6 problems

Let $\mathcal{L}_2^S\subset\mathbb{C}^{m\times m}$ be the variety of square matrices of rank at most $2$ with zero pattern $S=\{(1,1),\ldots,(s,s)\}$ for some $s\ge2$. Quadratic-gr…

Let $\mathcal{L}_2^S\subset\mathbb{C}^{m\times n}$ be the variety of matrices of rank at most $2$ with diagonal zero pattern $S=\{(1,1),\ldots,(s,s)\}$, where $s\in[4]$, and set…

Assume that $\mathcal{L}_r^S$ is irreducible. Let $I\subset[n]$ satisfy $|I|=m$, and let $X_{[m],I}$ and $U_{[m],I}$ denote the corresponding $m\times m$ submatrices; write…

Consider the overlapping Hankel block low-rank completion problem, with matrix-size parameter $N$, and let $\hat{X}$ denote a candidate completed matrix. Quadratic-time completion…

Let $M\times M$ 2D mesh graphs be graphs with the corresponding vertex sets $\mathbb{V}_\mathbb{G}$, and let a Hamiltonian path be a path $\mathbb{P}$ visiting every vertex exactly…

Let $(A,\mathbb{G})$ be a GIRS-$c$ pair, and let $\mathbb{V}_\mathbb{G}$ denote the vertex set of $\mathbb{G}$. A DV representation is a representation with rank parameters $r_i$ i…