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Suppose you have done work in two subfields of a main field, and have a keen interest in both of them. Some examples might be,

  1. Main field: Physics, Subfields: Experimental Quantum Optics and Condensed Matter Theory
  2. Main field: English, Subfields: American Literature and Medieval Studies/Literature
  3. Main field: Mathematics, Subfields: Topology and Numerical Analysis

Is it a bad idea to apply to some programs in one subfield and some programs in the other subfield? I'm faced with this dilemma, and my hope is to choose which subfield to go into based on my acceptance offers.

Or is it better to just buckle down and only apply for programs in one subfield? Certainly that would make you more focused, and thus more desirable as a candidate (and also more focused as a researcher).

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    Do you mean at the same university? Because if you apply to one subfield in one university and a different subfield at another university, how will they know? – ff524 Sep 23 '16 at 16:59
  • At least in American math PhD programs, students don't have to pick a subfield before applying. You can express interest in more than one subfield in the same statement of purpose. – user37208 Sep 23 '16 at 17:22
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The main problem you'll face is the increased workload you'll face in preparing your application materials. Depending on the programs, you'll often be expected to identify faculty you'd be interested in working with, and you'll be expected to succinctly show why your research interests fit with that person. The statement will also be viewed as a whole, so you will inevitably need to either focus a single application around certain aspects or be clear that you are open to a range of sub-fields within a given discipline.

Some people like very focused statements, while others are still welcoming of more broadly stated interests, so one is not necessarily good or bad. That's part of your unique situation and interests, but the advice I've been given is if you really do have broad interests, express that because it will attract advisers and programs that value that. But if you really only want to study certain things, say that because that too attracts you to the right people you're more likely to be happy with in the long run.

Most people (all I've talked with, anyway) find preparing multiple drafts of all the materials stressful as it is, so having to prepare multiple versions with very different tones and a different focus likely will take you some more time and effort to do well. So if you are applying to only one sub-field per application you can still focus your statement on that field and just the right people to work with in that field - but you are going to have to create at least 2 sets of very different personal statements, each of which will be customized per program.

As long as you are OK with the extra workload, I am not aware of any other downsides beyond application fees if you are applying to more programs in total. Applying to programs with different sub-fields is fine if you really interested in both, and will not generally make you a less attractive candidate because no one but you (and maybe your letter writers) has any idea you're applying to a variety of programs.

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