Bruce Reznick

collaborators

3 papers

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…

math.NT2024

Sums of squares of k-term forms

Charu Goel, Bruce Reznick

In this paper we study the cones corresponding to sums of squares of $n$ -ary $d$ -ic forms with at most $k$ terms. We show that these are strictly nested as $k$ increases, leading t…