Border rank under tensor product: geometry and complexity
- Fulvio Gesmundo (University of Copenhagen)
The border rank of a tensor generalizes the rank of a matrix and provides a measure of the complexity of the associated bilinear map. We present some recent results on the behaviour of border rank under two different notions of tensor product. The first one, the Segre product, offers a completely geometric framework; the second one, the Kronecker product, is related to the geometry of the matrix multiplication tensor. We highlight similarities and differences between the two settings.