This course would be a survey of fundamental results as well as current research. Topics will be related to the following areas: geometric structures on surfaces, hyperbolic 3-manifolds, Riemann surfaces and Teichmüller theory, and will focus on the various interactions between these fields. Students will be encouraged to explore open-ended questions and/or write related computer programs. The following is the course plan:
Part I
Part II
Part III
Part IV