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DTSTART:20200329T030000
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BEGIN:VEVENT
DTSTAMP:20260405T122143Z
UID:1573572600@ist.ac.at
DTSTART:20191112T163000
DTEND:20191112T173000
DESCRIPTION:Speaker: Gábor Pete\nhosted by M. Beiglboeck\, N. Berestycki\,
  L. Erdoes\, J. Maas\nAbstract: A probabilistic definition of groups with
  Kazhdan's property (T)\, due to Glasner  & Weiss (1997)\, is that on an
 y Cayley graph G of the group\, for any ergodic group-invariant random bla
 ck-and-white colouring of the vertices\, with the density of each colour b
 ounded away from 0\, the density of edges connecting black to white vertic
 es remains bounded away from zero. Amenable groups and free groups do not 
 have property (T)\, while SL_d(\\Z) with d\\geq 3 do. The cost of a transi
 tive graph is one half of the infimum of the expected degree of invariant 
 connected spanning subgraphs. Amenable transitive graphs and Cayley graphs
  of SL_d(\\Z) with d\\geq 3 have cost 1\, while any Cayley graph of the fr
 ee group on d generators has cost d\, by Gaboriau (2000). A question of Ga
 boriau aims to connect cost with the first L^2-Betti number of groups. For
  Kazhdan groups\, the latter has been known to be 0 since Bekka & Valett
 e (1997)\, and Gaboriau's question then suggests that the cost of any Kaz
 hdan Cayley graph should be 1. This is what we prove\, in joint work with
  Tom Hutchcroft (Cambridge).
LOCATION:SR 14\, 2 OG.\, OMP 1\, University of Vienna\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Gábor Pete: Kazhdan groups have cost 1
URL:https://talks-calendar.ista.ac.at/events/2389
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