BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Demi Allen (University of Bristol\, UK) DTSTART:20210415T150000Z DTEND:20210415T160000Z DTSTAMP:20260404T110741Z UID:OSUanalysis/1 DESCRIPTION:Title: Dyadic approximation in the middle-third Cantor set\nby Dem i Allen (University of Bristol\, UK) as part of Analysis seminar OSU\n\n\n Abstract\nMotivated by a classical question due to Mahler\, in 2007 Levesl ey\, Salp\, and Velani showed that the Hausdorff measure of the set of poi nts in the middle-third Cantor set which can be approximated by triadic ra tionals (that is\, rationals which have denominators which are powers of 3 ) at a given rate of approximation satisfies a zero-full dichotomy. More p recisely\, the Hausdorff measure of the set in question is either zero or full according to\, respectively\, the convergence or divergence of a cert ain sum which is dependent on the specified rate of approximation. Natural ly\, one might also wonder what can be said about dyadic approximation in the middle-third Cantor set. That is\, how well can we approximate points in the middle-third Cantor set by rationals which have denominators which are powers of 2? In this talk I will discuss a conjecture on this topic du e to Velani\, some progress towards this conjecture\, and why dyadic appro ximation is harder than triadic approximation in the middle-third Cantor s et. This talk will be based on joint work with Sam Chow (Warwick) and Han Yu (Cambridge).\n LOCATION:https://stable.researchseminars.org/talk/OSUanalysis/1/ END:VEVENT END:VCALENDAR