This award is made as part of the FY 2015 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 Dennis Kriventsov is "Regularity of Solutions to Elliptic Equations." The host institution for the fellowship is Courant Institute of Mathematical Sciences, New York University, and the sponsoring scientist is Dr. Fanghua Lin.