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SUMMARY:Equations in virtually nilpotent groups - Motiejus Valiunas\, Univ
 ersity of Southampton
DTSTART:20171103T150000Z
DTEND:20171103T160000Z
UID:TALK87461@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:Given an equation in a group\, one may ask what is the probabi
 lity that randomly chosen elements will satisfy it. Although a priori this
  question only makes sense for finite groups\, one may generalise it to th
 e family of amenable groups\, as they are endowed with a measure that assi
 gns 'size' to any subset. In fact\, they often possess many measures\, and
  the size of a subset might depend on the choice of a measure. In the talk
  I will consider a particular subfamily of discrete amenable groups - fini
 tely generated virtually nilpotent groups - computations in which can be d
 escribed by a finite set of polynomials. I will explain why the size of th
 e solution set of a given equation in such a group does not depend on the 
 measure chosen.\nThis is joint work with Yago Antolin\, Armando Martino an
 d Enric Ventura.
LOCATION:CMS\, MR14
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