BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nimish Shah DTSTART:20210811T134000Z DTEND:20210811T141000Z DTSTAMP:20260417T010117Z UID:MSR80/16 DESCRIPTION:Title: S harp conditions for equidistribution of translates of a subspace of a horo sphere by a diagonal flow in the space of unimodular lattices\nby Nimi sh Shah as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nWe consider the action of the one-parameter subgroup $a(t) = \\text{exp}((n-1)t\, -t\, \\ldots\, -t)$ of\nSL(n\,R) on the space X of unimodular lattices in $R^n$. Let C be an analytic curve on the expanding\nhorosphere of a(t) in X through the standard lattice $Z^n$ . Let μ be a smooth probability measure on\nC. We describe necessary and sufficient conditions\, in terms of Diophantine approximation and\nalgebra ic number fields\, on the smallest affine subspace containing C so that th e translated\nmeasures a(t)μ get equidistributed in X as $t \\rightarrow \\infty$. This generalizes my earlier result showing equidistribution of t ranslates of curves not contained in proper affine subspaces. The result a nswers a question of Davenport and Schmidt on non-improvability of Dirichl et’s approximation.\n[The case of n = 3 is a joint work with D. Kleinboc k\, N. DeSaxe\, and P. Yang\; and the general case is a joint work with P. Yang.]\n LOCATION:https://researchseminars.org/talk/MSR80/16/ END:VEVENT END:VCALENDAR