BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mikolaj Fraczyk (University of Chicago) DTSTART:20220414T161500Z DTEND:20220414T173000Z DTSTAMP:20260423T021927Z UID:NEDNT/47 DESCRIPTION:Title: T hin part of the arithmetic orbifolds\nby Mikolaj Fraczyk (University o f Chicago) as part of New England Dynamics and Number Theory Seminar\n\nLe cture held in Online.\n\nAbstract\nLet X be a symmetric space. The collar lemma\, also known as the Margulis lemma\, says that there exists an epsil on=epsilon(X)\, such that the epsilon-thin part of a locally symmetric spa ce X/\\Gamma looks locally like a quotient by a virtually unipotent subgro up. It turns out that in the arithmetic setting we can improve this lemma by making the epsilon grow linearly in the degree of the number filed gene rated by the traces of elements of \\Gamma. I will explain why this is the case and present several applications\, including the proof of the fact t hat an arithmetic locally symmetric manifold M is homotopy equivalent to a simplicial complex of size bounded linearly in the volume of M and degree s of all vertices bounded uniformly in terms of X. Based on a joint work w ith Sebastian Hurtado and Jean Raimbault.\n LOCATION:https://researchseminars.org/talk/NEDNT/47/ END:VEVENT END:VCALENDAR