Border rank = rank for Kruskal tensors

Kruskal’s uniqueness theorem gives a simple criterion ensuring that a 3-way tensor admits a unique expression as a sum of r product tensors. This talk will present a geometric proof of Kruskal's theorem, and show that rank and border rank coincide for tensors which satisfy Kruskal's uniqueness condition. The talk will also serve as an introduction to the notions of tensor rank and border rank. We will briefly touch on applications of tensor rank decompositions in the sciences.