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SUMMARY:Correspondences between harmonic functions and algebraic propertie
 s of groups. - Matthew Tointon (University of Cambridge)
DTSTART:20161021T124500Z
DTEND:20161021T140000Z
UID:TALK68560@talks.cam.ac.uk
CONTACT:Maurice Chiodo
DESCRIPTION:Let G be a group generated by a finite symmetric set S. By ana
 logy with harmonic functions on manifolds\, one can define the space H(G) 
 of harmonic functions on G with respect to S as consisting of those functi
 ons 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 conjectures rel
 ating certain properties of H(G) to certain algebraic properties of G. In 
 particular\, I will present a proof that H(G) is finite dimensional if and
  only if G is virtually cyclic. The proof uses functional analysis\, polyn
 omials on groups\, and random walks\, amongst other things.\n\nQuestions o
 f this type are to some extent motivated by Kleiner's proof of Gromov's po
 lynomial growth theorem.\n\nSome of the work I will discuss is joint with 
 Meyerovitch\, Perl and Yadin.
LOCATION:CMS\, MR13
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