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UID:20250919T141616EDT-30991pIixG@132.216.98.100
DTSTAMP:20250919T181616Z
DESCRIPTION:Title: Arboreal structures on groups and the associated boundar
 ies - I\n\nAbstract: Geometers are very much used to endowing manifolds wi
 th additional structures (Riemannian\, symplectic\, etc.). Likewise\, a gr
 oup can be equipped with a probability measure which gives rise to the ass
 ociated 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 behaviou
 r of the sample paths of the random walk at infinity.\n	\n	The Poisson bound
 ary can usually be identified with the natural geometric boundary of the g
 roup (provided the latter is well-defined) endowed with an appropriate hit
 ting distribution (e.g.\, for hyperbolic groups\, cf. the classical Poisso
 n formula for the hyperbolic plane in the disk model). Still\, a number of
  very natural questions about the identification of the Poisson boundary (
 or even just about its non-triviality) for general groups remain wide open
 . It has been known for nearly 40 years that amenable groups can be charac
 terized as the ones for which there *exists* a measure with the trivial Po
 isson boundary. According to a very recent result of Frisch - Hartman - Ta
 muz - Vahidi Ferdowsi the hyper-FC-central groups are precisely those for 
 which the boundary of *any* measure is trivial. The key ingredient of this
  result is the existence of a measure with a non-trivial boundary on any g
 roup with infinite conjugacy classes (ICC). I will talk about a joint work
  with Anna Erschler\, in which we introduce a new arboreal structure on an
  arbitrary ICC group and subsequently identify the Poisson boundary in ter
 ms of this structure.\n
DTSTART:20190424T200000Z
DTEND:20190424T210000Z
LOCATION:Room 4336\, CA\, Pav. André-Aisenstadt
SUMMARY:Vadim Kaimanovich\, Université d'Ottawa
URL:/mathstat/channels/event/vadim-kaimanovich-univers
 ite-dottawa-296379
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