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Invariants of Phylogenetic Networks

Joseph Cummings (University of Notre Dame)
Friday, January 20, 2023
3:00-4:00 PM
4088 East Hall Map
Our goal is to analyze a family of ideals associated with phylogenetic networks. Roughly, these ideals are used to infer the evolutionary history of a collection of species. We will start by reviewing a result of Sturmfels and Sullivant where they showed that the ideal is toric and quadratically generated by binomials which are determined by splits in the tree. The story is not over, however, since trees fail to capture evolutionary behavior such as horizontal gene transfer and hybridization. We will analyze the situation where these behaviors are sufficiently sparse in the network. In this case, we provide a full combinatorial description of the quadratics in the ideal while also showing the ideal is quadratically generated when there are no cycles of length greater than 8. This project is joint with Ben Hollering and Chris Manon.
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics, Combinatorics Seminar - Department of Mathematics