Phylogenetic Algebraic Geometry
Nicholas Eriksson, Kristian Ranestad, Bernd Sturmfels, Seth Sullivant
Abstract
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover classical geometric objects, such as toric and determinantal varieties and their secant varieties, but larger trees lead to new and largely unexplored territory. This paper gives a self-contained introduction to this subject and offers numerous open problems for algebraic geometers.
Create a lesson
Related papers
Heavy-Light Wall Crossings and Motivic Asymptotics of Moduli Spaces of Curves. Part I: Stabilization Graphs and Euler Characteristics
Giordano Cotti
The pliability of del Pezzo surfaces
Elias Kurz, Egor Yasinsky
Hessenberg character
Patrick Brosnan, Jaehyun Hong, Donggun Lee
On the geometric degree of the prolongation varieties of the differential system x1'=x22, x2'=x12
Mattia Puddu
The super Weil-Petersson asymptotic expansion and the coefficients
Xuanyu Huang, Kefeng Liu, Hao Xu
On the proof of multi-variable n/d-conjecture for hyperplane arrangements
Rui Tan, Fanghan Xiang