Hey all, I'm a math and physics graduate who will be starting math grad school in a little over a month, and, though I know I have time to decide, I'm a bit conflicted about what to concentrate in. I'm broadly interested in the applications of math in physics. Specifically, I've always had quite a penchant for general relativity, and there are still a number of open mathematical problems in that field. It would seem like a natural fit for me to pursue research in mathematical relativity, but the thing is . . . I'm not sure that I'm all that interested in PDEs/analysis, which is ultimately what the subject boils down to. I realize it's not as if all analysts do is grind out solutions to PDEs; there's a lot of manifold theory and geometric concepts to learn that would interest me. But at the end of the day, I'm just not sure that I can motivate myself to develop solution methods for PDEs, even though I'd be fascinated by the physics they reveal. Algebra, on the other hand, is something that I actually enjoy doing. Taking abstract algebra as a junior felt new and different to me, and I was refreshed the short, crisp proofs. However, the physical applications of algebra are more limited as I understand, and it really loses points for me because of this. Just as I'm not sure if I could do PDE-heavy stuff, I'm also not sure that I could be a completely pure mathematician. I know that algebraic geometry and representation theory have connections to quantum field/string theory though. This might interest me since I love learning about links between math and physics, but I don't know enough about these topics yet to say for certain. So, I could do something that I don't find as mathematically stimulating for the sake of the physics in analysis, or I could do something I find very mathematically stimulating without much physical motivation in algebra. What do guys think? Also, do you think career outlooks are radically different for these concentrations? My aim is a career in academia, but I'd prefer something that also gives me a solid fallback elsewhere.