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. To this end, we will examine the contraction variety of a tensor, an invariant central to the proof. The talk will also serve as an introduction to the notions of tensor rank and border rank.