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Texas A&M University

Student/Postdoc Working Geometry Seminar

Date: January 20, 2021

Time: 10:00AM - 11:00AM

Location: zoom

Speaker: A. Casarotti, Ferrara


Title: Defectiveness and Identifiability: a geometric point of view on tensor analysis

Abstract: Identifiability problems arise naturally in many fields of mathematics, from the abstract world of birational geometry to the applied setup of tensor analysis. In this talk we link the identifiability property for a variety X to its secant behavior and the geometry of the tangential contact loci. In the first part, after reviewing the main properties of the tangential contact locus associated to h general points of X, we give a numerical bound under which the non h-secant defectiveness ensures the h-identifiability, with h subgeneric. Note that this result is of birational nature and so does not strictly depend on the geometry of the particular tensor variety we choose. Finally we apply our result to many classes of varieties which play a central role in tensor analysis. In the second part we move on the generic rank case, where a clever use of the infinitesimal Bertini's theorem and an implementation of Noether-Fano's inequalities enable us to link the generic identifiability with the infinitesimal tangential contact locus. This finally shows the non generic identifiability for many partially symmetric tensors satisfying a mild numerical bound on their dimensions and degrees