Ranks and Simultaneous Ranks of Symmetric Tensors

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo - Sala Seminari 1
Ore: 9:30

Relatore:

• Emanuele Ventura (Texas A&M University)

Abstract:
A symmetric tensor can be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank of the symmetric tensor which are related by chains of inequalities.  We show how the study of the simultaneous symmetric rank of partial derivatives of the homogeneous polynomial associated to the symmetric tensor can used to prove equalities among different partially symmetric ranks.  We apply this to the special cases of binary forms, monomials, and elementary symmetric functions. This is joint work with F. Gesmundo and A. Oneto. 

Referenti: Edoardo Ballico e Alessandra Bernardi