Speaker: Joseph Gubeladze, San Francisco State University, USA.
Date/Time: 4 March 2022, 7:30pm IST/ 2:00pm GMT / 9:00am ET (joining time
7:15pm IST).
Gmeet link: meet.google.com/xcw-ukrb-rtw
Title: Normal polytopes and ellispoids.
Abstract: Lattice polytopes are the combinatorial backbone of toric
varieties. Many important properties of these varieties admit purely
combinatorial description in terms of the underlying polytopes. These
include normality and projective normality. On the other hand, there are
geometric properties 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 talk we present the following recent results:
(1) unimodular simplices in a lattice 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 ellipsoid in R^3 has a unimodular cover,
and (3) for every d at least 5, there are ellipsoids in R^d, such that the
convex hulls of the lattice points in these ellipsoids are not even
normal. Part (3) answers a question of Bruns, Michalek, and the speaker.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar