Abstract:
A tensor of order d is a d-dimensional array, so matrices are tensors of order 2. The notion of matrix rank generalizes to tensors of arbitrary order. In this talk I will discuss some applications of the tensor rank such as chemometrics and the complexity of matrix multiplication. I will also present other notions of rank and their applications. In particular, I will introduce the slice rank, the G-stable rank and their application to the cap set problem in additive number theory.