March 17

Bruce Reznick ( UIUC )

On Hilbert's construction of positive polynomials which are not a sum of squares

Abstract: In 1888, Hilbert described how to find real polynomials which take only non-negative values, but are not a sum of squares of polynomials. His construction was so restrictive that no examples appeared until the 1960s, under a variation of his original plan. We revisit and generalize Hilbert's original construction and show how the underlying mechanism can be simplified and generalized.