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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Commuting probability in infinite groups - Matthe
w Tointon (University of Neuchâtel)
DTSTART;TZID=Europe/London:20171124T134500
DTEND;TZID=Europe/London:20171124T150000
UID:TALK94990AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/94990
DESCRIPTION:In a finite group G one can ask what the probabili
ty is that two elements chosen independently unifo
rmly at random commute. It is \nclear that if G ha
s an abelian subgroup of bounded index then this p
robability should be bounded from below. A beautif
ul theorem of Peter Neumann from the 1980s shows t
hat the converse is also true in a certain precise
sense. \n\nAntolin\, Martino and Ventura consider
the same question for infinite groups\, choosing
the two random elements with respect to a certain
limit of finite probability measures. They conject
ure that for any "reasonable" sequence of measures
Neumann's result should still hold. They also pro
ve some special cases of this conjecture. \n\nIn t
his talk I will show that the Antolin-Martino-Vent
ura conjecture holds with effective quantitative b
ounds if we take the sequence of measures defined
by the successive steps of a simple random walk\,
or the uniform measures on a Folner sequence. I wi
ll also present a concrete interpretation of the w
ord "reasonable" that is sufficient to force a seq
uence of measures to obey the conjecture. If I hav
e time I will present an application to conjugacy
growth.
LOCATION:CMS\, MR13
CONTACT:Maurice Chiodo
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