Schur apolarity and how to use it

Venue: The event will take in presence only for the Phd student and part of the commission and online through the ZOOM platform. To get the access codes please contact the secretary office (phd.maths [at] unitn.it)
Time: 14.00

Reynaldo Staffolani - PhD in Mathematics, University of Trento

Abstract:
Structured tensors are mutilinear objects that satisfy specific symmetry relations. The aim of the thesis is to investigate the tensor decomposition of such objects in terms of elementary tensors which are naturally parametrized by points of SL(n)-rational homogeneous varieties. This set of varieties includes also Veronese varieties (symmetric tensors), Grassmann varieties (skew-symmetric tensors), and flag varieties. Symmetric tensors have been classically studied using the apolarity theory. An analogous skew-symmetric apolarity theory for skew-symmetric tensors has been developed only few years ago. In this talk we introduce the Schur apolarity theory, which is a general apolarity theory suitable for structured tensors related to SL(n)-irreducible representations. The key result called Schur apolarity lemma, that links a decomposition of a tensor to an inclusion of ideals, is also presented.

Supervisor: Alessandra Bernardi