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.