A famous theorem of Kruskal gives the simplest and arguably most fundamental criterion under which a tensor is guaranteed a unique minimum-rank decomposition. Kruskal's condition requires that the sum of the Kruskal ranks $\{k_i\}_{i=1}^m$ of the components satisfies $\sum_{i \in [m]} k_i \ge 2r + m - 1$, where $r$ ... more >>>

We study the question of explicitly constructing variety-evasive subspace families, a pseudorandom primitive introduced by Guo (Computational Complexity 2024) that generalizes both hitting sets and lossless rank condensers. Roughly speaking, a variety-evasive subspace family $\mathcal{H}$ is a collection of subspaces such that for every algebraic variety $V$ in a fixed ... more >>>

The problem of recognizing $(k,l)$-tight graphs is a fundamental problem that has close connections to well studied problems
like graph rigidity. The problem is better understood for planar graphs as compared to general graphs. For example, deterministic
NC-algorithms for the problem are known for planar graphs, but no such ... more >>>