The Fukaya category is a powerful tool in symplectic topology. However, its practical application is often hindered by computational difficulty. To avoid the obstruction on computation, one can focus on Weinstein manifolds, i.e., symplectic manifolds with nice properties. Then, the nice properties make the computation feasible.
In this talk, I will explain techniques for making computations of Fukaya categories of Weinstein manifolds, by computing examples. The examples will contain the cotangent bundles of spheres, the cotangent bundles of punctured spheres, and plumbing spaces.