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SUMMARY:Uniform rank gradient\, cost and local-global convergence
DTSTART:20170615T130000
DTEND:20170615T140000
DTSTAMP:20260925T090705Z
UID:adc45f863bda7d033a944687d6f46a78138ed6d7474a5e38a45579bb
CATEGORIES:Conferences - Seminars
DESCRIPTION:László Márton Tóth (Budapest)\nThe notion of combinatorial
  cost for sequences of graphs was introduced by Elek as an analogue of the
  cost of measure preserving equivalence relations. We show that if a graph
  sequence is local-global convergent\, then its combinatorial cost equals 
 the cost of the limit graphing.\nThis in particular implies previous resul
 ts of Elek on combinatorial cost\, and gives an alternate proof of the Abe
 rt-Nikolov theroem that connects the rank gradient of a chain of subgroups
  to the cost of its profinite completion.\nIt also turns out that local-gl
 obal convergence is a useful tool in reinforcing previous results on the r
 ank gradient. We obtain a uniform continuity result for the rank gradient 
 for Farber sequences of subgroups in groups with fixed price\, and show va
 nishing of the rank gradient in finitely presented amenable groups for arb
 itrary sequences (with index tending to infinity).
LOCATION:MA 12 http://plan.epfl.ch/?room=ma12
STATUS:CONFIRMED
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