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SUMMARY:Mishel Skenderi (Brandeis University)
DTSTART:20201023T161500Z
DTEND:20201023T173000Z
DTSTAMP:20260423T021347Z
UID:NEDNT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/6/">Sm
 all values at integer points of generic subhomogeneous functions</a>\nby M
 ishel Skenderi (Brandeis University) as part of New England Dynamics and N
 umber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis talk wil
 l be based on joint work with Dmitry Kleinbock that has been motivated by 
 several recent papers (among them\, those of Athreya-Margulis\, Bourgain\,
  Ghosh-Gorodnik-Nevo\, Kelmer-Yu). Given a certain sort of group $G$ and c
 ertain sorts of functions $f: \\mathbb{R}^n \\to \\mathbb{R}$ and $\\psi :
  \\mathbb{R}^n \\to \\mathbb{R}_{>0}\,$ we obtain necessary and sufficient
  conditions so that for Haar-almost every $g \\in G\,$ there exist infinit
 ely many (respectively\, finitely many) $v \\in \\mathbb{Z}^n$ for which $
 |(f \\circ g)(v)| \\leq \\psi(\\|v\\|)\,$ where $\\|\\cdot\\|$ is an arbit
 rary norm on $\\mathbb{R}^n.$ We also give a sufficient condition in the s
 etting of uniform approximation. As a consequence of our methods\, we obta
 in generalizations to the case of vector-valued (simultaneous) approximati
 on with no additional effort. In our work\, we use probabilistic results i
 n the geometry of numbers that go back several decades to the work of Sieg
 el\, Rogers\, and W. Schmidt\; these results have recently found new life 
 thanks to a 2009 paper of Athreya-Margulis.\n
LOCATION:https://researchseminars.org/talk/NEDNT/6/
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