This award is made as part of the FY 2014 Mathematical Sciences Postdoctoral Research Fellowships Program. Each of the fellowships supports a research and training project at a host institution in the mathematical sciences, including applications to other disciplines, under the mentorship of a sponsoring scientist. The title of the project for this fellowship to Blake H. Barker is "Numerical Investigation of Problems in Stability, Including Numerical Analysis, Development of a Software Package, and Numerical Proof." The host institution for the fellowship is Brown University, and the sponsoring scientist is Dr. Bjorn Sandstede.