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SUMMARY:Seonhee Lim (Seoul National University)
DTSTART:20210512T100000Z
DTEND:20210512T110000Z
DTSTAMP:20260423T024744Z
UID:hnts/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/31/">Ef
 fective Hausdorff dimension of bad sets</a>\nby Seonhee Lim (Seoul Nationa
 l University) as part of Heilbronn number theory seminar\n\n\nAbstract\n**
 NOTE THE UNUSUAL TIME**\n\nIn this talk\, we consider the inhomogeneous Di
 ophantine approximation: the distribution of $qa$ modulo integers near a t
 arget real $b$ (for integer $q$ and a real $a$)\, or more generally $Aq$ m
 odulo integral vectors near a target vector $b$ (where $q$ is an integer v
 ector\, and $A$ is a real matrix). We prove that for all $b$\, the Hausdor
 ff dimension of the set of matrices that are epsilon badly approximable fo
 r the target $b$ is not full\, with an effective upper bound. We also give
  an effective bound on the dimension of the set of targets badly approxima
 ted by $Aq$ in terms of epsilon\, if the matrix $A$ is not singular on ave
 rage. The main part of the talk is joint work with Taehyeong Kim and Wooye
 on Kim.\n
LOCATION:https://researchseminars.org/talk/hnts/31/
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