Department of

# Mathematics

Seminar Calendar
for events the day of Monday, April 12, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, April 12, 2021

3:00 pm in zoom,Monday, April 12, 2021

#### Integrable systems and Hamiltonian S^1-spaces

###### Joseph Palmer (UIUC)

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.