The Kingman Coalescent as a Density on a Space of Trees

Randomly pick n individuals from a population and look at their genealogy. The Kingman n-coalescent is a probabilistic model for the tree one obtains this way. It can be described by a probability density function on the space of equidistant trees with its fine fan structure, given by the Bergman fan of the complete graph.

I will describe this density and report on work in future with Lena Walter about relations of population genetics and algebraic geometry via the tropical connection.