Punctured Holomorphic Curves in Symplectic Geometry

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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.