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SUMMARY:Nikolay Moshchevitin (Technion)
DTSTART:20240418T161500Z
DTEND:20240418T173000Z
DTSTAMP:20260423T021928Z
UID:NEDNT/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/74/">B
 ounded ratios and badly approximability</a>\nby Nikolay Moshchevitin (Tech
 nion) as part of New England Dynamics and Number Theory Seminar\n\nLecture
  held in Online.\n\nAbstract\nWe will discuss relatively new criteria of b
 adly approximability in terms of ratios of best approximations. Let qν be
  convergents of continued fractions to real irrational α. It is well know
 n that\n\nα is badly approximable   iff   supν qν+1/qν is finite 
   iff   infν||qν+1α||/||qνα||>0.\n\nWe will discuss how this prop
 erty may be generalised to Diophantine Approximation in higher dimensions.
  The answer seems to be rather non-trivial. Some of the related properties
  may be expressed in terms of Parametric Geometry of Numbers recently deve
 loped by Schmidt\, Summerer\, Roy and the others. Also we discuss some pro
 perties of ratios under the consideration in accordance with the study of 
 multidimensional Dirichlet spectra.\n
LOCATION:https://researchseminars.org/talk/NEDNT/74/
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