Algebraic geometry and the evolution of species

Seminar in Applied Mathematics and Statistics

Speaker: Marta Casanellas, Universitat Politècnica de Catalunya.

Many statistical models of evolution can be viewed as algebraic varieties. As a consequence, tools from algebraic geometry can add information in the phylogenetic reconstruction problem. Indeed, the generators of the ideal of a statistical model of evolution should allow to determine the tree formed by a set of living species. We will present methods of phylogenetic inference based on algebraic geometry and, comparing to other exiting methods, we will discuss what are the advantages of these new methods. We will also see how an in-depth study of the geometry of the model leads to major
improvements on the reconstruction methods based on algebraic geometry.