I'm entering my final year as a math/physics undergraduate, and I'm looking into grad schools to apply to. In particular, I'm interested in topological quantum field theory. As a student, I'm fairly well-off academically and research-wise, and comparing myself to people who I've known the past few years, I'd be a reasonable candidate at pretty much any grad school, though I wouldn't be guaranteed a spot at top tier schools of course. I'm interested in topological quantum field theory, and connections with low-dimensional topology and knot theory, which is an area somewhere in the intersection of math and physics. From what I've seen, the research is done both by mathematicians and physicists. While it's physically motivated, a great deal of the language is that of pure math (i.e. categories, algebraic topology), which the average physicist might not be familiar with. No one at my university is very close to the area, nor were they very knowledgable beyond the big names that everyone knows (Witten, Jones, Atiyah, and other similarly famous people who probably aren't even taking students). What U.S. graduate schools (in either math or physics) would be good choices for someone interested in topological quantum field theory? (I'm open to other countries with good programs, but only if the grad school is primarily English-speaking) I'd be open to going to grad school in either math or physics. I think my application is roughly the same calibur in both, but it might be a little stronger in physics, since I've done a bit more research in physics. In physics, I'm not terribly concerned whether the connection is with condensed matter theory or with particle theory. I mildly favor grad school in math, since I think there is more freedom as to what classes to take. I'm also more comfortable with the mathematician's way of doing quantum field theory than the physicist's. Niether of these is a deal-breaker for a strong program from a physics department. For reference, I've taken courses in ordinary QFT, algebraic topology, differential geometry, as well as pretty much everything that pedagologically comes earlier and some other random classes (algebraic number theory, general relativity, etc.). Over the summer I've been reading Atiyah and Bott's "Yang Mills Equations over Riemann Surfaces" as well as Witten's "Quantum field theory and the Jones polynomial". A program with the same flavor as these would be ideal.