4 problems

Let $n=\sum_{j=1}^k n_j$ and consider a $(k+1)$-tensor space $V$ of format $(n_1+1,\dots,n_k+1,n+2)$, with $T\in V$ a general tensor. Higher-factor defective-span conjecture. If…

Let $V=\mathbb{C}^{n_1+1}\otimes\dots\otimes\mathbb{C}^{n_k+1}\otimes\mathbb{C}^{n+2}$, where $n=\sum_{j=1}^k n_j$, and let $T\in V$ be a general tensor. Let $\alpha_T$ be the coho…

Let $G$ be a forest on vertex set $V=\\{1,\ldots,d\\}$, with each connected component a tree having at least three nodes, and let $A$ be its adjacency matrix. Let $\mathcal{V}_G$ b…

Gram locus conjecture. The Gram locus $\mathcal{G}(\mathcal{B})$ is given by