BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Bersudsky (Technion) DTSTART:20211209T171500Z DTEND:20211209T183000Z DTSTAMP:20260423T021858Z UID:NEDNT/37 DESCRIPTION:Title: O n the image in the torus of sparse points on expanding analytic curves \nby Michael Bersudsky (Technion) as part of New England Dynamics and Numb er Theory Seminar\n\nLecture held in Online.\n\nAbstract\nIt is known that the projection to the 2-torus of the normalised parameter measure on a ci rcle of radius $R$ in the plane becomes uniformly distributed as $R$ grows to infinity. I will discuss the following natural discrete analogue for t his problem. Starting from an angle and a sequence of radii {$R_n$} which diverges to infinity\, I will consider the projection to the 2-torus of th e n’th roots of unity rotated by this angle and dilated by a factor of $ R_n$. The interesting regime in this problem is when $R_n$ is much larger than n so that the dilated roots of unity appear sparsely on the dilated c ircle.I will discuss 3 types of results:\n\nValidity of equidistribution f or all angles when the sparsity is polynomial.\nFailure of equidistributio n for some super polynomial dilations.\nEquidistribution for almost all an gles for arbitrary dilations.\nI will discuss the above type of results in greater generality and I will try to explain how the theory of o-minimal structures is related to the proof.\n LOCATION:https://researchseminars.org/talk/NEDNT/37/ END:VEVENT END:VCALENDAR