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Monday, October 13, 2014

**Abstract:** In Riemannian geometry the length spectrum is a rich source of invariants of the manifold. In the symplectic setting there is no notion of length, hence no possibility to define the length spectrum. Frederic Le Roux proposed the following construction: pick a ball of a fixed radius and translate it by a Hamiltonian isotopy along a given homotopy (or homology) class. The minimal Hofer energy required for such translation behaves in a very similar way to the Riemannian length spectrum. We will discuss some estimates for this energy in the two-dimensional case.