Bruce Reznick

Sums of squares of polynomials in mathematics: past, present and future.

We will discuss the twin topics of positive polynomials and the representation of polynomials as a sum of squares as they weave through many different areas of mathematics, including algebra, algebraic geometry, analysis and number theory. We will cover the history of Hilbert's 17th problem and the current interest in implementing practical algorithms for writing positive polynomials as a sum of squares. No specialized background will be assumed.

reading:

A survey paper for the participants