Abstract

Tensors and their ranks play a central role in mathematics, physics and computer science: from constructing fast matrix multiplication algorithms, to understanding entanglement in quantum physics, to the study of combinatorial structures in discrete mathematics. Despite tremendous interest, much is still unknown.

We will give a brief introduction to tensors and their applications, building on Strassen's pioneering perspective developed in his quest to understand the complexity of matrix multiplication. We will then focus on the study of the asymptotic behaviour of tensors via asymptotic spectrum duality and via techniques from representation theory (Schur-Weyl duality and moment polytopes). We will survey recent results in this direction (in particular explicit computation of moment polytopes), and discuss open problems.

Video Recording