Sums of Squares: a real projective story

Abstract: A multivariate real polynomial is nonnegative if its value at any real point is greater than or equal to zero. These special polynomials play a central role in many branches of mathematics including algebraic geometry, optimization theory, and dynamical systems. However, deciding whether a given polynomial is nonnegative is a hard problem. In this talk, we will review some general methods for certifying that a polynomial is nonnegative. We will then present optimal certificates in some important cases. This talk is based on joint work with Grigoriy Blekherman, Rainer Sinn, and Mauricio Velasco.

Mathematics

Audience: general audience

VCU Mathematics and Applied Mathematics Colloquium Series

Series comments: A series of public lectures in Mathematics and Applied Mathematics from Virginia Commonwealth University.

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Zoom Meeting ID: 822 7853 4531 Password: VCUMATH101