I will be applying for grad school this Winter, but from January 2009-September 2009, I will be done with any course work and will not have any money to commute to my school to continue to do research. So I figured it would be a good opportunity to go further in my mathematics and physics studies. In graduate school I really want to focus on mathematical physics in a math phd program. I know this is a very broad term and means different things to different people. Some math departments actually have physicists on the faculty and actually are thesis advisers for math phds. Anyway, I have been studying GR and QM and I would like to study quantum field theory in grad school. Particularly constructive quantum field theory. Looks like i'm frankly **** out of luck. I don't see this happening in grad school. I have been looking very diligently for professors who even list constructive quantum field theory as a research interest and the only person I found was Leonard Gross from Cornell. Seems like the two founders of the field are Arthur Jaffe and James Glimm. Jaffe is in Harvard's Physics department, and even then, I am not even going to bother applying to Harvard's math department. James Glimm is emeritus at Stony Brook, so I don't think that is going to happen either. I think John Baez has worked on constructive quantum field theory (big surprise, this guy is a great mathematical physicist). One of my professors said that I would probably have a difficult time finding a professor who would supervise a thesis related to constructive quantum field theory, unless I go overseas. I have looked on many European math departments, and they really blur the line between math and physics. I have found a few in the Netherlands and some in Germany, among others. However, I don't think I have a good chance of being admitted to European universities and from what I hear, it is difficult for Americans to get funding. Would CQFT just fall under the general heading of C* algebras? Any thoughts on this? Should I set my sights on maybe a more tangible phd topic? I know this is still very far away, but I would like to have an idea of what is plausible and what isn't. OK, thanks a lot guys!