Seminar:
Spring 2008, Fridays, Milner 317, 3:00–3:50 p.m.
(Joint with Algebraic Geometry on Monday!)



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 nonnegative 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.





