This award is made as part of the FY 2013 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 Daniel Halpern-Leistner is "Derived Categories of Coherent Sheaves and Geometric Invariant Theory." The host institution for the fellowship is Columbia University, and the sponsoring scientist is Dr. Andrei Okounkov.