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SUMMARY:Osama Khalil (University of Utah)
DTSTART:20200615T140000Z
DTEND:20200615T150000Z
DTSTAMP:20260423T041341Z
UID:HSPETDS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HSPETDS/14/"
 >Singular Vectors on Fractals and Homogeneous Flows</a>\nby Osama Khalil (
 University of Utah) as part of Horowitz seminar on probability\, ergodic t
 heory and dynamical systems\n\n\nAbstract\nThe theory of Diophantine appro
 ximation is underpinned by Dirichlet’s fundamental theorem. Broadly spea
 king\, the main questions in the theory concern quantifying the prevalence
  of points with exceptional behavior with respect to Dirichlet’s result.
  The work of Dani and Kleinbock-Margulis connects these questions to the r
 ecurrence behavior of certain flows on homogeneous spaces. For example\, d
 ivergent orbits of such flows correspond to so-called singular vectors. Af
 ter a brief overview of the subject and the motivating questions\, I will 
 discuss new results giving a sharp upper bound on the Hausdorff dimension 
 of divergent orbits of certain diagonal flows emanating from fractals on t
 he space of unimodular lattices. Time permitting\, connections to the theo
 ry of projections of self-similar measures will be presented.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/14/
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