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I am currently interviewing in several universities across the U.S. for PhD programs in computer science. In every one of my interviews so far, there are always 1 or 2 professors that are eager to know which specific problems I am interested in researching (and it normally comes out as the most important question they are going to ask me). This question stumps me every time because I am not trying to enter a PhD program and start working on a specific problem right away. Instead, I want to do some lab rotations first and get a deeper feeling for the work of the institution's faculty (that works on my subarea of interest) and then, after these rotations, pick a specific problem (perhaps this is the wrong motivation?).

It does not seem to me that interest is a reliable determiner of success in completing a PhD. I could say that I am interested in Dr.X's research on complex manifolds because I skimmed through some of his papers. However, from my personal experience, I think there is a very big discrepancy between having read a little bit about a topic and claiming it as an interest, and actually doing research in that area. In other words, one might be interested in doing research in modelling the response of cancer patients to drug Y (because they want to defeat cancer or something similar) but a lot of times that person might realize that the actual research is far from his expectations and end up switching to different area.

I could list a few other reasons why I think interest is not a good measure of student's commitment but I might be wrong since professors like to ask this question. Why is this and what would be an honest way to answer it?

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    Well, if you express interest in Problem Y that's related to the work of Dr. X, the interviewer can say "Hey, that's great, Dr. X works on that. You should definitely come here." (Remember, interviews serve for them to recruit you as well as to help decide if you should be admitted.) Conversely, if you appear dead-set on working on Y, and nobody in this department works on that, they can let you know that this department is not a good fit for you. But I don't think there's anything wrong with saying that you want to try some things before making a decision. – Nate Eldredge Feb 22 '16 at 3:31
  • @NateEldredge I looked into the research of the faculty before applying to each school and I saw some problems that looked interesting but I am still an undergrad. Naturally, I don't have the time to start some in depth reading of the research of the faculty at each school and if I say "I am interested in Dr.X's research in Problem Y", then I would look ridiculous if the interviewer asks something along the lines of "In problem Y, how would you deal with Y_1, Y_2, and Y_3 and what do you know about Y_4?". – Lucas Alanis Feb 22 '16 at 3:37
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    @Lucas: In my field at least (math: that's close!) it would be surprising for an undergraduate student to have read the research of the faculty at the school. However they may have some coursework or done some outside reading in the research area. Thus for instance if Dr. X does research on complex manifolds (in the CS department? really?? cool!) it would be relevant to say that you know something about manifolds. I would find it strange if they asked you about specific problems -- much of the PhD training (in my field...) comes before students choose specific problems to work on. – Pete L. Clark Feb 22 '16 at 5:24
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    @PeteL.Clark Of course we don't have PhD interviews in math, so in this sense we're not too similar to CS. – Kimball Feb 22 '16 at 14:06
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    @Kimball: Well, usually not. In my program we have a grad student visitation day, and not all of the students who are visiting have been admitted to the program. It can happen that impressions gained during the day impact the admissions decisions....a little bit, in edge cases. Moreover we ask for a personal statement which is somewhat in the same ballpark. But of course you're right that a formal interview is an entirely different kettle of fish. – Pete L. Clark Feb 22 '16 at 16:42
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Other than the previous answer, we ask this question because a candidate may be interested in an area that is not in fact well represented in the department. If someone wanted to do research on numerical methods for optimization, my department has nobody to advise such a thesis -- but the candidate may not be aware of this.

I personally ask this question because too many graduate students come to me and ask whether I could be their adviser and then expect me to pose a problem they should work on for the 3-4 years. But I don't want to do that: if a student doesn't know what they want to do for research, yes, sure, I can give them a topic, but if it doesn't match their interest, it's going to be a painful 3-4 years for everyone involved. So I typically want that my students come up with topics they find interesting themselves, and then we can see how that fits into my research group and program.

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    This is an important one. "You're interested in Dr. So-and-so's work on X, but we all know that grant didn't get renewed...". Or just no one really works on that. – Fomite Feb 22 '16 at 20:42
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I'm not familiar with CS departments in particular, but I think this is less a "we ask because we want to know what we can expect you to hit the ground running on" and more of a "we ask to see what you know about us and where your general interests are". It's pretty much a job interview, so take it as a job interview type of question. A company wants you to show an interest in their company that goes beyond simply submitting a job application. They want to know what you know about them, and how that influences your job hunting. People that simply throw in an application and demonstrate no knowledge or specific interest in the company are unlikely to be hired unless the position is rather non-competitive. Companies want interested, happy, inspired workers; not some guy just looking to cash in his next paycheck, and likely biding his time for something he'd enjoy more to come along.

Look into the department before you arrive and see what things the faculty are working on now, or have worked on recently, and single out ones that seem most interesting to you. If you find there are none, this probably is not the right university for you.

This isn't something that binds you in any way. As one of the qualifying exams for my Ph.D., I was to present a talk on some recent research to demonstrate my knowledge and interest in doing research. Ostensibly, interest specifically in the subject matter of the talk, but in no way was that binding. My actual thesis could, and ultimately did, have absolutely nothing to do with the subject matter of this oral exam. To this day I have not produced a single piece of research that's relevant to the topic of that talk.

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A candidate with no intrinsic motivation and own research interest appears to be only in for the name of the lab and the title of PhD, not the topic.

You want creative students that are eager to pursue research and come up with ideas of their own. When you are reading the research topics of the lab, and you don't come up with ideas, then you are the wrong guy. It may be possible to choose the advisor later - but you really need to be highly motivated for the specific topic of at least one of them...

I'd never accept a candidate with a "tell me what to do now" attitude, or a "maybe I will find out later what I like" attitude. It's okay if you switch topics (if it's early enough) but you have to burn to do this.

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