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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Homogeneous dynamics\, unitary representations\, a
nd Diophantine exponents - Nevo\, A (Technion - Is
rael Institute of Technology)
DTSTART;TZID=Europe/London:20140703T160000
DTEND;TZID=Europe/London:20140703T165000
UID:TALK53302AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53302
DESCRIPTION:We will describe an explicit quantitative form of
the duality principle in homogeneous dynamics. Thi
s allows the reduction of a diverse set of quantit
ative equidistribution problems on homogeneous spa
ces G/H to the problem of giving explicit spectral
bounds for the restriction of automorphic represe
ntations of G to the stability subgroup H. We will
demonstrate this approach by deriving bounds for
Diophantine approximation exponent on homogeneous
varieties\, a problem raised by Serge Lang already
in 1965\, but which have seen little progress sin
ce then. The Diophantine exponents we derive are i
n many cases best possible\, a remarkable fact tha
t follows from an important and useful representat
ion-theoretic phenomenon which we will highlight.
Based on Joint work with Alex Gorodnik (Bristol Un
iversity) and on joint work with Anish Ghosh (TIFR
Mumbai) and Alex Gorodnik. \n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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