====== Emanuele Delucchi (Fribourg/Freiburg) ======

====== Fundamental Polytopes of Metric Spaces via Parallel Connection of Matroids ======

===== Abstract for the Combinatorics and Geometry/Topology Seminars 2019 October 15 =====

Motivated by applications in phylogenetics, Linard Hoessly and I tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. We consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.


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