Tensor network methods for computing the spectral norm of symmetric tensors

It is a classical fact that the sequence of powers of a symmetric matrix converges, up to scaling, to the orthogonal projection onto the eigenspace determined by its largest eigenvalue. We explore analogous statements for symmetric tensors, where the matrix powering operation is replaced by tensor contractions encoded by the combinatorics of a graph. I will discuss some positive and negative recent results in this direction. This is joint work with A. Uschmajew.