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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Effectivity and Complexity Results in Hilbert&\
;#39\;s 17th problem Marie-Fran&\;ccedil\
;oise Roy Universit&\;eacute\; de Rennes 1\, F
rance - Marie-Françoise Roy (Université de Rennes
1)
DTSTART;TZID=Europe/London:20170628T110000
DTEND;TZID=Europe/London:20170628T120000
UID:TALK73092AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/73092
DESCRIPTION:Hilbert 17th problem asks whether a polynomial tak
ing
 \; only non-negative
values is
a sum of squares (in the field of
 \; r
ational
functions). \; Its positive solutio
n around
1925 by Artin
 \; does not
make it
possible to construct the sum of square
s. Since
 \; then\, some
progress ma
de it possible to give such contructions and
 \; to bound the
degrees of the polynomia
ls appearing in the sum of
 \; squares.
An
explicit recent proof gives elementary recu
rsive degree
 \; bounds. The
method
of construction illustrates the current renewal
 \; of constructive
algebra.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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