2017 Hellman Fellow
Assistant Professor, Mathematics
Project Title: The Yang-Mills equations and geometry
Adam Jacob is a pure mathematician who works in the area of differential geometry. In general, he studies nonlinear partial differential equations that arise from the geometry of manifolds, with a special emphasis on manifolds which admit a complex structure. This current project focuses on the Yang-Mills equations, which were originally formulated in context of particle physics, yet can be studied from a purely geometric viewport. The goal of this project is to understand the structure of solutions near singularities, in addition to proving existence of solutions to the Yang-Mills equations and related equations on special higher dimensional manifolds.