Two days ago, J. Gauntlett and company posted a very interesting paper on the web (hep-th/0209114), in which they found an M-theory analog of the Godel universe. This is a homogeneous solution of Einstein's equations on spacetime with trivial topology and closed timelike curves. From the point of view of this course, this solution is particularly interesting as it represents a simple example of a solution with an exotic fraction of supersymmetry (5/8).
Notice from the picture of the Godel universe as it appears in Hawking and Ellis that the closed timelike curves are in a sense "topologically large". The assignment is to identify preferred holographic screens (in the sense of Bousso, hep-th/9906022) associated with inertial observers in the Godel geometry, and see whether they can help with the problem of closed timelike curves.
NEW (Dec.9): The results of the bonus assignment have now been posted, as hep-th/0212087.