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SUMMARY:Hyperbolic polynomials\, interlacers and sums of squares - Plauman
 n\, D (Universitt Konstanz)
DTSTART:20130719T083000Z
DTEND:20130719T090000Z
UID:TALK46296@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A real polynomial is hyperbolic if it defines a hypersurface c
 onsisting of maximally nested ovaloids. These polynomials appear in many a
 reas of mathematics\, including convex optimisation\, combinatorics and di
 fferential equations. We investigate the relation between a hyperbolic pol
 ynomial and the set of polynomials that interlace it. This set of interlac
 ers is a convex cone\, which we realize as a linear slice of the cone of n
 onnegative polynomials. We combine this with a sums-of-squares-relaxation 
 to approximate a hyperbolicity cone explicitly by the projection of a spec
 trahdedron. A multiaffine example coming from the Vmos matroid shows that 
 this relaxation is not always exact.\n
LOCATION:Seminar Room 1\, Newton Institute
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