion.\n If time permits\, I will tr
y to explain the idea of a constructive proof\, using a boundary unitary r
epresentation\, of a result due to de la Harpe and Jolissaint asserting th
at hyperbolic groups satisfy property RD.\n\nhttps://indico.math.cnrs.fr/e
vent/5702/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/5702/
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