## Geometry Seminar

Date: September 25, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: F. Gesmundo, Copenhagen

Title: On multiplicativity of various notions of rank

Abstract: Matrix rank has several different generalizations to the setting of tensors. Whereas for matrices it is easy to show that rank is multiplicative over tensor product (the matrix Kronecker product), multiplicativity is not straightforward (and in most cases false) in the setting of tensors. We discuss this problem for various notions of rank: tensor rank, partially symmetric tensor rank and tensor border rank in particular. The geometric framework allows for further generalizations, that we briefly present.