The Geometry of Tensors - Carolina Araujo
Channel: ICTP Mathematics
Date: 2018-06-01

1 June 2018

Carolina Araujo (IMPA)

Abstract:
Tensors are fundamental objects in multilinear algebra, with important applications to the complexity of matrix multiplication, signal processing, phylogenetics and algebraic statistics. In applications, one generally looks for minimal decomposition of tensors as linear combinations of undecomposable tensors. The smallest integer r needed to write a tensor T as a linear combination of r undecomposable tensors is called the rank of T. Determining the rank of a tensor is a problem that has received much attention in recent years, and has a nice geometric interpretation.
In this talk I will explain some applications of tensors decomposition and interpret the problem from the point of view of algebraic geometry. In particular, I will present new results about ranks of tensors, in collaboration with Alex Massarenti and Rick Rischter.