Singular t-ples of tensors and their geometry

Abstract: There is a natural invariant metric on the space of tensors, called Frobenius metric. In optimization setting one considers the (complex) critical points on the Segre variety of the distance function from a given tensor, they are called singular t-ples, among them there is the best rank one approximation. Their number is the EDdegree of the Segre variety. The geometry of the critical points is appealing, since they lie in a linear space called critical space, which has dimension smaller than the number of critical points, in other words the critical points are linearly dependent, unless the matrix case. We expose some properties of singular t-ples. In a following talk Emanuele Ventura will lecture about the asymptotic behaviour of EDdegree and other more advanced properties.

Mathematics

Audience: researchers in the topic

Comments: Applied Algebraic Geometry 2020-2021: web.math.unifi.it/gruppi/algebraic-geometry/AppliedAlgebraicGeometry20202021.html

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.