MSI Weekly Bulletin - Week starting Monday 11 June, 2007

Modern phylogenetics seeks to reconstruct evolutionary family trees of contemporary species using data such as DNA sequences. Important in this enterprise are various random mechanisms for wandering around ``tree space'' by a sequence of simple rearrangements, and this motivates questions about how such mechanisms behave on large trees. As the number of leaves goes to infinity, one is led to consider stochastic processes that move around continuously in a space of tree-like metric spaces. The study of these limiting dynamics uses ideas from metric geometry such as the Gromov-Hausdorff distance and analytic tools such as Dirichlet forms. Also, it is intimately connected with Aldous's continuum random tree, a canonical model for the limit of many natural families of large random trees.