Quantum difference equations (QDEs) for quiver varieties govern the K-theoretic enumeration of rational curves in these spaces. Recent developments in 3d mirror symmetry relate the monodromy of these equations to elliptic stable envelopes.
In this talk, I will explain how the monodromy of the QDE is sufficiently rigid to determine the equation itself. This provides a method for reconstructing the quantum difference equation directly from elliptic stable envelopes. I will illustrate this procedure in the example of the Hilbert scheme of points on the complex plane.