%0 Journal Article %T Symplectic curvature flow %A Jeffrey Streets %A Gang Tian %J Mathematics %D 2010 %I arXiv %X We introduce a parabolic flow of almost Kahler structures, providing an approach to constructing canonical geometric structures on symplectic manifolds. We exhibit this flow as one of a family of parabolic flows of almost Hermitian structures, generalizing our previous work on parabolic flows of Hermitian metrics. We exhibit a long time existence obstruction for solutions to this flow by showing certain smoothing estimates for the curvature and torsion. We end with a discussion of the limiting objects as well as some open problems related to the symplectic curvature flow. %U http://arxiv.org/abs/1012.2104v4