Luca Schaffler: Point configurations, phylogenetic trees, and dissimilarity vectors

Abstract: In 2004 Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. In this seminar we give a negative answer to this question, and propose a weighted variant of the higher dissimilarity map for which the weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter-Speyer envisioned. Moreover, we provide a geometric interpretation of this tropical subvariety in terms of configurations of points on rational normal curves. This is joint work with Alessio Caminata, Noah Giansiracusa, and Han-Bom Moon.

Zoom link: https://kth-se.zoom.us/j/65455623260
Zoom meeting ID: 654 5562 3260