BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Asaf Katz (University of Michigan) DTSTART:20210426T161500Z DTEND:20210426T173000Z DTSTAMP:20260423T022037Z UID:NEDNT/23 DESCRIPTION:Title: A n application of Margulis’ inequality to effective equidistribution\ nby Asaf Katz (University of Michigan) as part of New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nRatner’s celebrated equidistribution theorem states that the trajectory of any poin t in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is h orospherical\, one can deduce an effective equidistribution result by mixi ng methods\, an idea that goes back to Margulis’ thesis. When the homoge neous space is non-compact\, one needs to impose further “diophantine co nditions” over the base point\, quantifying some recurrence rates\, in o rder to get a quantified equidistribution result. In the talk I will discu ss certain diophantine conditions\, and in particular I will show how a ne w Margulis’ type inequality for translates of horospherical orbits helps verify such conditions. This results in a quantified equidistribution res ult for a large class of points\, akin to the results of A. Strombreggson dealing with the \\textrm{SL}_2 case. In particular we deduce a fully effe ctive quantitative equidistribution for horospherical trajectories of latt ices defined over number fields\, without pertaining to the strong subspac e theorem.\n LOCATION:https://researchseminars.org/talk/NEDNT/23/ END:VEVENT END:VCALENDAR