I will present the proof of the split-generation of the compact Fukaya categories of certain Milnor fibers by vanishing cycles. The proof is based on the verification of the Koszul duality between compact and wrapped Fukaya A_\infty algebras of these manifolds. If time permits, I'll also explain how to use a bigraded version of Koszul duality between Fukaya A_\infty algebras to study closed monotone Lagrangian submanifolds in an 8-dimensional Weinstein manifold.