From Gromov to the Moon

I will present some recent applications of symplectic geometry to the restricted three body problem. More specifically, I will discuss how Gromov's original study of pseudoholomorphic curves in the complex projective plane has led to the construction of global surfaces of section, and more generally finite energy foliations, below and slightly above the first Lagrange point in the regularized planar circular restricted three body problem. The talk will be accessible to a general mathematical audience.