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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
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.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons