I'm a PhD student in mathematics, working in a quite unpopular field (recursion theory). As I'm now applying for postdoctoral positions in the US, I've encountered the following problem: The number of mathematics departments in the US having notable researchers in my field is quite small. As I'm quite flexible with my research interests, I added departments with researchers in related fields (such as model theory and set theory) to my list. But even then, there are less than 20 relevant departments across the US to which I can apply. I heard that in order to maximize the chances of getting a postdoctoral position, mathematicians often apply to 50 positions or even more. I'd like to do the same thing, but I have some questions about it:
- Are there any arguments against applying for postdoc positions in math departments where your research interests are not even remotely represented?
- What should I do in order to increase my chances of getting a postdoc position in such a department? More specifically, what should I write in my cover letter (where applicants usually mention relevant faculty members, and sometimes also explain why they fit the position)? Should I contact a faculty member? What should I write to him/her? Any other useful advice?
- Assuming that I have a strong application, do I have a reasonable chance of getting a position in such departments?
- Bottom line question: Should I invest time and effort applying for positions in such departments?