There are two ways to write explicit spectrum of certain operators (like modified Mathieu operator). The first uses so called classical conformal blocks (Zamolodchikov in CFT; Nekrasov-Shatashvili in gauge theory). The second uses c=1 conformal blocks and comes from the theory of topological strings (Grassi, Hatsuda, Marino). I plan to explain CFT meaning of both construction and then show their equivalence.
Based on joint work with P. Gavrylenko and A. Grassi.