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SUMMARY:Uniform Spectral Gaps and Paradoxical Decompositions: the Affine P
 lane - Lam Pham\, Yale University
DTSTART:20181121T134500Z
DTEND:20181121T144500Z
UID:TALK114061@talks.cam.ac.uk
CONTACT:Aled Walker
DESCRIPTION:It is well-known that the non-abelian free group on two genera
 tors is paradoxical using 4 pieces. More generally\, for a given space X\,
  an action of this group on X may be paradoxical. In this talk\, we will e
 xplain how paradoxical decompositions are directly related to spectral gap
 s for related unitary representations\, and how the number of pieces requi
 red in the paradoxical decompositions relates to the actual value of the s
 pectral gap. We will present some results on how to find paradoxical decom
 positions of the plane using affine transformations along with some applic
 ations to Kazhdan's Property (T).
LOCATION:MR5\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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