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DTSTAMP:20250916T120336Z
DESCRIPTION:Title: Martin and Floyd boundaries of finitely generated groups
 .\n\nAbstract:\n\nThe talk is based on two recent preprints:\n\n\n	[GGPY]\,
  I. Gekhtman\, V. Gerasimov\, L.P.\, W. Yang\, Martin boundary covers Floy
 d boundary \n	[DGGP]\, M. Dussaule\, I. Gekhtman\, V. Gerasimov\, L.P.\, Th
 e Martin boundary of relatively hyperbolic groups with virtually abelian p
 arabolic subgroups \n\n\nWe study two different compactifications of finit
 ely generated groups. The first is the Martin compactification which comes
  from random walks on the Cayley graph of a group equipped with a symmetri
 c probability measure. The second compactification is the Floyd compactifi
 cation which is the Cauchy completion of the Cayley graph equipped with a 
 distance obtained by a rescaling of the word metric. The corresponding bou
 ndaries are the remainders of the group in these compactifications. Our fi
 rst main result from [GGPY] states that the identity map on the group exte
 nds to an equivariant and continuous map between Martin and Floyd compacti
 fications. The proof is based on our generalization of the Ancona inequali
 ty proved by A. Ancona for hyperbolic groups in the 80s. Using these resul
 ts we prove in [DGGP] that the Martin boundary of a hyperbolic group G rel
 ative to a system of virtually abelian subgroups is a 'parabolic blow-up s
 pace'. It is obtained from the limit set X of the relatively hyperbolic ac
 tion of G by replacing every parabolic fixed point p∈X by the euclidean sp
 here of dimension k−1 where k is the rank of its parabolic stabilizer. All
  other points of X are conical and they remain unchanged.\n\n \n
DTSTART:20190410T200000Z
DTEND:20190410T210000Z
LOCATION:Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue Sherbrooke 
 Ouest
SUMMARY:Leonid Potyagailo (Université de Lille)
URL:/mathstat/channels/event/leonid-potyagailo-univers
 ite-de-lille-296077
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