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Daily Overview |
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RAG3: Real Algebraic Geometry Location: M629 Session Chair: Daniel Plaumann Session Chair: Claus Scheiderer | |
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Spectrahedral Relaxations of Rigidly Convex Sets TU Dresden, Germany A multivariate polynomial with real coefficients is called real zero if it has only real zeros along each line through the origin and does not vanish at the origin. The Euclidean closure of the connected component of the non-vanishing set of a real zero polynomial containing the origin is called a rigidly convex set. These convex sets generalize spectrahedra. It is not known whether all rigidly convex sets are spectrahedra; this is known as the Generalized Lax Conjecture. We introduce a nested hierarchy of spectrahedra that relaxes a given rigidly convex set. We do this by adapting another spectrahedral relaxation developed by Schweighofer and by using an approximation result due to Fang and Fawzi. If a real zero polynomial has only two variables, our hierarchy of relaxations converges to the rigidly convex set of that real zero polynomial. | |
