Abstract: I will explain how to define a t-structure on the wrapped Fukaya category of a complex conic symplectic manifold, whose heart is the global sections of a perverse sheaf of categories on the core of the symplectic manifold. Here, a perverse sheaf of a categories is just a sheaf of categories whose hom sheaves are (shifted) perverse. I will also show that the subcategory of objects with bounded microstalks (morally, the part of the wrapped Fukaya category coming from compact Lagrangians) admits Bridgeland stability conditions compatible with this t-structure.