Bounds on the number of connected components for tropical prevarieties

For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−

Eigenvectors of tensors - A primer

We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their discussion. The intent is to give practitioners an overview of fundamental notions, results and techniques