Phylogenetics is the study of evolutionary relationships between organisms. Our goal is to reconstruct the evolutionary history of collections of species by building phylogenetic trees (family trees) from biological data. While mathematically interesting, trees are often too simple to model the complex nature of real gene transfers. This leads to the study of phylogenetic networks, which incorporate hybridization, allowing separate species to come together. This talk explores assigning algebraic invariants to phylogenetic networks in order to find the network that best explains the data given. One approach to assigning these invariants involves using matrices of conditional probabilities to describe models of DNA sequence evolution.

References: Gross, E., Long C., Rusinko J. (2019). Phylogenetic Networks. arXiv:1906.01586v1. Sullivant, S. (2018). Phylogenetic Models. Algebraic Statistics. American Mathematical Society.