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Sum-of-squares proofs

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A polynomial that is a sum of squares of other polynomials can only take nonnegative values. This trivial observation is surprisingly powerful: many inequalities in mathematics have simple sum-of-squares proofs. I will discuss algorithms that can automatically search for sum-of-squares proofs for polynomial inequalities, and the extent to which they can be considered as “automatic proof machines”.

This talk is part of the Trinity Mathematical Society series.

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