The quantization of irregular Riemann–Hilbert maps

This talk gives an introduction to the Stokes phenomenon and the Riemann–Hilbert–Birkhoff (RHB) map of meromorphic connections at a $k$-th order pole. It then introduces the quantum Stokes matrices at a $k$-th order pole, and proves that they give rise to a quantization of the RHB map. In the case of second order pole, it becomes a dictionary between the Stokes phenomenon and the theory of quantum groups