The Geometry of the Group of Symplectic Diffeomorphism

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Spectral invariants, analysis of the Floer moduli spaces and geometry of the Hamiltonian diffeomorphism group (2004, background): “This upper estimate depends on the choice of homotopy (H, j) and is related to the curvature estimates of the relevant Hamiltonian fibration (see [Po1], [En1]).”
Calabi quasimorphism and quantum homology (2002, background): “The case of the 2-torus is settled in [ 35 ], Section 8.4.”
Commutator length of symplectomorphisms (2001, background): “A closed connected symplectic surface (M, ω) of positive genus is symplectically aspherical and Ham(M, ω) = ] Ham(M, ω) (see [ 40 ]).”
Growth of maps, distortion in groups and symplectic geometry (2001, background): “[ P1 ]). The length structure L has an L2-cousin which is used in hydrodynamics.”
Symplectic quasi-states and semi-simplicity of quantum homology (2007, neutral): “[29], [36] for preliminaries on Hamiltonian symplectomorphisms.”