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SUMMARY:Distribution of values of linear maps on quadratic surfaces. - Sar
 gent\, O (University of Bristol)
DTSTART:20140612T103000Z
DTEND:20140612T113000Z
UID:TALK52951@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We discuss the distribution of values of linear maps on quadra
 tic surfaces. The problem can be set up in the framework of unipotent dyna
 mics and then Ratner's Orbit Closure Theorem can be used to establish cond
 itions sufficient to ensure that the set of values is dense. We also indic
 ate how a quantitative version of this result follows from equidistributio
 n properties of unipotent flows on homogeneous spaces. A crucial ingredien
 t in the latter is a non-divergence result for certain spherical averages.
  In order to establish this result we show how one can use ideas of Y. Ben
 oist and J.F. Quint that were developed in the context of random walks on 
 homogeneous spaces.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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