Punctured Holomorphic Curves (I)

The aim of this project is to systematically apply punctured holomorphic
curves to questions in symplectic geometry. This is particularly
promising for Lagrangian embeddings, where we expect new results on
Lagrangian intersections, intersections of Lagrangian submanifolds
with balls, Maslov class and symplectic area class rigidity, and
unknottedness in dimension four. Moreover, we will lay the foundations
for further applications by studying punctured holomorphic curves in
cotangent bundles and their relations to closed geodesics and harmonic
maps.