FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

December 20, 18:00 ~ 18:20 - Room B11

## Degree Bounds in Rational Sums of Squares Representations on Curves

### Greg Blekherman

### Georgia Tech, USA - greg@math.gatech.edu

Let $X$ be a curve with dense real points. It is well-known that any polynomial $p$ nonnegative on $X$ can be written as a sum of squares of rational functions in the coordinate ring of $X$. I will present new degree bounds for these rational sums of squares representations, which depend on the Hilbert series of $X$ only. The bound can be shown to be tight in many instances. It is an open question whether the bound is tight for any curve $X$ with dense real points.

Joint work with Greg Smith (Queens University) and Mauricio Velasco (Universidad de los Andes).