Entanglement measures for phylogenetic branching models via plethysms and classical invariant theory

Linear models of change in stochastic systems often entail assumptions of independence amongst subsystems. In an appropriate tensor setting, the analysis of this independence is the same as that of the analysis of the entanglement of state vectors in quantum systems, and is at base an application of classical invariant theory.

The talk will review continuous time Markov models on trees as commonly used in phylogenetics, and will explain how various entanglement measures (some of which can be lifted from the physics literature on the analysis of multi-qubit systems) are informative about phylogenetic relationships. Specifically they are relevant to distance-based tree reconstruction methods, and have been shown (under simulation) to improve some algorithms.

The talk will also introduce the major group theoretical tool applied to this problem, namely the theory of plethysms, for the enumeration of multilinear invariants. In the biological context the appropriate invariance group is the (finite dimensional) affine group.

(Joint work with Jeremy Sumner, School of Mathematics and Physics, University of Tasmania)