3–6 Feb 2025
MPI-CBG
Europe/Berlin timezone

Aida Maraj - Toric Geometry in Brownian motion tree models and their generalizations

4 Feb 2025, 16:15
45m
Large auditorium (MPI-CBG)

Large auditorium

MPI-CBG

Pfotenhauerstr. 108 01307 Dresden

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.

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