Abstract
Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the real-valued rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a multivariate Gaussian distribution, and find formulas that relate this average to problems in random matrix theory. This count is a specific instance of (average) Euclidean distance degrees of algebraic varieties, and I will briefly discuss other instances inspired by applications. The talk is based on joint work with Emil Horobet (arxiv:1408.3507) and with Horobet-Ottaviani-Sturmfels-Thomas (arxiv:1309.0049) and with Jasmijn Baaijens (arxiv:1405.0422).