Abstract: Perverse schobers, introduced by Kapranov and Schechtman, are a conjectural categorification of perverse sheaves. In this talk, we will present Merlin Christ’s framework for perverse schobers parametrized by spanning ribbon graphs embedded in surfaces with boundary, formulated in terms of constructible sheaves of stable ∞-categories. It can provide an ∞-category of global sections of perverse schober supported on a ribbon graph, and describe the monodromy around the singularities. As an application, we also use perverse schobers to study the space of stability conditions on triangulated categories.