Symplectic actions of tori on four-manifolds (Séminaire commun avec la physique mathématique).

I will present a classification of symplectic actions of
2-tori on compact, connected symplectic 4-manifolds, up to equivariant
symplectomorphisms. The classification is in terms of a collection of
invariants of the topology of the manifold, of the torus action and of
the symplectic form. I will construct explicit models of such symplectic
manifolds with torus actions, defined in terms of these invariants. Some
results are joint with J.J. Duistermaat.