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CATEGORIES:Combinatorics Seminar
SUMMARY:Essential Expansion is Forceable - Gabor Kun (Rény
i Institute)
DTSTART;TZID=Europe/London:20161116T143000
DTEND;TZID=Europe/London:20161116T153000
UID:TALK68664AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68664
DESCRIPTION:We say that a sequence of bounded degree graphs is
locally\n(Benjamini-Schramm) convergent if for ev
ery r the probability distribution on the isomorph
ism classes of rooted r-balls obtained by picking
a vertex x uniformly at random and considering the
r-ball centred at x converges in distribution. No
t much is known about approximation of large graph
s by small ones. We do not even know if every Cayl
ey graph can be approximated by\nfinite graphs: Th
is is the famous problem if every group is sofic.\
n\nWe prove Bowen's conjecture that for every grou
p G with Kazhdan Property (T) if a sequence of bou
nded degree graphs locally converges to a Cayley g
raph of G then\nthe sequence is essentially a vert
ex-disjoint union of expander graphs. We character
ize such sequences in terms of the Markov operator
.\n
LOCATION:MR5
CONTACT:Andrew Thomason
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