Séminaire de géométrie le 6 novembre 2024

Mercredi 6 novembre 2024 - Salle de conférences du CMLS

Michael Joswig (TU Berlin) - "Tropical medians by transportation"

We start out with a general introduction to tropical convexity and its relationship with geometric combinatorics.

The resulting methods are then applied to computing Fermat-Weber points with respect to an asymmetric tropical distance function.  It turns out that they correspond to the optimal solutions of a transportation problem.  The results are applied to obtain a new method for computing consensus trees in phylogenetics.  This method has several desirable properties; e.g., it is Pareto and co-Pareto on rooted triplets.

Joint work with Andrei Comăneci