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DTSTART:19810329T020000
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DTSTART:19961027T030000
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BEGIN:VEVENT
UID:news1299@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20220301T152844
DTSTART;TZID=Europe/Zurich:20220310T170000
SUMMARY:Number Theory Web Seminar: Dmitry Kleinbock (Brandeis University)
DESCRIPTION:Let $\\psi$ be a decreasing function defined on all large posit
 ive real numbers. We say that a real $m \\times n$ matrix $Y$ is "$\\psi$-
 Dirichlet" if for every sufficiently large real number $T$ there exist non
 -trivial integer vectors $(p\,q)$ satisfying $\\|Yq-p\\|^m < \\psi(T)$ and
  $\\|q\\|^n < T$ (where $\\|\\cdot\\|$ denotes the supremum norm on vector
 s). This generalizes the property of $Y$ being "Dirichlet improvable" whic
 h has been studied by several people\, starting with Davenport and Schmidt
  in 1969. I will present results giving sufficient conditions on $\\psi$ t
 o ensure that the set of $\\psi$-Dirichlet matrices has zero (resp.\, full
 ) measure. If time allows I will mention a geometric generalization of the
  set-up\, where the supremum norm is replaced by an arbitrary norm. Joint 
 work with Anurag Rao\, Andreas Strombergsson\, Nick Wadleigh and Shuchweng
  Yu.\\r\\nFor further information about the seminar\, please visit this we
 bpage [https://www.ntwebseminar.org/].
X-ALT-DESC:<p dir="ltr">Let $\\psi$ be a decreasing function defined on all
  large positive real numbers. We say that a real $m \\times n$ matrix $Y$ 
 is "$\\psi$-Dirichlet" if for every sufficiently large real number $T$ the
 re exist non-trivial integer vectors $(p\,q)$ satisfying $\\|Yq-p\\|^m &lt
 \; \\psi(T)$ and $\\|q\\|^n &lt\; T$ (where $\\|\\cdot\\|$ denotes the sup
 remum norm on vectors). This generalizes the property of $Y$ being "Dirich
 let improvable" which has been studied by several people\, starting with D
 avenport and Schmidt in 1969. I will present results giving sufficient con
 ditions on $\\psi$ to ensure that the set of $\\psi$-Dirichlet matrices ha
 s zero (resp.\, full) measure. If time allows I will mention a geometric g
 eneralization of the set-up\, where the supremum norm is replaced by an ar
 bitrary norm. Joint work with Anurag Rao\, Andreas Strombergsson\, Nick Wa
 dleigh and Shuchweng Yu.</p>\n<p>For further information about the seminar
 \, please visit this <a href="https://www.ntwebseminar.org/">webpage</a>.<
 /p>
DTEND;TZID=Europe/Zurich:20220310T180000
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