Spectral curves and irregular singular differential operators

Establish an analogous correspondence between differential operators with irregular singular points on a smooth algebraic curve and singular spectral curves defined over the same curve.

Background

The paper reviews a biholomorphic correspondence between holomorphic differential operators, opers, and spectral curves for smooth projective curves of genus greater than one. It then emphasizes that enumeration problems produce differential equations with irregular singularities and asks whether the holomorphic correspondence extends to that setting. Such an extension would provide a geometric framework for quantum curves and could illuminate the geometry underlying the irrationality of ζ(3).