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Mauricio Velasco (Universidad de los Andes, Bogotá): The geometry of SOS-multipliers on varieties

Ort: MPI für Mathematik in den Naturwissenschaften Leipzig,  , Videobroadcast

Video broadcast: Nonlinear Algebra Seminar Online (NASO) A homogeneous polynomial F admits an SOS-multiplier certificate on a real projective variety X if there exist sums of squares g and s such that Fg=s in the homogeneous coordinate ring of X. Such an expression certifies the nonnegativity of F and is thus of considerable theoretical and practical importance. In this talk I will present ongoing work with G. Blekherman, R. Sinn and G.G. Smith on the geometry of such nonnegativity certificates. Our main results are effective bounds on the degrees of possible g's on algebraic curves and surfaces which depend on classical geometric invariants of the varieties. These bounds are, in some cases, provably optimal.

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Beginn: 23. Februar 2021 17:45

Ende: 23. Februar 2021 18:30