Karen Shuman writes: As for the signal processing, I would like to see the different types of basis elements which my weird group produces. These basis elements are functions of 2 complex variables and they map into the complex numbers, so it is not completely trivial to see that the group is actually doing to different types of functions. Even simpler but also as interesting (perhaps the first thing to do?) is the fundamental domain for the discrete group action. It would be nice to be able to see it--it lives in the product of a half complex plane and a complex plane. One time I drew by hand several different snapshots of where the boundary of the domain goes under different group elements (non-discrete) and it was tedious, but it also looked pretty cool. Part of the action is going on in hyperbolic space but the other half is going on in Euclidean space, so things get twisted around (at least my little drawings indicated this.) None of this sounds like signal processing, but as I was thinking about my problem the thing that bugged me all the way through my own thesis was that these things were hard to visualize, and this would be a good opportunity to see some of them. Not ground-breaking research, since I imagine experts in the Jacobi group know these things intuitively, but I don't and when I talked about what I was doing no one else could see it very clearly either. Then there is the actual signal processing question---if this group will work, what types of functions, which group elements should be used to generate the functions, etc---I think all of these questions could be answered much better if we could see things first.