Phylogenetic Algebraic Geometry

Explore phylogenetic algebraic geometry in this 58-minute lecture by Seth Sullivant from North Carolina State University. Delve into the phylogenetics problem of finding trees that explain species history, and discover various applications and methodologies. Learn about using sequence data to build trees, the algebraic perspective on phylogenetic models, and how to use phylogenetic invariants for tree reconstruction. Examine the SVDQuartets method and the identifiability of phylogenetic models from a geometric perspective. Investigate the process of gluing trees and graphs, group-based models, and equations for the CFN Model. Gain insights into the Buczynska-Wisniewski Theorem and the Hilbert Scheme as they relate to phylogenetic algebraic geometry.

Intro
Phylogenetics Problem Given a collection of species, find the tree that explains their history.
Applications of Phylogenetics
Phylogenetics Methodologies Traditional Method: Clacistics
Using Sequence Data to Build Trees
Algebraic Perspective on Phylogenetic Models
Phylogenetic Algebraic Geometry
Using Phylogenetic Invariants to Reconstruct Trees
SVDQuartets (Chitman, Kubatko, Long)
Identifiability of Phylogenetic Models
Geometric Perspective on Identifiability
Generic Identifiability
Proving Identifiability with Algebraic Geometry
Phylogenetic Models are Identifiable
Gluing Two Trees at a Leaf
Gluing more complex graphs
Group-based models
Equations for the CFN Model
Buczynska-Wisniewski Theorem
The Hilbert Scheme
Summary