BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Akshat Das (University of Houston) DTSTART:20220203T171500Z DTEND:20220203T183000Z DTSTAMP:20260423T021929Z UID:NEDNT/38 DESCRIPTION:Title: A n adelic version of the three gap theorem\nby Akshat Das (University o f Houston) as part of New England Dynamics and Number Theory Seminar\n\nLe cture held in Online.\n\nAbstract\nIn order to understand problems in dyna mics which are sensitive to arithmetic properties of return times to regio ns\, it is desirable to generalize classical results about rotations on th e circle to the setting of rotations on adelic tori. One such result is th e classical three gap theorem\, which is also referred to as the three dis tance theorem and as the Steinhaus problem. It states that\, for any real number\, a\, and positive integer\, N\, the collection of points na mod 1\ , where n runs from 1 to N\, partitions the circle into component arcs ha ving one of at most three distinct lengths. Since the 1950s\, when this th eorem was first proved independently by multiple authors\, it has been rep roved numerous times and generalized in many ways. One of the more recent proofs has been given by Marklof and Strömbergsson using a lattice based approach to gaps problems in Diophantine approximation. In this talk\, we use an adaptation of this approach to the adeles to prove a natural genera lization of the classical three gap theorem for rotations on adelic tori. This is joint work with Alan Haynes.\n LOCATION:https://researchseminars.org/talk/NEDNT/38/ END:VEVENT END:VCALENDAR