Hilbert's 17th Problem

Laura Phillips

Frank Adams 1,

Hilbert's 17th problem asks whether a polynomial in n variables over R^n
 that is non-negative on all of R^n can be written as the sum of squares of rational functions. In this seminar I'll present a (positive) solution to the problem and describe the wider context that it sits in. If there's time I'll talk about some of the more quantitative aspects of the problem and some variants.

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