Abstract

Hypersymplectic structure on a 4-manifold is a triple of symplectic forms such that any nontriviallinear combination of them is symplectic. The hypersymplectic flow is a natural geometric flowdesigned with the goal of deforming one given hypersymplectic structure in its cohomology class toa hyperKhler structure. This flow also has close relation with Brvants G 2-Laplacian flow on 7.manifold. In this talk, we will present some long time existence and convergence results about theflow, and in particular one recent convergence result on 4-torus proved together with Joel Fine andWeiyong He.