16 jan 2019 -- 12:00

Sala Tricerri, DiMaI, Firenze

**Abstract.**

In the first part of this talk, we outline the main properties of the ED polynomial of a real algebraic variety, where ED stands for "Euclidean Distance". Then we focus on the ED polynomial of the dual of the d-th Veronese variety of P^{n,} showing its close relationship with the spectral theory of symmetric tensors. In particular, we investigate its lowest and highest coefficients and their corresponding vanishing loci. The main result is a closed formula for the product of the Euclidean eigenvalues of a symmetric tensor, which generalizes the known fact that the determinant of a symmetric matrix is the product of its eigenvalues.