Hebrew University topology and geometry seminar

Abstract: The space of positive Lagrangians in an almost Calabi-Yau manifold is an open set in the space of all Lagrangian submanifolds. A Hamiltonian isotopy class of positive Lagrangians admits a natural Riemannian metric, which gives rise to a notion of geodesics. We will talk about geodesics of positive $O_n(\mathbb{R})$ invariant Lagrangian spheres in n-dimensional $A_m$ Milnor fibers. These Lagrangian spheres are known in the literature as matching cycles. As it turns out, the initial value problem and the boundary value problem have unique smooth solutions in this class of positive Lagrangians.
All the funny words will be explained in the talk. Definitions and examples will be given.
Joint work with Jake P. Solomon.