I completed my PhD in pure math but wound up in industry immediately after completing the program. I dislike industry but love academia and research; and so as quixotic as it is, I would like to find some sort of academic position. It's been suggested to me that finding a mentor in academia would be helpful. I've tried doing so but haven't had much luck with my networking (and, honestly, if I had a stronger academic network, I wouldn't have this problem in the first place). Any more concrete suggestions for finding one? Frankly, I'm not sure what I'd have to offer over a real grad student or postdoc, which positions are already limited and competitive.
Specifically, I would want to find a mentor who would be willing to help me with some sort of research project and to:
1) Help me find suitable research topics: ones that are amenable to completion by someone working by himself, yet are nontrivial enough to be worthy of publication. (This is normally something one picks up in grad school, but my advisor assigned me very specific research problems and refused to allow me to change them).
2) Chat about math with occasionally. (Being in industry, I don't really have anyone to talk about nontrivial math with or bounce ideas off.)
3) Get the results published and promoted, if the project is successful. (Simply, say, posting a preprint on the arxiv without any further promotion wouldn't really be conducive to getting an academic position.)
So, how should I proceed?