In evolutionary biology, the relationships between species are often described using a phylogenetic tree which visually illustrates how species are related to one another. “Phylogenetic invariants”; a class of polynomials useful in the study of phylogenetic trees were first introduced in the 1980’s, but significant challenges arose for using them directly for inferring phylogenetic trees. Starting in the 2000’s research by algebraic geometers as well as representation theorists overcame many of the early challenges. However, while simulation work by Casanellas and Fernandez — Sanchez showed significant improvements over the early studies, there was still much room for improvement. It turns out that perspective (algebraic geometry vs. representation theory) is an important consideration in this study as is understanding the statistical structure of the measure one constructs. I will present some of the history of this problem, briefly present the two perspectives (algebraic geometry vs. representation theory) and then discus how we use representation theory to develop a statistically powerful measure for tree inference. I will finish with simulation results. Comfort with linear algebra and elementary abstract algebra will be sufficient to follow the discussion.
A no host luncheon will be held at noon. Please contact Stephen Scarborough if you wish to attend.