| Grace Stadnyk, NC State University |
| Title: Some Combinatorial Results on the Edge-Product Space of Phylogenetic Trees |
| Abstract: I will discuss a topological space that arises in evolutionary biology called the edge-product space of phylogenetic trees. In particular, I will discuss some of the combinatorial properties of a particularly natural CW decomposition of this space. It is known that intervals in the resulting face poset are shellable, but the manner in which the maximal faces intersect is still not well-understood. In particular, the poset in its entirety is not known to be shellable. I will introduce a partial order on the maximal faces of the edge-product space of phylogenetic trees called the enriched Tamari poset, which can be viewed as a generalization of the Tamari lattice. I will use this poset to show that the edge-product space of phylogenetic trees is gallery-connected. I will conclude by discussing the question of whether the face poset of this topological space is shellable. I will define most of the notions that appear in the talk, so it should be accessible to all. |
Monday, Nov 26, 11:00AM-12:00 Noon, Fretwell 315
Categories: Spring 2022