BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesco Cellarosi (Queen’s University (Canada)) DTSTART:20200528T150000Z DTEND:20200528T160000Z DTSTAMP:20260423T023052Z UID:DinAmicI/3 DESCRIPTION:Title: Rational Horocycle lifts and the tails of Quadratic Weyl sums\nby Fra ncesco Cellarosi (Queen’s University (Canada)) as part of DinAmicI: Anot her Internet Seminar\n\n\nAbstract\nEquidistribution of horocycles on hype rbolic surfaces has been used to dynamically answer several probabilistic questions about number-theoretical objects. In this talk we focus on horoc ycle lifts\, i.e. curves on higher-dimensional manifolds whose projection to the hyperbolic surface is a classical horocycle\, and their behaviour u nder the action of the geodesic flow. It is known that when such horocycle lifts are `generic’\, then their push forward via the geodesic flow bec omes equidistributed in the ambient manifold. We consider certain ‘non-g eneric’ (i.e. rational) horocycle lifts\, in which case the equidistribu tion takes place on a sub-manifold. We then use this fact to study the tai l distribution of quadratic Weyl sums when one of their arguments is rando m and the other is rational. In this case we obtain random variables with heavy tails\, all of which only possess moments of order less than 4. Depe nding on the rational argument\, we establish the exact tail decay\, which can be described with the help of the Dedekind $\\psi$-function.\n\nJoint work with Tariq Osman.\n\nZoom link: https://unipd.zoom.us/j/91625758001? pwd=NzU1SG5LZkxKVTI5SXBsSUpNUW5XQT09\n LOCATION:https://researchseminars.org/talk/DinAmicI/3/ END:VEVENT END:VCALENDAR