UBC Mathematics Department
This will be a lecture, intended for a general audience, about the variational problem of finding least volume Lagrangian submanifolds of Kahler or symplectic manifolds. Motivations for this problem arise in Kahler geometry, mirror symmetry, and nonlinear elasticity. We will describe the connections with special Lagrangian geometry. We will outline the progress which has been made on this variational problem, and describe what we see as the main obstacles toward a better understanding.