Abstract: We will discuss geometry of Hamiltonian diffeomorphisms on symplectic surfaces with respect to the Hofer metric. Despite of very elementary setup much in this subject is still unexplored. In Riemannian geometry the length spectrum is defined as the minimal length of a closed curve in each homotopy class. It is a rich source of invariants of the manifold. In symplectic setting there is no notion of length, hence no possibility to define the usual length spectrum. However, one can construct a similar invariant by measuring Hofer's length of closed 'trajectories' of disks. We will provide some estimates for this construction.

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