BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Suxuan Chen (Ohio State) DTSTART:20251028T164500Z DTEND:20251028T174500Z DTSTAMP:20260423T022037Z UID:NEDNT/94 DESCRIPTION:Title: T he Hausdorff dimension of the intersection of \\psi-well approximable numb ers and self-similar sets\nby Suxuan Chen (Ohio State) as part of New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nA bstract\nLet \\psi be a monotonically non-increasing function from N to R\ , and let \\psi_v be defined by \\psi_v(q)=1/q^v. Here\, we consider self- similar sets whose iterated function systems satisfy the open set conditio n. For functions \\psi that do not decrease too rapidly\, we give a conjec turally sharp upper bound on the Hausdorff dimension of the intersection o f \\psi-well approximable numbers and such self-similar sets. When \\psi=\ \psi_v for some v greater than 1 and sufficiently close to 1\, we give a l ower bound for this Hausdorff dimension\, which asymptotically matches the upper bound as v approaches 1. In particular\, we show that the set of ve ry well approximable numbers has full Hausdorff dimension within self-simi lar sets.\n LOCATION:https://researchseminars.org/talk/NEDNT/94/ END:VEVENT END:VCALENDAR