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SUMMARY:Dzmitry Badziahin (University of Sydney)
DTSTART:20200916T100000Z
DTEND:20200916T110000Z
DTSTAMP:20260423T021437Z
UID:hnts/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/1/">Dio
 phantine approximation on the Veronese curve</a>\nby Dzmitry Badziahin (Un
 iversity of Sydney) as part of Heilbronn number theory seminar\n\n\nAbstra
 ct\nPLEASE NOTE THE UNUSUAL TIME\n\nIn the talk we discuss the set $S_n(\\
 lambda)$ of simultaneously $\\lambda$-well approximable points in $\\mathb
 b R^n$. That are the points $x$ such that the inequality $|| x - p/q||_\\i
 nfty < q^{-\\lambda - \\epsilon}$ has infinitely many solutions in rationa
 l points $p/q$. Investigating the intersection of this set with a suitable
  manifold comprises one of the most challenging problems in Diophantine ap
 proximation. It is known that the structure of this set\, especially for l
 arge $\\lambda$\, depends on the manifold. For some manifolds it may be em
 pty\, while for others it may have relatively large Hausdorff dimension. W
 e will concentrate on the case of the Veronese curve $V_n$. We discuss\, w
 hat is known about the Hausdorff dimension of the set $S_n(\\lambda) \\cap
  V_n$ and will talk about the recent joint results of the speaker and Buge
 aud which impose new bounds on that dimension.\n
LOCATION:https://researchseminars.org/talk/hnts/1/
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