Scattering coefficients from Monodromies

Scattering can teach us a good deal, both about the underlying physical processes, and about the partial differential equations (PDEs) that describe it mathematically. The scattering of fields off black holes is particularly insightful into quantum gravity questions and into the structure of the PDEs -the Klein-Gordon wave equation on a curved background- that govern the process. The scattering coefficients corresponding to this problem have been only fully understood analytically in special cases –the low/high frequency regimes. In this talk, I will use analytic properties of the complexified wave equation to relate the monodromies around the wave equation's singularities to the scattering data. This new technique to compute scattering coefficients is valid in full generality and leads to new perturbative and numerical methods which both are in good agreement with, and significantly extend, previous results.