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Friday, March 4, 2022

**Abstract:** On a symplectic manifold, one has two types of symmetries. Namely, the symplectomorphisms, which are diffeomorphisms preserving the symplectic form, and Hamiltonian diffeomorphisms, which are generated by Hamiltonian functions. Every Hamiltonian diffeomorphism is also a symplectomorphism. The flux homomorphisms is a tool that enables us to write the symplectomorphism group as an extension of the Hamiltonian group by a (finite-dimensional) abelian group. In this talk, I will go over the definition of the flux homomorphism, and show some basic properties. The aim is to arrive at some nice and pretty exact sequences. In the end I also hope to explain some important and deep results related to it. The nice thing about the flux homomorphism is that it requires very little experience with symplectic structures, so I hope it is accessible for anyone familiar with differential geometry.