Proudfoot, NicholasBibby, Christin2015-08-182015-08-182015-08-18https://hdl.handle.net/1794/19273An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement is unimodular, we provide a combinatorial presentation for a differential graded algebra (DGA) that is a model for the complement, in the sense of rational homotopy theory. Moreover, this DGA has a bi-grading that allows us to compute the mixed Hodge numbers. If the arrangement is chordal, then this model is a Koszul algebra. In this case, studying its quadratic dual gives a combinatorial description of the Q-nilpotent completion of the fundamental group and the minimal model of the complement of the arrangement. This dissertation includes previously unpublished co-authored material.en-USAll Rights Reserved.Hyperplane arrangementsElectronic Thesis or Dissertation