Grad School Acceptance: Concerns Over Math Deficiency for String Theory

[GeorgeThe4th]

Hello everyone. I am an undergraduate senior anticipating degrees in both physics and astrophysics this spring. Until about a year ago I wasn't particularly sure what I wanted to do after graduation. However, after taking upper division QM and particle physics courses I've developed a great interest in pursuing high energy theory.

So for this admissions season I sent out 13 applications to various top 40 physics graduate schools. I stated HET and particularly string theory as my research interests. Just a few days ago I received my first acceptance, and so naturally I am quite happy and relieved.

However, I do have one big concern. In the process of getting my double major I never had any scheduling room to take math courses beyond the standard requirement. That is, I took the Calc 1-4 sequence and one additional course in "foundations", which was basically a course on proofs. It has been over two years since then, and I am concerned that my deficiency in higher level math courses could make it challenging for me to pursue string theory. I am aware that real/complex analysis, group theory, topology, differential geometry, and many advanced topics are important to string theory.

My fear is that I may be shoved into some other research area or not be able to join my desired research group due to this deficiency in the aforementioned topics.

Is this a valid concern, or is it normal for theory graduate students to need additional coursework in those topics after arrival? To my understanding, new physics grad students are kept busy with all the advanced courses related directly to the major. Would there be much room (or would it even be possible) to cram a few math courses in there? Or, is the required depth in those topics not enough to justify taking entire courses on them? I.e, do most students just cover them through self study?

In any case, there are basically three options I have:
1) Decline all my offers and go into a 5th year as an undergrad and take several relevant math courses.
2) Accept one of the offers and just hope it doesn't matter.
3) Accept, but ask for a 1-year deferral and take courses in the mean time.

I am really hoping that it will be ok for me to just accept an offer and that my fears are poorly based. If anyone has had a similar experience or has a suggestion for what I should do, it would be greatly appreciated.

 

[Mépris]

Hi George,

You might be interested in this.
http://www.claymath.org/library/monographs/cmim01c.pdf

 

[Nabeshin]

As someone who is in a not too dissimilar situation, I'd say let the admissions committees decide for you. Presumably, with 13 places applied to you will get into at least one. Since you (again, presumably) stated in your applications you wanted to do Hep-th/strings, that means that when they admit you they're essentially saying you're qualified enough (or that any gaps can be filled easily enough).

Besides this, go talk to your academic advisor, or professors who you want to work with at whichever graduate schools you end up getting accepted to. These are the people most qualified to tell you what preparation is necessary (I can't think of anyone off the top of my head here at the forums who is actively involved with, or has a research level understanding of string theory).

 

[chiro]

Hi George,

You might be interested in this.
http://www.claymath.org/library/monographs/cmim01c.pdf

Hey Mepris.

Thanks for that link. I've got a few documents on string theory but not in the same focus or perspective as this one.

 

[hadsed]

I visited a school in Kentucky and spoke with a string theorist. When I asked him a similar question about math, he told me that it was much more important to have solid foundations in the basics of physics, particularly classical mechanics (mainly formalisms), statistical mechanics, quantum mechanics, and of course e&m (though I got the impression the first three were most important, but they all are). When I specifically asked about things like differential geometry or topology, I still got the impression that it wasn't too important.

There are different types of work being done in string theory, just as in any other field. Besides, the worst that can happen is that you need to take a little more time, but that would happen regardless of whether you started now or later, and it would be beneficial to learn in the academic environment.

Just some thoughts.

 

[Vanadium 50]

None of the above. Go to grad school. When you get there, meet with whomever is in charge of entering grad students, explain your situation and then do what he says. That may mean more classes, that may mean a different schedule, it may mean business as usual.

 

[MobiusPrime]

If you got accepted, then your background is fine.
They would never accept someone who wasn't good enough.
Get stuck in and have fun! :D

 

[GeorgeThe4th]

Thanks for the replies everyone, you all bring up great points. When I visit a couple grad schools next month I'll talk to the HET professors about this. I think I've pretty much ruled out the option of staying another year as an undergraduate. The only other reason I had been considering that was to potentially boost my PGRE score and apply to higher ranked universities next year. However, that's a gamble - there's no guarantee I'd be able to boost the score.

Also, thanks Mépris for the link. That looks like a very nice introduction to many of the relevant topics. I'll definitely have to try working through that over the summer.