The Symplectic Geometry of Monge-Ampere Equations
The classical Monge-Ampere equations have arisen in a number of novel analytical contexts in fairly recents times. In work with Patrick Shipman it has also arisen in our study of a collection of PDE problems related to Lorentzian/Riemannian mean surface theory and pattern formation. In this talk I want to introduce an elegant geometric tool that emerges from contact geometry and the canonical formalism to provide a direct route to analyzing Monge-Ampere equations that may aid in studying our problems. Time permitting, I may also say a few words about possible relations to mass transport.