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SUMMARY:Homogeneous dynamics\, unitary representations\, and Diophantine e
 xponents - Nevo\, A (Technion - Israel Institute of Technology)
DTSTART:20140703T150000Z
DTEND:20140703T155000Z
UID:TALK53302@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We will describe an explicit quantitative form of the duality 
 principle in homogeneous dynamics. This allows the reduction of a diverse 
 set of quantitative equidistribution problems on homogeneous spaces G/H to
  the problem of giving explicit spectral bounds for the restriction of aut
 omorphic representations of G to the stability subgroup H. We will demonst
 rate this approach by deriving bounds for Diophantine approximation expone
 nt on homogeneous varieties\, a problem raised by Serge Lang already in 19
 65\, but which have seen little progress since then. The Diophantine expon
 ents we derive are in many cases best possible\, a remarkable fact that fo
 llows from an important and useful representation-theoretic phenomenon whi
 ch we will highlight. Based on Joint work with Alex Gorodnik (Bristol Univ
 ersity) and on joint work with Anish Ghosh (TIFR Mumbai) and Alex Gorodnik
 . \n\n
LOCATION:Seminar Room 1\, Newton Institute
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