Mathematical aspects of population genetics

Population genetics deals with the evolution of genomes as a result of the drift of point mutations throughout a population over long timescales. Mathematically, mutations, genetic drift and natural selection are modelled as Markovian processes which lead to a type of partial differential equation known as the forward Kolmogorov equation. There are a number of interesting unanswered questions in this field related to the estimation of mutation rates from allele frequencies, modelling the effects of growing or shrinking populations, and the relationship of population genetics with phylogenetics. Any one of these open questions would make a suitable starting point for a project in this area.