BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joseph Gubeladze (San Francisco State University) DTSTART:20220304T140000Z DTEND:20220304T150000Z DTSTAMP:20260423T021032Z UID:VCAS/124 DESCRIPTION:Title: N ormal polytopes and ellispoids\nby Joseph Gubeladze (San Francisco Sta te University) as part of IIT Bombay Virtual Commutative Algebra Seminar\n \n\nAbstract\nLattice polytopes are the combinatorial backbone of toric va rieties. Many important properties of these varieties admit purely combina torial description in terms of the underlying polytopes. These include nor mality and projective normality. On the other hand\, there are geometric p roperties of polytopes of integer programming/discrete optimization origin \, which can be used to deduce the aforementioned combinatorial properties : existence of unimodular triangulations or unimodular covers. In this tal k we present the following recent results: (1) unimodular simplices in a l attice 3-polytope cover a neighborhood of the boundary if and only if the polytope is very ample\, (2) the convex hull of lattice points in every el lipsoid in R^3 has a unimodular cover\, and (3) for every d at least 5\, t here are ellipsoids in R^d\, such that the convex hulls of the lattice poi nts in these ellipsoids are not even normal. Part (3) answers a question o f Bruns\, Michalek\, and the speaker.\nChaiperson - Siamak Yassemi\n LOCATION:https://researchseminars.org/talk/VCAS/124/ END:VEVENT END:VCALENDAR