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This volume contains articles based on talks presented at the Thirteenth Conference of African American Researchers in the Mathematical Sciences (CAARMS), held at Northeastern University and the University of Massachusetts, Boston on June 19–22, 2007. The representation theory of Lie groups and its applications were a major focus of the talks. An overview is included of the recent achievements of the Atlas of Lie Groups Project and the work that remains to be done by the Atlas Project to fully understand the unitary representations of reductive groups. Other articles highlight the significance of scientific computing in Lie Theory and applications of the representation theory of Lie groups to the physics of black holes. This volume contains two research papers not related to Lie Theory: one on the geometry of coisotropic submanifolds of Poisson manifolds and one on recent results on the structure of the set of ultrafilters on the collection of finite subsets of an infinite set. It concludes with a survey of CAARMS12 participants. For volumes based on previous CAARMS proceedings, see: African Americans in Mathematics (volume 34 in the AMS series, DIMACS), African Americans in Mathematics: Volume II (volume 252 in the AMS series Contemporary Mathematics), African Americans in the Mathematical Sciences: Volume III (volume 275 in the Contemporary Mathematics series) and Volume IV (volume 284 in the Contemporary Mathematics series).