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UID:20250704T105551EDT-908934jpbm@132.216.98.100
DTSTAMP:20250704T145551Z
DESCRIPTION:Title: Arboreal structures on groups and the associated boundar
 ies - II\n\nAbstract: Geometers are very much used to endowing manifolds w
 ith additional structures (Riemannian\, symplectic\, etc.). Likewise\, a g
 roup can be equipped with a probability measure which gives rise to the as
 sociated random walk (in the same way as a Riemannian metric gives rise to
  the associated Brownian motion). This setup produces the Poisson boundary
  as a measure space which describes the stochastically significant behavio
 ur of the sample paths of the random walk at infinity.\n	\n	The Poisson boun
 dary can usually be identified with the natural geometric boundary of the 
 group (provided the latter is well-defined) endowed with an appropriate hi
 tting distribution (e.g.\, for hyperbolic groups\, cf. the classical Poiss
 on formula for the hyperbolic plane in the disk model). Still\, a number o
 f very natural questions about the identification of the Poisson boundary 
 (or even just about its non-triviality) for general groups remain wide ope
 n. It has been known for nearly 40 years that amenable groups can be chara
 cterized as the ones for which there *exists* a measure with the trivial P
 oisson boundary. According to a very recent result of Frisch - Hartman - T
 amuz - Vahidi Ferdowsi the hyper-FC-central groups are precisely those for
  which the boundary of *any* measure is trivial. The key ingredient of thi
 s result is the existence of a measure with a non-trivial boundary on any 
 group with infinite conjugacy classes (ICC). I will talk about a joint wor
 k with Anna Erschler\, in which we introduce a new arboreal structure on a
 n arbitrary ICC group and subsequently identify the Poisson boundary in te
 rms of this structure.\n
DTSTART:20190425T200000Z
DTEND:20190425T210000Z
LOCATION:Room 4336\, CA\, Pav. André-Aisenstadt
SUMMARY:Vadim Kaimanovich\, Université d'Ottawa
URL:/mathstat/channels/event/vadim-kaimanovich-univers
 ite-dottawa-296381
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