Colloquium: Hypersymplectic Flow on 4-manifold

Abstract: Hypersymplectic structure is a triple of symplectic structures on 4-manifold such that any of their linear combinations is a symplectic structure. It is one subclass of symplectic Calabi-Yau four manifold and is conjectured to be deformable to a hyperKahler structure and thus diffeomorphic to the later by Donaldson. We will describe one geometric flow aiming at deforming a given hypersymplectic structure in its cohomology class to a hyperKahler structure, and will talk about some partial results. Part of this is joint work with Joel Fine.