GEOMETRY/DYNAMICAL SYSTEMS

We will discuss some recent SFT-type compactness results for J-curves (i.e. pseudo-holomorphic curves) in the symplectization of a contact manifold which is stretched along a special hypersurface. This procedure is called "sideways stretching" and encompasses a variety of geometric degenerations of contact manifolds, including degenerating connected sums of contact manifolds as well as higher dimensional isotropic handle attaches.