Determining phylogenetic invariants

One research thread in algebraic statistics is focused on hidden Markov models, particularly in the context of phylogenetics. Hidden Markov models are used for inferring trees that best describe the evolutionary history of a collection of living species. The algebraic method for tree reconstruction relies on phylogenetic invariants, polynomials that vanish on the variety defined by the model. For the general Markov model, these phylogenetic invariants have been challenging to understand, and, in fact, the defining ideal of the variety associated to the 4-state general Markov model on the 3-leaf claw tree is still unknown. In this talk, we will describe the general Markov model, its defining polynomials, and its connection to tensors of bounded border rank. Specifically, we will explain how the variety associated to the 4-state general Markov model on the 3-leaf claw tree is the zero set of polynomials of degrees 5, 6, and 9.

Event Topic

Nonlinear Algebra and Statistics (NLASTATS)