1) I'd develop a theory of board games based upon game graphs. I think there's huge potential in the area, enough to even change the way we think about games. W

1) I'd develop a theory of board games based upon game graphs. I think there's huge potential in the area, enough to even change the way we think about games. When viewing games as graphs you can start doing interesting things like enumerate all games that can be described in N nodes, find isomorphisms between game sub-graphs, and create a mathematically measurable concept of "difficulty". or 2) The application of cryptography to anonymous financial trading. At the moment a lot of anonymous trading happens via "dark pools" which are third party providers that match up anonymous counterparties, however this is less than ideal because you have to have a trusted third party and it also introduces latency issues.