Bruce Reznick

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math.AG2026

Stubborn Polynomials

Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3

The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} $f$ on a real variety $X$ …

math.AG2024

On odd powers of nonnegative polynomials that are not sums of squares

Grigoriy Blekherman, Khazhgali Kozhasov, Bruce Reznick

We initiate a systematic study of nonnegative polynomials $P$ such that $P^{k}$ is not a sum of squares for any odd $k \geq 1$ , calling such $P$ \emph{stubborn}. We develop a new inva…