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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, FranceAdd to your list(s) Download to your calendar using vCal - Marie-FranÃ§oise Roy (UniversitÃ© de Rennes 1)
- Wednesday 28 June 2017, 11:00-12:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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