During the 2015-2016 year, Harvard University's Center of Mathematical Sciences and Applications (CMSA) hosted a year-long thematic program on nonlinear equations and their connections to geometry, physics, and computer science. This volume presents articles contributed by some of the participants in this program, and builds on the activities of that special year. Specific topics include: general existence and regularity for elliptic and parabolic equations, the theory of minimal surfaces, the Weyl and Minkowski problems, transport and conservations laws, Navier-Stokes, and the Calderon problem. This volume, the second in the series, will benefit scholars working in nonlinear analysis and its connections with geometry and physics.