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Monday, April 12, 2021

**Abstract:** A Hamiltonian S^1 space is a four dimensional symplectic manifold equipped with an action of S^1 generated by a real-valued function known as the Hamiltonian. If there exists an additional real-valued function which is independent from the Hamiltonian function and Poisson commutes with it, then we say that the given Hamiltonian S^1 space can be "lifted" to a completely integrable system. We study when Hamiltonian S^1 spaces can be lifted to four dimensional completely integrable systems, and, depending on the properties of the original S^1 space, we study the properties of the resulting integrable systems. This talk is based on joint work with S. Hohloch.