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SUMMARY:Dorsa Hatefi (University of Oxford\, University of York)
DTSTART:20260922T120000Z
DTEND:20260922T130000Z
DTSTAMP:20260915T102149Z
UID:OWNS/170
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/170/">H
 ausdorff dimension of differences of badly approximable sets</a>\nby Dorsa
  Hatefi (University of Oxford\, University of York) as part of One World N
 umeration seminar\n\n\nAbstract\nThe set of badly approximable numbers (re
 al numbers with bounded continued fraction partial quotients)\, denoted by
  $\\mathbf{Bad}$\, has zero Lebesgue measure yet full Hausdorff dimension.
  In fact\, it satisfies the stronger property of being a winning set in th
 e sense of Schmidt’s game. The inhomogeneously badly approximable set\, 
 $\\mathbf{Bad}^\\gamma$\, is also known to have full Hausdorff dimension. 
 In this talk\, we revisit these classical notions and proceed to prove tha
 t the set difference $\\mathbf{Bad}^\\gamma \\setminus \\mathbf{Bad}$ like
 wise has full Hausdorff dimension. Our proof relies on the dynamical inter
 pretation of the problem on the space of unimodular grids and introduces a
  new variant of Schmidt’s game\, the rapid game.\n
LOCATION:https://researchseminars.org/talk/OWNS/170/
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