Convexity in Tree Spaces

Abstract

We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all ultrametrics. The $CAT-0$ metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric exhibit properties that are desirable for geometric statistics, such as geodesics of small depth.

Publication
SIAM Journal on Discrete Mathematics, 2017, 31(3), 2015-2038
Bo Lin
Bo Lin
Visiting Assistant Professor

My research interests include mathematical biology, tropical geometry and combinatorics.

Bernd Sturmfels
Bernd Sturmfels
Professor
Xiaoxian Tang
Xiaoxian Tang
Associate Professor
Ruriko Yoshida
Ruriko Yoshida
Associate Professor

Related