Appears in collection : Summer School 2015: Moduli Problems in Symplectic Geometry

In work-in-progress with Katrin Wehrheim, we aim to bind together the Fukaya categories of many different symplectic manifolds into a single algebraic object. This object is the "symplectic A-infinity-2-category", whose objects are symplectic manifolds, and where hom(M,N):=Fuk(M-xN). At the core of our project are witch balls -- certain pseudoholomorphic quilts with figure eight singularity. I will discuss recent progress: toward the construction of the moduli space of domains on one hand, and toward establishing the Fredholm property on the other.