BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiyoung Han (TIFR) DTSTART:20220210T171500Z DTEND:20220210T183000Z DTSTAMP:20260423T021828Z UID:NEDNT/39 DESCRIPTION:Title: T he asymptotic distribution of the joint values of the integral lattice poi nts for a system of a quadratic form and a linear form\nby Jiyoung Han (TIFR) as part of New England Dynamics and Number Theory Seminar\n\nLectu re held in Online.\n\nAbstract\nLet Q be a quadratic form and let L be a l inear form on the n-dimensional real vector space. We are interested in th e distribution of the image of the integral lattice under the map (Q\, L). Developing the celebrated work of Eskin\, Margulis\, and Mozes in 1998\, we provide the conditions of systems of forms which satisfy that the numbe r of integral vectors in the ball of radius T whose joint values are conta ined in a given bounded set converges asymptotically to the volume of the region given by the level sets of the quadratic form and the linear form\, intersecting with the ball of radius T\, as T goes to infinity. This cond ition is introduced by Gorodnik in 2004.\nFor this\, we need to classify a ll intermediate subgroups between the special orthogonal group preserving Q and L and the special linear group. Among them\, only two closed subgrou ps are of our concern. We will introduce Siegel integral formulas and equi distribution theorems for each subgroup\, and show how to reach our main t heorem. This is joint work with Seonhee Lim and Keivan Mallahi-Karai.\n LOCATION:https://researchseminars.org/talk/NEDNT/39/ END:VEVENT END:VCALENDAR