mathematical physics grad school: math vs physics departments

Monocles

I'm a junior physics major at a school in the US and I've recently come to the conclusion that I think that I like math better than I like physics. I'm thinking I might like to do mathematical physics in grad school, but since I've spent the last 3 years thinking I'd go to grad school for "normal" physics I'm suddenly very lost and confused.

First: I'm mostly confused about which department one interested in mathematical physics should apply to. Most mathematical physicists seem to reside in math departments, but there are still some in physics departments. Should I apply to both?

Second: GREs. Should I take both the math and physics GRE? Should I only take whichever one corresponds to the departments I'm applying to? I suspect that I'd do better on the math GRE than the physics GRE - perhaps even significantly so, so maybe it would be to my benefit to not take the physics GRE?

Third: Coursework. I'm currently just majoring in physics. If I decided to go this route I'd add on a second major in math, but I'd end up with the bare minimum coursework to graduate (1 semester of algebra, 2 semesters of analysis, 1 semester of complex analysis, 1 semester of numerical analysis, 1 semester of prob/stat, 1 semester of combinatorics, and then 5 other upper division classes of my choice). Would this be enough to get into a competitive grad school?

Finally, what do mathematics grad schools look for, and does it change if you want to do mathematical physics? For physics I know that the most important things are research, recommendations, grades, GREs. Mathematical research ability seems more difficult to gauge to me - do they care more about recommendations, for example? What about Putnam scores? Do they factor in? Research?

Finally, how do I know if I am even cut out for this? I'm pretty certain that I can handle the math - I've gotten all A's in my math classes (though I have only taken a few upper division) hardly lifting a finger. But I am not the best at physics. I especially found statistical mechanics to be extremely challenging and frustrating and ended up with a B in it despite pouring ungodly amounts of time into it (and still don't feel that I know it very well). I feel like all of the mathematical physicists I've met are godlike at both!

dx

Just curious, are you using the term 'mathematical physics' as distinct from 'theoretical physics'?

Monocles

Yes, I am using it in the sense of people who look primarily at math relevant to physics, such as low-dimensional topology, lie groups, quantum topology, rigorous quantum field theory etc. So more mathematician than physicist, but not leaving physics entirely. I have a pretty good idea in my head of what it is (I do research under a mathematical physicist at my school) but I have a hard time putting it into words.

Troponin

Althought I don't have any experience to offer, I am in the same situation and am curious to see what advice you may get.

MathematicalPhysicist

Which topic interest you the most thusfar?

Monocles

I'm interested in algebra, algebraic topology, algebraic geometry, and category theory (and wherever they apply in physics). So far that's been in condensed matter, but I haven't found any good reasons to be picky as to the field of physics it applies to. I've just been doing stuff in condensed matter because that's what my advisor works in. I don't know any quantum field theory which seems to be the biggest area most mathematical physicists work in, but I strongly suspect that I'll become very interested in it once I start learning it.

Also, why is there so much apparent contention surrounding category theory? My advisor says it is completely worthless and I know a couple of other professors who feel the same way, but I've also read some stuff online (such as at the n-category cafe) that proclaims category theory as the greatest thing ever. I find it fun to learn at the very least, but I don't know enough of it to really have any kind of opinion on it.

martin_blckrs

Well there's quite a lot of Algebraic Geometry in String Theory (especially if you're interested in Calabi-Yau compactifications and Mirror Symmetry) and also there are some concepts that are nicely formulated in terms of Category Theory (D-Branes, Topological Field Theories or also this "Categorification" stuff John Baez is working on). I think today pure math is becoming more and more important for physicists, especially for those working in High Energy Physics, so given your interests, I think you're on a good way to join this kind of research later on.