Mathematics PhD route to theoretical research?

[ran13]

Hi PFers,

I'm a senior physics/math major and very interested in pure mathematics (esp. algebra and number theory) but I'm also interested in the very abstract side of physics like string/particle, some QFT and unification theory.

If I pursue mathematics as a graduate as opposed to physics, how disadvantaged will I be in entering these research areas? I'd still love to be able to contribute to pure math, but what I am keen on is learning how physical theories and pure math overlap, and being active in that area too.

I find my upper div physics classes awesome (quantum, EM and electrodynamics, nuclear, etc.) but I find the 'artistic' methods (don't mean to sound pretentious...) of problem solving in math to be really exciting and rewarding, especially as a break from the strictly applied stuff.

Any advice? Application cycle for 2012-2013 has started and I'm about to decide which programs to apply to and how to craft my SOP.

Thank you :)

 

[bpatrick]

Granted, I'm at about the same stage of career whatnot as you (about to start graduate school), and even though I'm going into applied mathematical neuroscience / biophysics ... I'm pretty sure there programs in mathematical physics that are specifically designed to spit out PhDs who work with the mathematics of theoretical physics?

I could swear I have seen PhD programs that are more or less the classes you'd take to earn a masters in pure math plus the classes you'd take for a masters in mathematical / quantum physics ... then after qualifiers you do your dissertation in the theoretical physics area.

Umm, I don't recall where all I've seen them but I know for a fact I have seen them so at least one of the schools my fiancee and I are applying to have the programs I'm talking about:

U Pittsburgh, Northwestern, Penn State, Harvard, Iowa State, U Maryland, Renssellaer, U Washington, and probably a bunch more have stuff like this ... maybe look at any of those school's math / physics departments and see what degree programs they offer ... I swear that there are a few who do interdisciplinary PhDs in mathematical-theoretical physics.

p.s. after you find whatever school(s) I saw those programs at, just look at where the profs of theoretical / mathematical physics got their degrees, and you'll start to generate a much bigger tree-list of programs that are exactly in that area.

 

[homeomorphic]

I'm trying to do something similar. I ended up getting sucked more into pure math because I got into a school that didn't have too much mathematical physics and it's just hard to do both. The stuff I am doing is very close to loop quantum gravity, and fractional quantum hall systems, but I only know enough physics to see the connection, not enough to understand the physics papers. It's possible to work in my area without knowing much physics.

I didn't get a double major. I only took a couple extra physics classes in undergrad.

You can probably resist the pull towards pure math if you go to the right place, but it's just hard to do both. It's hard enough to do one of them. That's why real mathematical physicists are pretty rare these days. There are physicists who dabble in math and vice versa, but only a few who really know both.

 

[ran13]

I'll look into those mathematical physics programs then. Shame that they're rare... It seems like a fascinating field. I could only register for one subject GRE (math) so hopefully that will not be an issue?

Any other tips on this topic? Anyone who's made this transition or achieved something similar? Thanks again.

 

[ran13]

Bump! Any advice at this point in time would be appreciated. I don't want to end up enrolling into the wrong program... PhDs don't really allow room for double dipping :(

 

[bpatrick]

http://www.math.indiana.edu/graduate/mathphysics.phtml

I found one of the programs I remembered seeing ... it's from a school Debra and I crossed off our list (due to the program she was looking into not the strength of their math department).

If you haven't found more programs like this yet, I'd start by looking at where all the profs that are listed as chairs/profs/advisers got their degrees.

*on an additional note, a friend from undergrad did (from what I understood of the program) grad school at the University of Miami where you go into their physics department and then take all of the graduate level "mathematical physics" classes they offer along with whatever else you need to learn in order to pass your physics qualifiers, then you take 7-8 graduate level pure math courses, take the math PhD qualifiers, then switch back to do the rest of your physics PhD (most likely in theoretical / QFT / particle physics or whatever ... sorry I'm not really a physicist), and technically I think they award you a PhD in Physics and a M.S. in Mathematics.

So yeah, not sure if that's something of interest, but if nothing else, there are two programs you might not have heard of that sound like what you're into.

 

[homeomorphic]

Funny you should mention Indiana--that is where I am. It's pretty pure-math oriented here, despite the presence of the mathematical physics program. We have an algebra/number theory guy who has dabbled in some quantum computing stuff, an algebraic geometry guy with links to string theory, a couple topology profs with ties to quantum stuff (more like gauge theory for topology's sake, and then, there's my adviser, Turaev, who has had a big impact on the TQFT world, though, really, my impression is that he's pretty pure math, despite doing things that have somewhat physical flavor), some guys in PDE who do Ginzburg-Landau theory, fluid mechanics, Navier-Stokes. So, there's some stuff. But, there aren't a whole lot of options as far as classes to take or seminar talks. If you want physics, it's mostly in the physics department. I guess you can be in either department with the math physics degree. On that side, I'm not very familiar with the physics department, aside from knowing a few grad students and having taken two classes. However, my impression is they might be a little on the non-mathematical side, with maybe a couple exceptions.

There's a condensed matter theorist who is cross-listed in physics and math. I know a student of his who is very mathematical, but he's in the physics department.

Maybe, UC Riverside? Perhaps, not the highest ranked, but I guess Baez is going back there (he quit quantum gravity, but maybe he'll still take students doing it?), and they have other people there, too, doing quantum mathematics.