As a grad student who will be on the job market in the not-too-distant future, I'm starting to wonder about how best to prepare. I work in stable homotopy theory, and will be applying for both tenure track teaching jobs in the US and post-docs in both the US and in Europe (with the job market as it is, it seems prudent to cast a wide net), but probably not at an R1 school. I have never come across an open problem that I think an undergrad could do meaningful work on (ignoring the small set of really amazing undergrads who frequent MO and would probably not end up at my hypothetical REU). If I found such a problem, I'd probably solve it myself rather than hanging onto it as a possible REU project. 

> (1) should I spend some time seeking out a suitable REU problem in case a job asks me for project ideas?

I have no idea how common it is to ask a job applicant this type of question, but it seems like the sort of thing a small teaching college might want to know. 

> (2) Supposing that I did find a good problem and stopped myself from solving it, where would be the best place to display that in my job application material? 

I've read up on teaching statements ([on MO][1] and elsewhere), but it seems that is not really the place to discuss plans for REUs. Similarly, it shouldn't go in the research statement. Is this just something I bring to the interview and hope they ask about?

> (3) Do REU ideas need to be in the same field as my PhD research or could I just think up a good problem in a different field (e.g. graph theory where the background is more reasonable for an undergrad)

I'm amazed this hasn't been asked on MO before. I hope it's suitable, since many grad students frequent this site and would I suspect care about questions they may be asked in the job process. If it has been asked, please forgive the duplication. All I could find were questions about the [merits][2] of research if you are an undergrad, where to find [info][3] on REU type experiences, and the pros/cons for [publishing with undergrads][4] if you're looking to get tenure.


  [1]: http://mathoverflow.net/questions/812/teaching-statements-for-math-jobs
  [2]: http://mathoverflow.net/questions/45802/undergraduate-math-research
  [3]: http://mathoverflow.net/questions/13847/research-experience-for-undergraduates-summer-programs
  [4]: http://mathoverflow.net/questions/39572/publishing-with-undergraduates