Effectivity and Complexity Results in Hilbert's 17th problem Marie-Françoise Roy Université de Rennes 1, France
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About this item
| Description: |
Roy, M
Wednesday 28th June 2017 - 11:00 to 12:00 |
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| Created: | 2017-07-20 13:05 |
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| Collection: | Big proof |
| Publisher: | Isaac Newton Institute |
| Copyright: | Roy, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| 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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