Seminari del Dipartimento
Geometria Phylogenetic Trees, Tropical Geometry, and Rational Normal Curves Alessio Caminata 19-05-2022 - 14:15 Largo San Leonardo Murialdo,1 - Pal.C
In 2004 Pachter and Speyer introduced the dissimilarity maps for phylogenetic trees and asked two important questions about their relationship with 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 talk, we present a negative answer to this second question. Then, we introduce a weighted variant of the dissimilarity map and show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. This tropical variety has a geometric interpretation in terms of point configurations on rational normal curves. The talk is based on a joint work with Noah Giansiracusa, Han-Bom Moon, and Luca Schaffler. |