Speaker: Ruth Charney (Brandeis)
Title: Phylogenetics and the Geometry of Tree Space
Abstract: I will discuss some recent work of Billera, Holmes, and Vogtmann in which they apply techniques of geometric group theory to problems in phylogenetics. One of the key problems in phylogenetics is to reconstruct evolutionary trees from DNA data. The space of all possible trees (with fixed number of leaves) has a natural metric. This metric turns out to be CAT(0), that is, it has certain properties analogous to the path metric on a manifold of non-positive curvature. I will discuss these properties and how they can be used to help solve some problems in phylogenetics.