# Eva Philippe:Sweep polytopes and sweep oriented matroids

**Time: **
Wed 2021-09-29 10.15 - 11.15

**Location: **
Zoom meeting ID: 654 5562 3260

**Participating: **
Eva Philippe (Sorbonne Université)

Abstract: Consider a configuration of n labeled points in a Euclidean space. Any

linear functional gives an ordering of these points: an ordered

partition that we call a sweep, because we can imagine its parts as the

sets of points successively hit by a sweeping hyperplane. The set of all

such sweeps forms a poset which is isomorphic to a polytope, called the

sweep polytope.

I will present several constructions of the sweep polytope, related to

zonotopes, projections of permutahedra and monotone path polytopes of

zonotopes.

This structure can also be generalized in terms of oriented matroids.

For oriented matroids that admit a sweep oriented matroid, we gain

precision on the topological description of their poset of cellular

strings, refining a particular case of the Generalized Baues Problem.

This is joint work with Arnau Padrol.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260