This has been my main area of research for over 25 years. My list of publications is available in my vita. Much of this work has been joint work with my colleagues Alan Elcrat at WSU and John Pfaltzgraff at UNC Chapel Hill.
Here is an article from SIAM News Jan./Feb. 2008 on our work to extend the Schwarz-Christoffel mapping for polygonal domains to the multiply connected case:SIAM News article