BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gaurav Aggarwal (TIFR) DTSTART:20240307T171500Z DTEND:20240307T183000Z DTSTAMP:20260423T021859Z UID:NEDNT/71 DESCRIPTION:Title: J oint Equidistribution of Approximates\nby Gaurav Aggarwal (TIFR) as pa rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On line.\n\nAbstract\nThe distribution of integer points on varieties has occ upied mathematicians for centuries. In the 1950’s Linnik used an “ergo dic method” to prove the equidistribution of integer points on large sph eres under a congruence condition. As shown by Maaß\, this problem is clo sely related to modular forms. Subsequently\, there were spectacular devel opments both from the analytic as well as ergodic side. I will discuss a m ore refined problem\, namely the joint distribution of lattice points in c onjunction with other arithmetic data. An example of such data is the “s hape” of an associated lattice\, or in number theoretic language\, a Hee gner point. In a completely different direction\, a “Poincaré section ” is a classical and useful tool in ergodic theory and dynamical systems . Recently\, Shapira and Weiss\, constructed a Poincaré section for the g eodesic flow on the moduli space of lattices to study joint equidistributi on properties. Their work in fact is very general but crucially uses the f act that the acting group has rank one. In joint work with Anish Ghosh\, w e develop a new method to deal with actions of higher rank groups. I will explain this and\, if time permits\, some corollaries in Diophantine analy sis.\n LOCATION:https://researchseminars.org/talk/NEDNT/71/ END:VEVENT END:VCALENDAR