Luca Sodomaco: Open problems on singular vector tuples of tensors and ED degrees of Segre­-Veronese varieties

Abstract

In the first part of the talk, we recall the definition and the main properties of singular vector tuples of partially symmetric tensors. We formalize their connection to the computation of the distance from a given tensor to the Segre-Veronese variety X of tensors of rank at most one. A measure of the complexity of this problem is furnished by the Euclidean Distance degree of X. In recent years, there has been remarkable progress on the subject, although several open questions remain unsolved. Some of them will be stated during the talk and are inspired by recent works with Ottaviani, Shahidi, Turatti, and Ventura.