Summary
Potential theory is the study of functions satisfying Laplace’s equation, an elliptic partial differential equation of widespread scientific importance. A deep understanding of these functions provides valuable insight into many physical processes. Potential theory is very well-understood in simply connected settings, such as in the unit disk or the upper half-plane, and there are many exact solutions of models describing physical phenomena in these classical geometries. However, potential theory is arguably far less well-understood in more complicated multiply connected geometries, i.e. regio
