The Monge-Ampere equation is the most well-known and extensively studied second-order fully nonlinear elliptic partial differential equation. In this talk, I will motivate the study of this equation by explaining its connection with two interesting problems. The first is the optimal transport problem, which involves finding the most efficient way, relative to a given cost function, to move a continuous material from a given arrangement to a desired distribution of the material. The second is the geometric problem of finding a surface with a given Gauss curvature. Both of these problems can be approached by formulating and solving a PDE problem of Monge-Ampere type. I will then turn to the theoretical aspects of this equation and discuss existence and regularity of weak solutions, some results, open questions and ideas for future work.

Please join us beforehand for pizza.