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Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem

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abstract
It is a difficult problem to prove that a polynomial only takes non-negative values. One way to certify that a polynomial is non-negative is to express it as a sum of squares, however not all non-negative polynomials can be written as a sum of squares. The fundamental reason that there exist non-negative polynomials that cannot be written as sums of squares is that these polynomials satisfy linear inequalities that arise from linear relations known as the Cayley-Bacharach relations.
subject
Algebraic Geometry
Commutative Algebra
contributor
Henderson, Kenneth Terrell (author)
Moore, William F (committee chair)
Kirkman, Ellen (committee member)
Robinson, Stephen (committee member)
date
2016-05-21T08:35:49Z (accessioned)
2016-05-21T08:35:49Z (available)
2016 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/59310 (uri)
language
en (iso)
publisher
Wake Forest University
title
Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem
type
Thesis

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