University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Effectivity and Complexity Results in Hilbert's 17th problem Marie-Françoise Roy Université de Rennes 1, France

Effectivity and Complexity Results in Hilbert's 17th problem Marie-Françoise Roy Université de Rennes 1, France

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BPR - Big proof

Hilbert 17th problem asks whether a polynomial taking   only non-negative values is a sum of squares (in the field of   rational functions).  Its positive solution around 1925 by Artin   does not make it possible to construct the sum of squares. Since   then, some progress made it possible to give such contructions and   to bound the degrees of the polynomials appearing in the sum of   squares. An explicit recent proof gives elementary recursive degree   bounds. The method of construction illustrates the current renewal   of constructive algebra.



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