Georgia Institute of Technology College of Sciences

There are many interesting classes of polynomials in real algebraic geometry that are of modern interest. A polynomial is nonnegative if it only takes nonnegative values on R^n. A univariate polynomial is real-rooted if all of its complex roots are real, and a hyperbolic polynomial is a multivariate generalization of a real-rooted polynomial. We will discuss connections between these two classes of polynomials. In particular, we will discuss recent ideas of Saunderson giving new ways of proving that a polynomial is nonnegative beyond showing that it is sum-of-squares.

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