Emerging Applications of Algebraic Geometry

Volume 149 of the series The IMA Volumes in Mathematics and its Applications pp 271-324


Positivity and Sums of Squares: A Guide to Recent Results

  • Claus ScheidererAffiliated withFachbereich Mathematik und Statistik, Universität Konstanz Email author 

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This paper gives a survey, with detailed references to the literature, on recent developments in real algebra and geometry concerning the polarity between positivity and sums of squares. After a review of foundational material, the topics covered are Positiv- and Nichtnegativstellensatze, local rings, Pythagoras numbers, and applications to moment problems.

Key words

Positive polynomials sums of squares Positivstellensatze real algebraic geometry local rings moment problems