Compact degenerations of curves and derived categories

Consider a compact degeneration of curves, i.e., a flat family of curves over a disc such that the central fiber is a 1-nodal curve with two irreducible components and all other fibers are smooth. I will explain how the family of derived categories of the smooth fibers is related to a category glued from the derived categories of the components of the central fiber. This is a joint work in progress with Valery Alexeev.