Questions regarding post-PhD research jobs (specifically mathematics) I am currently a year or two away from a PhD in differential geometry.  I love doing research, and I would like to make my career doing research in some form (preferably mathematical), but I have no idea the jobs that are out there for pure mathematicians, or what skills are required in order to obtain them.  For what it is worth, I don't care about the money - as long as my family is not starving, I'm fine with a lack of significant disposable income.

So, I ask:

1) What are some areas (broad or narrow) of industry in which I should consider looking for employment?  Specific company recommendations are fine also; right now I have very limited knowledge of what's out there.

2) How should I tailor my skillset to be competitive for industrial jobs in math?  Right now I have a fairly diverse mathematical education, and rudimentary knowledge of a few programming languages, but not much else that might be useful to an employer.  What do you recommend I learn (either through courses or on my own) while I'm still in school? 

Note:  I have avoided asking about professorial positions because, while I'm not a bad teacher, and a position at a research institution would be great, I lack the prestige that comes with graduating from a top-tier school and I want to remain realistic about my job prospects.

Thanks for your time,

EDIT:  Recommended reading suggestions are also appreciated.
Discalimer: IANADG, I am not a differential geometrist...

Still, some potentially-relevant fields:


Architecture and materials industry: Surfaces and bodies with complex structures, their behavior, the forces applied to them, their expansion, contortion etc. with weather or with load changes and so on. Specifically, I can imagine a bunch of relevant applications in 3d-printing. This might be relevant (although it's not a specific workplace)
Car industry, for similar reasons
Computer vision and image/video  processing: lots of geometry and lots of derivation going on there. Just as an example, read this (but )


I'll also make another, more concrete suggestion: Various countries have academic-oriented placement/recruitment agencies. While those obviously don't know you perfectly well and can't cater to your interests exactly, they could interest you in a selection of potential positions which you might find appealing - or, at least, will help you realize what kind of work is out there. Also, an up-to-date LinkedIn profile has a bit of that same effect.