The demographic history of human populations is preserved in our DNA, yet extracting this information is challenging, because of the recent common ancestry and gene flow among human groups. I am interested in development and application of statistical methodology for analyzing genome-wide patterns of variation in dense genotype or sequence data from worldwide human populations. In particular, we have recently implemented a novel approach to accurately infer ancestry of chromosomal segments along genomes of individuals of mixed ancestry, and to use this information to infer the time of migrations. By using an admixed population one can capitalize on the property of the genome to recombine each generation, producing chromosomes that are a mixture of the parental genetic material. The structure of an admixed genome contains temporal information about an admixture event, as a greater number and narrower width of ancestry blocks indicate more recombination events, and hence greater time depth. We use spectral properties of the genome-wide admixture pattern to infer the time of admixture. We are currently extending this approach to allow dating of ancient admixture events, and are investigating the utility of this method for identifying candidate genes subject to local selection.