How to write a research statement for a math postdoc position? I am a graduate student in mathematics working on functional analysis of quantum information (basically using matrix techniques in some well-known problems). I am presently applying for postdoctoral positions (in both Mathematics and Quantitative Physics departments). However, I am not getting any reply from most of the places and got a few rejection letters as well. Since I am from Mathematics, I cannot apply to experimental groups (where there are more openings). Again, being a Mathematics student and working in Physics (even though there are obvious connections between them) is not seen as a good example among certain parts of the physics community and the majority of the Mathematicians in this part of the world (personal opinion based on certain bitter experiences). I do not know whether it is the same in other places as well.  

I feel that I have not projected myself by writing a good research statement. I have written it after reading the first few entries of Google search results as well as advice from the AMS. I have mostly highlighted my present work, with only a short discussion of future ideas.   

To make my life more complicated, I want to move out of the present problems which I am working presently and choose some new problems for my postdoctoral research. I have a peripheral knowledge about the works of different groups. However, modifying my research statement according to the research work of each group is, I think, difficult (as I need to spend time to read their works and spot exactly where my knowledge can be used in their problems and so on). The reason for not having time is I am simultaneously working on some research problem as well as writing my thesis, which I need to submit in the coming months.

In this situation, how do I write a good research statement? I want to convey the message to potential employers that, while I have not done research on their problem yet (though I know them to certain level), given an opportunity I can learn and do work in their areas.
Writing a postdoctoral research statement should not be a huge exercise. Unless you are applying for a major postdoctoral fellowship, I would not necessarily expect a huge research statement. In many cases, in fact, you may not need a research statement at all to apply for a postdoctoral appointment; a cover letter, CV, and list of references may suffice. (When I hired my current postdoctoral associate, those were the materials I asked for.)

Now, that said, your statement should provide a few pieces of information:


A brief description of your current project, and any major research skills or tools you have acquired as a result of your training.
A brief summary of the kinds of problems you would like to study as a postdoctoral associate. If these are aligned with the interests of the group you are applying to, this is even more helpful.


Ultimately, however, when you are applying for a postdoctoral position, you are applying to a specific individual, who will be the one reviewing the applications. What I am looking for is someone who has actually responded to my job posting, not just a job posting. That means I want to see a clear statement that the applicant has thought about what we do in my group, and how her skills will contribute to the project for which I'm advertising. If there's no such indication, I'm much less likely to take the application seriously, unless there are mitigating factors (lots of publications in top journals, strong recommendation letters from colleagues I know, and so on).

Finally, I should also point out that the quality of your written English could be improved. While this might seem to be a minor issue, a poorly written statement can be enough for me as an advisor to think twice about hiring someone, simply because I would worry about my ability to communicate with the candidate. (Furthermore, someone whose communication skills are somewhat deficient will have a harder time finding a position than someone proficient.)