# Mathematics Colloquia and Seminars

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### Deformations of Coxeter permutahedra and Coxeter submodular functions

**Algebra & Discrete Mathematics**

Speaker: | Federico Castillo, University of Kansas |

Location: | 2112 MSB |

Start time: | Mon, Mar 18 2019, 12:10PM |

One way to decompose a polytope is to represent it as a Minkowski of two other polytopes. These smaller pieces are naturally called summands. Starting from a polytope we want to explore the set of all summands. This set can be parametrized by a polyhedral cone, called deformation cone, in a suitable real vector space. We focus on the case where the starting polytope is a Coxeter permutahedron, which is a polytope naturally associated with a root system. This generalizes the type A case which correspond to generalized permutohedra. This is joint work with Federico Ardila, Chris Eur, and Alexander Postnikov.