Department of Mathematics Colloquium

University of Idaho

Spring 2013

Thursday,  February 28, 3:30-4:20 pm, room TLC 030

Refreshments in Brink 305 at 3:00 pm

Determining Phylogenetic Invariants


Elizabeth Gross

Department of Mathematics

University of Illinois at Chicago


Algebraic statistics applies algebraic geometry, combinatorics, and commutative algebra to the study of statistical models. In this talk, we will introduce algebraic statistics through the following problem: Given aligned DNA sequences from a collection of species, find the tree that best describes their evolutionary history. One method for inferring phylogenetic trees uses phylogenetic invariants, polynomials that vanish on the variety defined by the model. As an example of the algebraic geometry involved, the projectivization of the variety defined by the general Markov model is a secant variety of a Segre variety. In this talk, we will describe the general and group‐based Markov models, their defining polynomials, and their connections to tensors, hypergraphs, and toric algebra. We will end the talk by looking at statistical models with similar algebraic properties as such as Holland and Leinhardt’s p1 model for social networks.