Characteristic polynomials of tensors

We discuss one of the possible generalizations of the spectral theory of matrices to the tensor setting. Motivated by applications in hypergraph theory, we study the characteristic polynomial of a tensor and investigate the problem of recostructing a tensor from its eigenvalues. We focus on the setting of symmetric tensors, highlighting connections to intersection theory and projective geometry. This is based on joint work with Francesco Galuppi, Ettore Teixeira Turatti and Lorenzo Venturello.