Sums of Squares: A Real Projective Story

Abstract

The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynomials and sums of squares on a real variety. We survey the rich history of this area and focus on recent developments highlighting unexpected links to complex algebraic geometry and commutative algebra.

arXiv commentto appear in the Notices of the AMS

References in corpus (2)

• Sums of squares and varieties of minimal degree
• An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem

Cited by in corpus (2)

• On the extreme rays of the cone of $3\times 3$ quasiconvex quadratic forms: Extremal determinats vs extremal and polyconvex forms
• Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems