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I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in applied fields relating to the above areas: like medical imaging and computer vision. I've no prior knowledge in these areas, indeed in my department there's nobody I can talk to about these subjects. So I've recently started contacting people asking for notes and their current research so that I can at least begin in an amateur way. The notes/research I'm studying relate to use of quasiconformal maps, Riemann surface, differential geometry (for example, Ricci flow) to imaging and computer vision.

My plan is to apply for a postdoc next year in these areas, thereby switching from 'pure' to 'applied'. But the thing that concerns me is my zero-experience in this field. While some people did reply to my e-mail saying I've sufficient background for research in those areas, some other forwarded my CV etc. to the committee in case there's been a vacancy already, even though I didn't actually formally apply there, but it got rejected.

So, to you who specially work in theoretical/computational mathematical/medical imaging or computer vision problems, what will be your opinion on hiring somebody as postdoc who has lot of related pure mathematics experience and willingness to learn the skills related to these areas, but have almost zero experience in the fields themselves? How difficult will it be for me to switch fields now?

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    $\begingroup$ cross post: academia.stackexchange.com/questions/14214 (where it is much more appropriate) $\endgroup$
    – Christian Clason
    Commented Nov 18, 2013 at 20:38
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    $\begingroup$ Okay, thanks, It is indeed my post. The reason I thought I'd try mathoverflow is the presence of more math people, some of whose opinions might be valued. Of course acedemia is more suited, but I'm not sure whether I'll get the math peoples' opinions as much as here. Also, view-per-minute wise, mathoverflow is more active! $\endgroup$
    – Learning math
    Commented Nov 18, 2013 at 20:40
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    $\begingroup$ If you email me, we can talk (I know the particular area you talk about quite well), but it is probably not appropriate to discuss this in public. $\endgroup$
    – Igor Rivin
    Commented Nov 18, 2013 at 21:24
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    $\begingroup$ Perhaps the OP's related question, mathoverflow.net/q/135148/16302. may be relevant? $\endgroup$
    – jeq
    Commented Nov 18, 2013 at 21:44
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    $\begingroup$ Noah Goodman at Stanford stanford.edu/~ngoodman did a PhD in mathematics and now works in computer science and cognition with a position in the psychology department. $\endgroup$
    – Vijay D
    Commented Nov 18, 2013 at 23:27

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I switched from theoretical physics to math, long time ago, it has been a very painful experience (and I had a double graduation). But after 20 years, now, it's OK ;-) I have a good friend who switched 10 years ago from math to neuro-sciences (he implements some differential geometry techniques in the modeling of the brain functioning). He is professor in some famous university in Paris, and he just published a 170 pages paper on his new subject. You can say that his switch has been successful. My experience is that if you really want to switch because it's what you like, then switch, but don't think it will be easy. And it will take time for you to be productive in your new field, a few years, think about the consequence on your career. If you just switch because you are tired of what you are doing now, be careful you will may be tired of your new field too :-/

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    $\begingroup$ Patrick I-Z: thanks for your reply and frank opinion. Indeed you brought up the question why I'm planning to switch. Reasons: 1)I do have research projects in pure mathematics I'm working on, but since the 3rd or 4th year of my graduate school I've been wanting to see more applications of what I do, and I found enough such resources, which I feel motivated to research in these areas, without actually having a first-hand skills. 2)This is a negative reason, but very realistic I think: the number of jobs in applied areas are little more than that in pure mathemtics, and since (continue...) $\endgroup$
    – Learning math
    Commented Nov 18, 2013 at 21:10
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    $\begingroup$ tenure-track or so positions are being very difficult these days, it makes sense to work partially in applied areas (I think), so that my CV would look more balanced and I'd have option to apply to industry. I'm not tired of what I do, but your point of time taken to be productive in new areas make sense, but the switch should ideally use a lot of stuffs I'm using at present plus some computer programming, from a far view. $\endgroup$
    – Learning math
    Commented Nov 18, 2013 at 21:13
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I switched from the theory of Banach spaces, to fluid dynamics. I made the change after I got tenure. I am really glad that I waited until after tenure, because it had a huge negative impact on my career. I am glad I did it, because I love my new applied area. But I am also glad I waited until I had tenure and didn't have to worry so much about publish or perish.

My situation isn't quite the same as yours, so I don't really know how to advise you. But without a track record, and also without the connections that your Ph.D. adviser or other colleagues can provide, I think you are looking to go a hard way.

Continuing in your research area and waiting until you get tenure: is that an option? Also, you might be quite surprised at the extent to which your experience in pure mathematics will give you insights that are quite unique.

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