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I am currently applying to Ph.D programs in the US in Mathematics and am trying to decide what to list for my research interests. I am very interested in field Y, but I also have a background (and slightly less interested) in field X. I have enough knowledge to discuss both, but I definitely know more about field Y. That said, field Y is very small, with most departments I am applying to having only one or two people working in it, while X is definitely more common, popular topic. My question is, should I discuss more the topic which is less popular or more? Does it matter, or is it just my interests in something that is being assessed?

Edit: In this case Y=topological modular forms, and X=gauge theory, in particular floer homology.

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    I don't see much merit in being less than honest about your own research interests. As I see it, much of the advantage of being an academic mathematician is that you get to study whatever interests you (maybe the level of interest of others affects your interest, but that is for you to decide). Here's an idea: since you are anonymous here, why don't you tell us the values of X and Y? If Y turns out to be "showing that there are no odd perfect numbers", you'll probably get different advice from if Y turns out to be "the ergodic theory of numbers", although both meet your description. Nov 3, 2015 at 3:31
  • Note also that depending upon where you are applying, what you list as your research interests could be very important (e.g. in Europe, where you apply to work under a specific professor under a specific topic) or not very important at all except as a rough measure of your background (e.g. in the US, where students are expected not to know what they want to work on and/or change their minds to a greater or lesser degree). Nov 3, 2015 at 3:36

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I am impressed that an undergraduate student could speak knowledgeably about either Floer homology or topological modular forms, let alone both. I would include both interests in your applications: by describing both, it seems implicit that you are not wedded to either one, so I don't see your interest closing any doors.

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There is no downside to listing a topic that people might not be interested in. No one will think "We don't want any topological modular forms guys around here"! And it shows breadth of knowledge on your part, which is a positive.

On the other hand, there is a significant potential downside to not mentioning it. You might miss out on the opportunity to do a PhD in this area by not listing it, which would be a big loss if this is what you are most interested in.

Your judgment that the less popular area is less likely to lead to a PhD opportunity is not necessarily correct, either. There may be fewer people working on the more esoteric topic, but it is also quite likely that there are fewer potential PhD students in that area. Those who are studying it might have trouble finding good PhD candidates, and thus be quite pleased to have someone with your interests come along.

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In general, your goal in applying to schools is to get admitted. Anything that improves your chances in that respect is helpful. If that means listing some esoteric areas in the hopes that someone at the department sees that listing and thinks "I'd like to work with this candidate!", then by all means go for it. (That assumes, of course, you actually want to study that topic. Lying to gain admission will eventually backfire on you.)

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  • Thank you for your answer! Though this begs the question, do my chances increase or decrease by appealing to speciality? Is there a good way to guess? Nov 3, 2015 at 6:05
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    Either it increases your chances of being admitted to a department that likes your taste in research, or it decreases your chances of being accepted to a department that doesn't like your taste in research. Either way it helps you.
    – JeffE
    Nov 4, 2015 at 2:16

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