Before I start my question, I should probably mention that this question might not be the right question to ask here, but I tried academiabeta, and stackoverflow, but without getting any to-the-point responses. I also noticed that there were some questions of similar interest asked here, but mine is little different and more subject/situation-specific. Also I am afraid my question might be a little too long, pardon my slightly unnecessary detail!
Here is my situation: I am a pure mathematician finishing Ph.D., working in Riemann surfaces, Teichmueller theory and differential geometry (with published papers in decent journals), having backgrounds in these topics and some PDE and topology and have some introductory knowledge about programming. I have been wanting to switch to little more applied areas (described below) because: 1) I believe getting posts and grants are slightly easier in there, 2) my postdoc hunting in pure mathematics have resulted in vein (despite getting shortlisted twice in Europe). I wanted to switch later anyway but reason 2) is forcing me to think of it now.
By applied areas, I meant areas like medical imaging, computer vision or even theoretical biology (there are interesting works of Prof. Robert Penner on moduli spaces and protein folding, for example), where they use Riemann surface and differential geometry a lot, and I want to work in more theoretical problems, but would also like to learn more computational techniques (although secondary).
Without further ado, here is my question:
Since I have not published any single papers in those applied areas, or haven't had any formal training in them, what are my chances of getting a postdoc in these areas, being a pure mathematician all my life so far? If any of you have done so before, or are working in these applied areas, I would very much appreciate if you inform me! By informal communication with some people (who are Ph.D. students) working in these areas, I was informed that my backgrounds are good, but one or two professors I have contacted already mentioned that they want somebody with actual research experience in say imaging, which I do not have. So, I am not sure where I stand compared to other applicants. Your responses and honest opinion (even though not in my favor) will be highly appreciated! Thanks a lot in advance!
Best Answer
There is a newish emerging area, `applied algebraic topology'. It includes Topological Data Analysis (see work by Gunnar Carlsson and others). There is also new work again in Applied Algebraic Topology looking at Configuration spaces and probablity theory. Look for research assistant jobs at Post Doc level on specific topics in applied geometry and topology.
There is also an ESF programme (http://acat.lix.polytechnique.fr/) that gives some idea of what may be available. Some of this would provide a half way house between where you are and where you want to be! Good Luck. (Soon there is s summer school in Slovenia on these areas. Look at the program schedule and you may get some ideas on who to contact to see what they think, whetehr there are any positions coming up, short visits are a good way to start if they have money for such and seem interested. I think there is quite a good chance and all of this area is growing fast so it could be very interesting to get into it at the moment. (The topic of big data is even hitting the newspapers, and that forms part of this.)