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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Correspondences between harmonic functions and alg
ebraic properties of groups. - Matthew Tointon (Un
iversity of Cambridge)
DTSTART;TZID=Europe/London:20161021T134500
DTEND;TZID=Europe/London:20161021T150000
UID:TALK68560AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68560
DESCRIPTION:Let G be a group generated by a finite symmetric s
et S. By analogy with harmonic functions on manifo
lds\, one can define the space H(G) of harmonic fu
nctions on G with respect to S as consisting of th
ose functions f : G -> R for which f(x) is always
equal to the average of the values of f(xs) with s
in S.\n\nI will describe some results and conject
ures relating certain properties of H(G) to certai
n algebraic properties of G. In particular\, I wil
l present a proof that H(G) is finite dimensional
if and only if G is virtually cyclic. The proof us
es functional analysis\, polynomials on groups\, a
nd random walks\, amongst other things.\n\nQuestio
ns of this type are to some extent motivated by Kl
einer's proof of Gromov's polynomial growth theore
m.\n\nSome of the work I will discuss is joint wit
h Meyerovitch\, Perl and Yadin.
LOCATION:CMS\, MR13
CONTACT:Maurice Chiodo
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