Should you be interested in applying algebraic geometry, [IMA Thematic Year on Applications of Algebraic Geometry][1] may give you some inspiration, as can searching for "algebraic geometry applications" or similar. You may also wish to take a look at the Society for Industrial and Applied Mathematics's Activity Group on Algebraic Geometry [SIAM Algebraic Geometry group][2] or visit their wiki [SIAM Algebraic Geometry wiki][3].

Of course, you may need to take courses or do self-study in certain application areas, if they appeal to you. You may also need to develop skills in algorithms or computational techniques, assuming your background does not already include these.

All advice is perilous, but I suspect that you could increase your employment options if you know at least something of programming, statistics and optimization techniques. Perhaps there are opportunities to work for government institutions in areas such as planning or infrastructure for instance. You may find areas such as complex networks or machine learning quite accessible with your advanced background and ability to cope with abstraction.

Whatever you decide to do, the very best of luck!


  [1]: http://www.ima.umn.edu/AlgGeom/
  [2]: http://www.siam.org/activity/ag/
  [3]: http://wiki.siam.org/siag-ag/index.php/Main_Page