Below is a sketch of topics that are of interest to me, at various inconsistent levels of depth. I omitted "modular forms", which William will cover in great depth, but mentioned CM, which wasn't assigned to anyone, and Siegel/Hilbert modular forms which Lassina and Paul will presumably cover. I thought that some of the complex analytic approaches might be suitable to computation, and fun to implement. Although I call `G\H^*' a Riemann surface, I am thinking of this as a widget for invariants of the group action of G on H. As a Riemann surface, however, one could ask for the image of a special point (i.e. its equivalence class), and create divisors, integrate along paths, etc. It would be easy to stretch two weeks into a semester, so of course we need to decide on limitations of the scope. I will probably only cover 1 and 3; although 2 and 4 would be desirable (very classical stuff). Item 5 would probably fit better in the framework of Lassina's talks (see his comment after his additional topic 6)). 
