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SUMMARY:Hausdorff dimension estimates for bounded orbits on homogeneous sp
 aces of Lie groups - Kleinbock\, D (Brandeis University)
DTSTART:20140703T123000Z
DTEND:20140703T132000Z
UID:TALK53300@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:This work is motivated by studying badly approximable vectors\
 , that is\, ${f x}in {f R}^n$ such that $|q{f x} - {f p}| ge cq^{-1/n}
 $ for all ${f p}in {f Z}^n$\, $qin {f N}$. Computing the Hausdorff dime
 nsion of the set of such ${f x}$ for fixed $c$ is an open problem. I will
  present some estimates\, based on the interpretation of a badly approxima
 ble vector via a trajectory on the space of lattices\, and then use expone
 ntial mixing to estimate from above the dimension of points whose trajecto
 ries stay in a fixed compact set. Joint work with Ryan Broderick.\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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