BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vadim Semenov (NYU Courant) DTSTART:20230202T162000Z DTEND:20230202T172000Z DTSTAMP:20260422T070130Z UID:CJCS/108 DESCRIPTION:Title: T he Discrete Gauss Image Problem\nby Vadim Semenov (NYU Courant) as par t of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nThe Gauss I mage problem is a generalization to the question originally posed by Aleks androv who studied the existence of the convex body with the prescribed Al eksandrov's integral curvature. A simple discrete case of the Gauss Image Problem can be formulated as follows: given a finite set of directions in Euclidian space and the same number of unit vectors\, does there exist a c onvex polytope in this space containing the origin in its interior with ve rtices at given directions such that each normal cone at the vertex contai ns exactly one of the given vectors. In this talk\, we are going to discus s the discrete Gauss Image Problem\, and its relation to other Minkowski-t ype problems. Two different proofs of the problem are going to be addresse d: A smooth proof based on transportation polytopes and a discrete proof b ased on Helly’s theorem. Time permitting\, we will also discuss the uniq ueness statement for the problem.\n LOCATION:https://researchseminars.org/talk/CJCS/108/ END:VEVENT END:VCALENDAR