MATH Seminar

Title: Nonnegative Polynomials and Sums of Squares
Seminar: Algebra and Number Theory
Speaker: Greg Blehkerman of Georgia Tech
Contact: Vicki Powers, vicki@mathcs.emory.edu
Date: 2011-09-20 at 3:00PM
Venue: MSC E406
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Abstract: A multivariate real polynomial $p$ is nonnegative if $p(x)$ is at least $0$ for all $x \in \mathbb{R}^n$. I will review the history and motivation behind the problem of representing nonnegative polynomials as sums of squares. Such representations are of interest for both theoretical and practical computational reasons. However, much about the relationship between nonnegative polynomials and sums of squares remains unknown. I will present some recent results which establish links between nonnegative polynomials, sums of squares and classical algebraic geometry. In the smallest cases where there exist nonnegative polynomials that are not sums of squares I will describe a complete classification of the differences between these sets.