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DTSTAMP:20250808T080017Z
DESCRIPTION:Sharp threshold for Property (T) in the hexagonal model for ran
 dom groups.\n\nA random group in the hexagonal model is a group given by t
 he presentation where R is a set of random words of length 6 over the set 
 S. We consider properties of such a group as the cardinality of S goes to 
 infinty. Our main goal in the presentation is to prove that as the cardina
 lity of the set R increases (we increase the density defined as d =(1) *lo
 g_{|S|}(|R|)) there is a sharp transition between not having Property (T) 
 and having Property (T) for such group (this threshold is at density d=1/3
 ). First we will present a quick survey about what is known at the moment 
 about Property (T) for random groups. To proof thie main result we will pr
 esent a new method of constructing some good system of walls on the Cayley
  complex of a random group. This will allows us to find a proper action of
  a random group on a CAT(0) cube complex. The main idea behind constructin
 g our system of walls is to take hypergraphs in the Cayley complex (as Wis
 e and OIllivier did in their paper about cubulating random groups) and the
 n correct them to make them embedded trees.\n
DTSTART:20161102T190000Z
DTEND:20161102T200000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Tomasz\, Odrzygozdz
URL:/mathstat/channels/event/tomasz-odrzygozdz-263856
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