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Hamiltonian Gromov-Witten theory(see Mundet-Tian paper) corresponds to a new type of Symplectic vortex equations: Such type of models gives a connection to Hitchin-Kobayashi correspondence and Floer ...

Definition:Two symplectic manifolds $(X,\omega_X)$ and $(Y,\omega_Y)$ are defined to be symplectically equivalent if there exists a diffeomorphism $\phi:X\to Y$ such that $\phi^∗ω_Y$ is in the same ...

I am trying to understand the big picture around Seiberg-Witten invariants of 4-manifolds. Of course, this points to Taubes work on Gromov-Witten invariants of symplectic manifolds. It is striking ...