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Title:
Measuring space and time in symplectic geometry
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Abstract:
A basic question in symplectic geometry is to determine when one symplectic manifold with boundary (such as a domain in R^{2n}) can be embedded into another, preserving the symplectic structure. Another basic question is to understand periodic orbits of Hamiltonian vector fields. It turns out that these two questions are closely related: periodic orbits of Hamiltonian vector fields (recast as Reeb vector fields) on the boundaries of symplectic manifolds give rise to symplectic embedding obstructions. We will explain how this relation works, and discuss some recent results and conjectures about symplectic embeddings and periodic orbits of Reeb vector fields.
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