# 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.