Linear Algebra Seminar

Speaker: Luke Oeding

Title: Phylogenetics and Nonlinear Algebra

Abstract: In Mathematical Biology researchers are interested in determining the correct phylogenetic tree given a contingency table computed from aligned DNA sequences of several species. Because the associated statistical models are defined by polynomial equations (called phylogenetic invariants), nonlinear algebra can help for this type of model selection. Often some necessary phylogenetic invariants can be found, but it is more difficult to prove that the list is sufficient.

In this talk I'll discuss bifurcating trees, and efforts to understand all of their phylogenetic invariants. In particular, I'll show how nonlinear algebra, representation theory and numerical algebraic geometry have all played roles in this story.