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While applying for postdoc positions, candidates are asked to submit a statement of research interests or research plan. Some institutes want that write up to be less than two or three pages. I was just wandering how strictly one should obey this page restriction and whether one should add references (bibliography) in such a write up.

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You can, but you don't need to, include references to other works in the field. You may use them to explain in the first part of your statement what the big questions are that you are trying to answer. One could use review papers, or references to the really important papers that started a field here, but it is probably just as fine to write statements such as "In 1971, Grothendieck asked the question..." without further references -- whoever understands the question, will also know where it came from or how it fits into mathematics. (Obviously, the same is true in other fields, if you reference luminaries.)

What is really important, though, is that you reference your own papers to explain how your own (published) work fits into the field. If you apply for postdoc positions, your list of publications is likely not very long, so it is important that your statement explains not only what you are interested in or plan to do, but also where you expertise is in.

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