Phylogenetic invariants for time-reversible models

The main goal of Phylogenetics is to find evolutionary relations between biological entities.These relations are inferred from data and are encoded in a graph called a phylogenetic tree. Available data can come from DNA sequences or aminoacid sequences of different species but, once we have the data, how to determine which phylogenetic tree accurately represents the hidden evolutionary relations? In this talk we explore how understanding the so called phylogenetic variety helps us with model selection and phylogenetic reconstruction. We will start by introducing phylogenetic varieties and time-reversible models, then we present a general framework to study the phylogenetic reconstruction process for time-reversible models. Our main example will be the Tamura-Nei model for DNA, for which we give phylogenetic invariants for three and four species. This is joint work with Marta Casanellas and Roser Homs Pons.