The work discussed in this talk falls into the emerging area of Population Genomics. I will first introduce the area and then talk about specific problems and combinatorial algorithms involved in the inference of recombination from population data. A phylogenetic network (or Ancestral Recombination Graph) is a generalization of a tree, allowing structural properties that are not tree-like. With the growth of genomic and population data (coming for example from the HAPMAP project) much of which does not fit ideal tree models, and the increasing appreciation of the genomic role of such phenomena as recombination (crossing-over and gene-conversion), recurrent and back mutation, horizontal gene transfer, and mobile genetic elements, there is greater need to understand the algorithmics and combinatorics of phylogenetic networks. In this talk I will survey a range of our recent algorithmic, mathematical and practical results on phylogenetic networks with recombination and show applications of these results to several issues in Population Genomics. Various parts of this work are joint work with Satish Eddhu, Chuck Langley, Dean Hickerson, Yun S. Song, Yufeng Wu, V. Bansal, V. Bafna and Z. Ding.
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