How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics? 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?
 A: 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.
A: 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 :-/
