Phylogenetics from an algebraic perspective
Abstract: In the last years there has been an increase in the use of algebraic tools in phylogenetic reconstruction. As a Markov process of substitution of nucleotides along a phylogenetic tree can be viewed as a polynomial map, it is natural to use tools from algebraic geometry and computational algebra in this setting. We will explain how these tools are used in phylogenetics and we will introduce the use of semi-algebraic constraints, which mirror the probabilistic nature of the parameters used. We will show advantages and disadvantages of the use of these algebraic methods using real and simulated data.