Monday 10 November 2025
15:00–16:30*

Lukas Kühne (Bielefeld University) — Alcoved Polytopes and Arrangements

Alcoved polytopes are characterized by the property that all facet normal directions are parallel to the roots e_i - e_j. This fundamental class of polytopes appears in several applications such as optimization, tropical geometry or physics. Symmetric alcoved polytopes are dual to the fundamental polytopes attached to finite metric spaces.

This talk focuses on the type fan of alcoved polytopes which is the subdivision of the metric cone by combinatorial types of alcoved polytopes. The type fan governs when the Minkowski sum of alcoved polytopes is again alcoved. For symmetric alcoved polytopes, this fan is the intersection of the metric cone with the Wasserstein arrangement. I will discuss both theoretical and computational results for the symmetric and asymmetric type fan of alcoved polytopes.

This talk is based on joint works with Emanuele Delucchi, Nick Early, Leonid Monin, and Leonie Mühlherr.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.