16 jan 2019 -- 12:00
Sala Tricerri, DiMaI, Firenze
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 Pn, 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.