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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!

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You could try the Academia StackExchange –  dd3 Jun 29 '13 at 2:25
    
I asked there already as I mentioned above: see academia.stackexchange.com/questions/10792/… –  Let's talk math Jun 29 '13 at 8:34
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You could try writing to David Mumford for advice. He switched from algebraic geometry to computer vision. Few people can boast Mumford's track record in pure mathematics so I'm not saying his case is typical, but I would think he would have good suggestions for you. –  Timothy Chow Jun 29 '13 at 23:02
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2 Answers 2

up vote 6 down vote accepted

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.)

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Thanks Tim Poret a lot for this information, I will definitely look this up! If you knoa ahy further information, please let me know, and thanks again! –  Let's talk math Jun 28 '13 at 21:39
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It is best to continue this off MO, perhaps, although if others are interested we could summarise here. My e-mail address is on my profile page here. I gave a link on Linkedin some time ago and will post it here. –  Tim Porter Jun 29 '13 at 9:54
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Here is an interesting NYtimes article. bits.blogs.nytimes.com/2013/01/16/… –  Tim Porter Jun 29 '13 at 10:03
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Dear lets-talk-math, Good luck in your new position. The background stuff on TDA is in some good books on computational topology for instance Edelsbrunner and Harer in one of the AMS series. They are good reads and give a neat perspective on homology etc. ... almost a light bedtime read, and you will be able to see the subject for the future. –  Tim Porter Jul 3 '13 at 17:45
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I work in image processing. I work in an oil analysis laboratory. (Its kind of like a pathology for trucks and heavy machinery if you can imagine that). We test oil samples to detect engine trouble.

I've never done a Phd or even honours. I studied a dual degree in Math/IT. You'd probably be better at it than me!

I'm currently working on a project to detect bubbles in oil using image processing. The purpose is to automate lab processes.

The funny thing is, getting this job was kind of an accident. When I applied for the job, the job add just said that they were looking for a pascal programmer. I think they never even hoped to find someone with a math background (let alone image processing).

If you've got a phd and published papers, you're probably already plenty capable! The hard part now is finding the opportunities.

Yes there will be some learning curve in learning programming but I think you will pick this up pretty quickly.

If I were in your position and no other opportunities come up, I'd be looking to get an entry level programmer job in something like laboratory software. This may not entail math at first but provide an opportunity for you to move into that.

The previous job I worked in was insurance software, it had no maths at all.

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Sav: Thank you for sharing your experience and your input; your answer is positive, because you tried to point out that one can try gathering some initial experience working in a company and then try to pursue the higher academic platforms in the same area; but I am not sure how practical it is for an academician to switch to different kind of jobs to get into academia again; although if there is no other opportunities,that could be a decent option I suppose. Thanks anyway! –  Let's talk math Jun 28 '13 at 18:59
    
I am probably going to take a chance asking this question in other sites, e.g. signal processing beta etc. –  Let's talk math Jun 28 '13 at 19:02
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