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SUMMARY:Demi Allen (University of Bristol\, UK)
DTSTART:20210415T150000Z
DTEND:20210415T160000Z
DTSTAMP:20260422T225705Z
UID:OSUanalysis/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSUanalysis/
 1/">Dyadic approximation in the middle-third Cantor set</a>\nby Demi Allen
  (University of Bristol\, UK) as part of Analysis seminar OSU\n\n\nAbstrac
 t\nMotivated by a classical question due to Mahler\, in 2007 Levesley\, Sa
 lp\, and Velani showed that the Hausdorff measure of the set of points in 
 the middle-third Cantor set which can be approximated by triadic rationals
  (that is\, rationals which have denominators which are powers of 3) at a 
 given rate of approximation satisfies a zero-full dichotomy. More precisel
 y\, the Hausdorff measure of the set in question is either zero or full ac
 cording to\, respectively\, the convergence or divergence of a certain sum
  which is dependent on the specified rate of approximation. Naturally\, on
 e might also wonder what can be said about dyadic approximation in the mid
 dle-third Cantor set. That is\, how well can we approximate points in the 
 middle-third Cantor set by rationals which have denominators which are pow
 ers of 2? In this talk I will discuss a conjecture on this topic due to Ve
 lani\, some progress towards this conjecture\, and why dyadic approximatio
 n is harder than triadic approximation in the middle-third Cantor set. Thi
 s talk will be based on joint work with Sam Chow (Warwick) and Han Yu (Cam
 bridge).\n
LOCATION:https://researchseminars.org/talk/OSUanalysis/1/
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