the Salmon conjecture

The Salmon conjecture concerns the mathematical study of tensor decompositions—ways to break down complex multi-dimensional arrays into simpler components. It posits a precise characterization of the minimum rank (a measure of complexity) needed to represent certain tensors associated with algebraic structures. Confirming this conjecture helps deepen our understanding of the inherent complexity in multivariate data, with implications across algebra, geometry, and computational complexity. Essentially, it seeks to clarify the fundamental limits on simplifying these mathematical objects, guiding improvements in algorithms for data analysis, signal processing, and theoretical computer science.