OS Reelle Geometrie und Algebra und KWIM: Algebraic degrees of phylogenetic varieties

Freitag, 12. Juli 2024
13:30 bis 15 Uhr

F 426

Veranstaltet von

Vortragende Person/Vortragende Personen:
Rodica Dinu

Group-based models appear in algebraic statistics as mathematical models coming from evolutionary biology, namely in the study of mutations of genomes. Motivated also by applications, we are interested in studying the algebraic degrees of the phylogenetic varieties coming from these models. These algebraic degrees are called {\em phylogenetic degrees}. In this talk, we present concrete results on the phylogenetic degrees of the variety $X_{G, n}$ with $G\in\{\mathbb{Z}_2,\mathbb{Z}_2\times \mathbb{Z}_2, \mathbb{Z}_3\}$ and any $n$-claw tree. As these varieties are toric, computing their phylogenetic degree relies on computing the volume of their associated polytopes $P_{G,n}$. We present combinatorial methods used in our work and we give explicit formulas for these volumes. This talk is based on a joint work with Martin Vodicka.