Algebraic Approaches to Probabilistic
Problems in Population Genetics

Being continuous in both time and space, diffusion processes possess many nice properties not shared by discrete random processes. In particular, associated to a diffusion process is a fundamental differential operator (i.e., the generator) that can be used to obtain useful algebraic equations satisfied by certain expectations at stationarity. In this talk, the diffusion generator technique will be used to address some probabilistic problems in population genetics.