Abstract

The purpose of the talk is more modest than the title would suggest. The coalescent theory is quite young with many connections within and outside mathematics. Following the origins of the theory (Kingman’s work 1978-1982), I choose to introduce it in the framework of a stochastic population model. We will be interested in the question of how to model a genealogy. A powerful way to do it is to consider a process taking values in the space of the partitions of N. At any time t, the population is represented by a partition where each block corresponds to a family. The processes describing the evolution over time of these partitions are called exchangeable coalescents. I will follow closely Berestycki’s book, ch. 1 (Recent progress in coalescent theory) and Bertoin’s book, ch.4 (Random fragmentation and coagulation processes).