Title: Interleavings on Phylogenetics Trees
Speaker: Anastasios Stefanou (Ohio State University)
Abstract: There are many metrics available to compare phylogenetic trees since this is a fundamental task in computational biology. In this talk, I will discuss one such metric, the `$\ell^{\infty}$-cophenetic metric introduced by Cardona et al. This metric works by representing a phylogenetic tree with n labeled leaves as a point in $R^{n(n+1)/2}$ known as the cophenetic vector, then comparing the two resulting Euclidean points using the `$\ell^{\infty}$- distance. Meanwhile, the interleaving distance is a formal categorical construction generalized from the definition of Chazal et al., originally introduced to compare persistence modules arising from the field of topological data analysis. I will show that the `$\ell^{\infty}$-cophenetic metric is an example of an interleaving distance. To do this I will define phylogenetic trees with n leaves as a subcategory of merge trees with some additional structure and show that this category embedds on the poset $R^{n(n+1)/2}$. Finally I will discuss a follow up work, i.e. interleavings on phylogenetic networks.
Seminar URL: https://tgda.osu.edu/activities/tdga-seminar/
