Description
Algebraic geometry has recently provided a new approach to advancing problems in multivariate Gaussian models. This is achieved by identifying Gaussian distributions with symmetric matrices and analyzing the polynomials that vanish on these matrices, known as ideals. The talk will focus on Brownian motion tree (BMT) models, a type of Gaussian model used in phylogenetics, and their generalizations to phylogenetic trees with colored and zeroed nodes. The set of concentration matrices on BMT models has hidden toric geometry. We use it to provide formulas on the maximum likelihood degree and its dual. Their generalization is not always toric. We share conditions for toricness under a linear transformation.
