Title: Applied topology for phylogenetic networks
Speaker: Anastasios Stefanou (Ohio State University)
Abstract: In mathematical phylogenetics we are interesting in developing mathematical methods that model the structure of phylogenetic networks, which in turn, can be used for developing metrics so that any pair of phylogenetic networks can be compared. In practice we often encounter tree-like networks called phylogenetic trees whose structure is already very well understood: one can show (Sokal and Rohlf, 1962) that, via the so called cophenetic map (which will be defined and explained during the lecture), phylogenetic trees with n leaves embed as vectors in the $[n(n+1)/2]$-dimensional Euclidean space. There we pull back $l^p$ norms to define metrics on these trees. However very few are known for the general case of phylogenetic networks. In this talk I will explain why Reeb graphs is a natural model for phylogenetic networks and I will discuss a canonical way to decompose a phylogenetic network with $n$-labelled leaves and $s$ cycles into a set of phylogenetic trees with $(n + s)$-labelled leaves. By combining this tree-decomposition and the cophenetic map, any such network embed as a finite set of points in the $[(n+s)(n+s+1)/2]$-dimensional Euclidean space. Hence, we can utilize the Hausdorff metric as a metric for comparison of phylogenetic networks.
Note: The goal of Welcome Seminar is to give an opportunity to new postdoctoral fellows and tenure track professors to introduce themselves to their colleagues. The talks are intended to be non-technical and accessible to graduate students as well. Please plan to attend and encourage your graduate students to do so as well. The talk will be preceded by a colloquium-style reception at 4:00, in the area adjacent to Cockins Hall 240 on the second floor of the Math Building.
