We will discuss an explicit graph formula, in terms of boundary strata classes, for the wall-crossing of universal (over Mbargn) Brill-Noether classes. More precisely, fix two stability conditions and for universal compactified Jacobians that are on different sides of a wall in the stability space. Then we can compare the two universal Brill-Noether classes on the two compactified Jacobians by pulling one of them back along the (rational) identity map. The calculation involves constructing a resolution by means of subsequent blow-ups. If time permits, we will discuss the significance of our formula and potential applications. This is joint with Alex Abreu.