Random Trees

[ Français ]
August 12-16, 2013
Louigi Addario-Berry (McGill), Louis-Pierre Arguin (Montréal), Rick Durrett (Duke), Lea Popovic (Concordia)

Random trees will play an important role in several of the workshops. Trees represent the evolutionary relationships between species, and are reconstructed by phylogenetic algorithms. Trees appear in population genetics giving the relationships between a sample of individuals from a population. The simple coalescent of Kingman and more complex processes are used to describe the evolution in populations of constant or changing size, or when subject to natural selection. In models for ecology and epidemiology they are used to describe the phylodynamic evolution of populations with spatial or interaction dynamics. Spatial trees and branching particle models are also used to analyse fluctuations at the front of the propagation of traveling waves in evolutionary dynamics. In addition there are trees which arise as limits of critical branching processes, or from the use of randomized algorithms. This workshop will concentrate on the mathematical techniques that underlie these results and will thus serve as an introduction to the overall program, and a useful tutorial for individuals without much experience in applying mathematical ideas to biology. By featuring several different applications in the same workshop we hope to bring out parallel themes in the different subjects, and catalyze new mathematical developments.