5 problems

Simultaneous Waring identifiability conjecture. The polynomial vector admits a unique simultaneous Waring decomposition with

Let $d\ge3$ and $n_1\ge n_2\ge\cdots\ge n_d\ge2$. Let $\mathcal S=\operatorname{Seg}(\mathbb P\mathbb C^{n_1}\times\cdots\times\mathbb P\mathbb C^{n_d})$ be the Segre variety in…

Let $d \ge 3$ and $n_1 \ge \cdots \ge n_d \ge 2$. Let $\mathcal{S}_{\mathbb{F}}=\operatorname{Seg}(\mathbb{P}\mathbb{F}^{n_1}\times\cdots\times\mathbb{P}\mathbb{F}^{n_d})$ be the S…

Chiantini–Ottaviani–Vannieuwenhoven conjecture. $\mathcal{S}_\mathbb{C}$ is generically $r$-identifiable if

Identifiability conjecture. For all such $m$ and $k$, the binary Segre product $({\mathbb{P}}^1)^m$ is $k$-identifiable.