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UID:20251021T024711EDT-6415LgOcoH@132.216.98.100
DTSTAMP:20251021T064711Z
DESCRIPTION:Title: Twisted Patterson-Sullivan measure and applications to g
 rowth problems.\n\nAbstract: \n\nGiven a group G acting properly by isomet
 ries on a metric space X\, the exponential growth rate of G with respect t
 o X measures 'how big' the orbits of G are. If H is a subgroup of G\, its 
 exponential growth rate is bounded above by the one of G. We are intereste
 d in the following question: when do H and G have the same exponential gro
 wth rate?\n\nThis problem has both a combinatorial and a geometric origin.
  For the combinatorial part\, Grigorchuk and Cohen proved in the 80s that 
 a group Q=F/N (written as a quotient of the free group) is amenable if and
  only if N and F have the same exponential growth rate (with respect to th
 e word length in F). About the same time\, Brooks gave a geometric interpr
 etation of Kesten's amenability criterion in terms of the bottom of the sp
 ectrum of the Laplace operator. He obtained in this way a statement analog
 ous to the one of Grigorchuk and Cohen for the deck automorphism group of 
 the cover of certain compact hyperbolic manifolds. These works initiated m
 any fruitful developments in geometry\, dynamics\, and group theory.\n\nIn
  this talk\, we are interested in the case where G acts on an arbitrary Gr
 omov hyperbolic space and propose a framework that encompasses both the co
 mbinatorial and geometric point of view. We will see that as soon as the a
 ction of G on X is 'reasonable' (proper co-compact\, cuspidal with parabol
 ic gap\, or more generally strongly positively recurrent)\, then G and H h
 ave the same growth rate if and only if H is co-amenable in G. Our strateg
 y is based on a new kind of Patterson-Sullivan measure taking values in a 
 space of bounded operators.\n\nThis is joint work with R. Dougall\, B. Sch
 apira\, and S. Tapie.\n
DTSTART:20191009T190000Z
DTEND:20191009T200000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Rémi Coulon (Institut de recherche mathématique de Rennes) 
URL:/mathstat/channels/event/remi-coulon-institut-de-r
 echerche-mathematique-de-rennes-301356
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