# Pure Maths Colloquium: Kaie Kubjas

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Zoom 889 0436 9379 When: Feb 18 2021 @ 16.00 Video: Link (internal)
 Speaker: Kaie Kubjas Aalto University Title: Geometry of nonnegative rank

One of many definitions gives the rank of an $$m\times n$$ matrix $$M$$ as the smallest natural number such that M can be factorized as $$AB$$, where $$A$$ and $$B$$ are $$m\times r$$ and $$r\times n$$ matrices respectively. In many applications, one is interested in factorizations of a particular form. For example, factorizations with nonnegative entries define the nonnegative rank which is a notion that is used in data mining applications, statistics, complexity theory etc. Nonnegative rank has geometric characterizations using nested polytopes. I will give an overview how these nested polytopes are related to characterizations of the set of matrices of given nonnegative rank and uniqueness of nonnegative matrix factorizations.