Title: Identifiability of phylogenetic networks

Abstract: One of the main goals of phylogenetics is to understand the evolutionary history of a set of species. These histories are represented by directed graphs where the leaves represent living species and the interior nodes represent extinct species. While it is common to assume the evolutionary history is a tree, when events such as hybridization are present, networks are more realistic. However, allowing for networks rather than trees complicates the process of inference, and ways to overcome this complication are needed. One approach to phylogenetic network inference is rooted in computational algebraic geometry. In this talk, we discuss the role computational algebraic geometry has played in the statistical problems related to network inference with a focus on identifiability.