Date: Friday, March 01, 2013
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Thrifty approximations of convex bodies by polytopes
Abstract: Given a ddimensional convex body C containing the origin in its interior and a real t>1, we seek to construct a polytope P with as few vertices as possible such that P is contained in C and C is contained in tP. I plan to present a construction which breaks some longheld records and is nearly optimal for a vide range of parameters d and t. The construction uses the maximum volume ellipsoid, the John decomposition of the identity and its recent sparsification by Batson, Spielman and Srivastava, Chebyshev polynomials, and some tensor algebra.
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Speaker: Alexander Barvinok
Institution: University of Michigan
Event Organizer: Sergey Fomin
