Abstract: The group of Hamiltonian diffeomorphisms forms an infinite-dimensional Fréchet Lie group, whose Lie algebra is isomorphic to the space of zero-mean normalized functions, with the adjoint action given by pull-backs. We show that this action is flexible: for any nonzero normalized function u, any other normalized function can be expressed as a finite sum of elements from the orbit of u. Moreover, we provide an upper bound on the number of terms in this sum and discuss implications in Hofer's geometry and recent progress in the case of open symplectic manifolds. This is joint work with Lev Buhovsky.

This is a seminar in the Centre of Geometry and Physics seminar series.