Every nondesarguesian symplectic spread is also symplectic over its kernel. Any equivalence of nondesarguesian symplectic spreads preserves the resulting symplectic structures over the kernels. 2000 Mathematics Subject Classification. Primary 51A35, 51A40; Secondary 51A50

We classify symplectic actions of 2-tori on compact, connected symplectic 4-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin–Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants, which are invariants of the topology of the manifold, of the torus action and of the symplectic form. We construct explicit models of su...

We classify symplectic actions of 2-tori on compact, connected symplectic 4-manifolds, up to equivariant symplectomorphisms, hence extending the theory of Atiyah, Guillemin–Sternberg, Delzant and Benoist to actions of tori which are not necessarily Hamiltonian. The classification is in terms of a collection of up to nine invariants. We construct an explicit model of such symplectic manifolds wi...

In this paper we show that every degree 2 homology class of a 2n-dimensional symplectic manifold is represented by an immersed symplectic surface if it has positive symplectic area. Moreover, the symplectic surface can be chosen to be embedded if 2n is at least 6. We also analyze the additional conditions under which embedded symplectic representatives exist in dimension 4.

Periodic cyclic homology group associated to a mixed complex was introduced by Goodwillie. In this talk, I will explain how to apply this construction to the symplectic cochain complex of a Liouville domain and obtain two periodic symplectic cohomology theories, which are called periodic symplectic cohomology and finitely supported periodic symplectic cohomology, respectively. The main result i...

In this article, we construct simply connected symplectic Calabi-Yau 6-manifold by applying Gompf’s symplectic fiber sum operation along T. Using our method, we also construct symplectic nonKähler Calabi-Yau 6-manifolds with fundamental group Z. We also produce the first examples of simply connected symplectic Calabi-Yau and non-Calabi-Yau 6-manifolds via coisotropic Luttinger surgery on non si...

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D. Ebin’s long-time existence result for geodesics on the symplectomorphism group to metrics not necessarily compatible with the symplectic structure. We also study the dynamics of symplectic point vortices, desc...