Tensor Decomposition, a link between Algebraic Geometry and Applications

Tensor Decomposition problems are playing a central role in a number of fields, ranging from pure mathematics to very applied sciences such as Telecommunications and Quantum Physics. In the first part of this talk we present some concrete examples from the applied world where tensor decomposition is crucial in solving problems of actual interest. In the second part, we review how algebraic geometry techniques, such as secant varieties and representation theory, provide powerful tools to tackle these problems.