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

Presented by: 
Marie-Françoise Roy Université de Rennes 1, Université de Rennes 1
Date: 
Wednesday 28th June 2017 - 11:00 to 12:00
Venue: 
INI Seminar Room 2
Abstract: 
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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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons