BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julien Trevisan (Institut de Mathématiques de Jussieu) DTSTART:20220217T171500Z DTEND:20220217T183000Z DTSTAMP:20260423T021928Z UID:NEDNT/40 DESCRIPTION:Title: L imit laws in the lattice counting problem. The case of ellipses.\nby J ulien Trevisan (Institut de Mathématiques de Jussieu) as part of New Engl and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr act\nLet E be an ellipse centered around 0. We are interested in the asymp totic distribution\nof the error of the number of unimodular lattice point s that fall into tE when the lattice is random\nand when t goes to infinit y.\nBuilding on previous works by Bleher and by Fayad and Dolgopyat\, we s how that the error term\, when normalized by the square root of t\, conver ges in distribution towards an explicit distribution.\nFor this\, we first use harmonic analysis to reduce the study of the normalized error to the study of a Siegel transform that depends on t.\nThen\, and this is the key part of our proof\, we show that\, when t goes to infinity\, this last Si egel transform behaves in distribution as\, what we call\, a modified Sieg el transform with random weights. Such objects often appear in average cou nting problems.\nFinally\, we show that this last quantity converges almos t surely\, and we study the existence of the moments of its law.\nThis wor k was supervised by Bassam Fayad.\n LOCATION:https://researchseminars.org/talk/NEDNT/40/ END:VEVENT END:VCALENDAR