Seminar Algebra and Geometry: Jan Draisma (Bern)

Orthogonal tensor decomposition from an algebraic perspective

Every real or complex matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense. Higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention from theoretical computer science and scientific computing. Complementing this existing literature, I will present an algebro-geometric analysis of the set of orthogonally decomposable tensors. This analysis features a surprising connection between orthogonally decomposable tensors and semisimple algebras---associative in the case of ordinary or symmetric tensors, and of compact Lie type in the case of alternating tensors.
(Joint work with Ada Boralevi, Emil Horobet, and Elina Robeva.)

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