The quark propagator in the complex domain: A status report

In these proceedings I review the status of an ongoing project that aims at solving the quark propagator Dyson-Schwinger equation in the complex domain. The novel aspect of the approach is that the non-analyticities arising throughout the iteration of the equation are to be taken into account in an appropriate way through dynamic contour deformation. Because of the complexity of the approach, these studies are undertaken in a heavily truncated scenario that serves as a toy model for the development of the numerical techniques that are required to treat the system in a mathematically sound way.