BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Han Zhang (Souchow University) DTSTART:20250211T171500Z DTEND:20250211T183000Z DTSTAMP:20260423T021928Z UID:NEDNT/83 DESCRIPTION:Title: K hintchine’s theorem on self-similar measures on the real line\nby Ha n Zhang (Souchow University) as part of New England Dynamics and Number Th eory Seminar\n\nLecture held in Online.\n\nAbstract\nIn 1984\, Mahler prop osed the following question on Diophantine approximation : How close can i rrational numbers in the middle-thirds Cantor set be approximated by ratio nal numbers? One way to reformulate Mahler’s question is to ask if Khin tchine’s theorem extends to the middle-thirds Cantor set. In a joint wor k with Timothée Bénard and Weikun He\, we prove that Khintchine’s theo rem holds for any self-similar measures on the real line. In particular th is applies to the Hausdorff measure on the middle-thirds Cantor set. Our r esult generalizes the recent breakthrough work of Khalil-Luethi in dimensi on one. Our proof is inspired by the work of Bénard-He regarding the semi simple random walks on homogeneous spaces.\n LOCATION:https://researchseminars.org/talk/NEDNT/83/ END:VEVENT END:VCALENDAR