Research Interests
Mathematical population genetics: probability distributions of gene frequencies in populations modeled by diffusion processes; probability distributions of genealogical processes; probability distributions of gene phylogenies which can be deduced from mutation patterns on DNA sequences; measure-valued diffusion process; models in the evolution of gene frequencies and phylogenies; and computational algorithms for ancestral inference, such as algorithms to estimate mutation, recombination, migration and selection rates, the time to the most recent common ancestor of sequences, and ages of mutations. Stochastic processes in Mathematical Genetics. Combinatorial structure of stochastic processes involving random partitions. Multivariate orthogonal polynomials. Eigenfunctions and spectral expansions of stochastic process transition functions.