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Momentum maps for automorphism groups

Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018

October 11, 2018 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Tudor Ratiu (Shanghai Jiao Tong University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
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Abstract

In mathematical physics there are conservation laws that are discrete in nature, such as topological information. These conservation laws cannot be captured by the usual momentum  map and many of its extensions. I will present an enlarged definition of the momentum map with values in groups, that works also in infinite dimensions. It is inspired by the Lu-Weinstein momentum map for Poisson Lie group actions, but the groups involved do not necessarily have a Poisson Lie group structure on it. The most interesting applications include momentum maps for various automorphism groups which take values in Cheeger-Simons differential characters of the underlying manifolds. I will concentrate on Clebsch variables for fluids and show how this extended momentum map lads to new Clebsch variables admitting non-vanishing, but integer valued helicity.

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