Monodromy of linear differential equations is a very old and classical object, which for certain very special equations of geometric origin has been the subject of challenging conjectures of more modern flavor. One such conjecture, proposed by Bezrukavnikov and myself, identifies the monodromy of certain quantum differential equations with a generalization of the Hecke algebra that is important for representation theory in large prime characteristic. I will explain what this conjecture says and how we prove it for Nakajima quiver varieties.