Pietro Longhi (Uppsala Univ.)

Exact WKB analysis of q-difference equations and five-dimensional gauge theories

  • Date: 17 FEBRUARY 2026  from 15:00 to 16:00

  • Event location: IR-1A

Exact WKB analysis of q-difference equations and five-dimensional gauge theories

In this talk I will present a new approach to the study of second order q-difference equations through the framework of WKB analysis. As an application I will illustrate a monodromy computation for the q-Mathieu equation. In physics this corresponds to computing the expectation value of a Wilson loop operator in five dimensional minimally supersymmetric SU(2) Yang-Mills theory, and can be identified with the Hamiltonian of a corresponding q-Painlevé equation. Time permitting, I will comment on the physical interpretation of our framework in terms of vortex-kink boundstates in coupled 3d-5d QFT and their wall-crossing dynamics. Based on joint work with Fabrizio Del Monte.