Geometry and Topology Seminar

Symplectic embedding problems, i.e. the question whether one symplectic manifold embeds into another, are of central importance in symplectic geometry. Such problems are intimately related to Hamiltonian dynamics and this relationship has been used to construct a plethora of obstructions to symplectic embeddings. Going in the opposite direction, I will discuss how disk-like global surfaces of section, a concept from dynamics, can be used to construct symplectic embeddings. This yields partial progress towards Viterbo's conjecture on symplectic capacities of convex domains: The cylindrical embedding capacity agrees with the minimal action of an unknotted Reeb orbit.