Pure Math Dept Colloquium

Gregory G. Smith, Queen's University

Sums of Squares and Projective Geometry

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, it is very difficult, in general, to decide whether a given polynomial is nonnegative.  In this talk, we will review some classical methods for certifying that a polynomial is nonnegative.  We will then present novel certificates in some important cases. This talk is based on joint work with Grigoriy Blekherman, Rainer Sinn, and Mauricio Velasco.

MC 5501