Topology for a DC-DC step up converter for a single AA battery with 50V 10mA output
This is not going to be easy since it's hard to make semiconductor circuits that switch nicely at only 700 mV supply.  I'd probably use a boost converter chip that can make 3.3 V from the 700 mV, then run the control electronics off of that.  Now you can use widely available digital logic to create a nice clean on/off signal that drives the final power switching element in the boost supply that makes the 50 V.

Unfortunately you are still left with two inconvenient choices.  If you use a NFET as the switch in the power boost converter, it will require probably around 10 V to switch properly.  Look around, but I don't think you're going to find a "logic level" fet that can handle the 50 V you need.  The other option is a NPN transistor.  That can easily be switched from 3.3 V logic and withstand the 50 V, but to maybe 200 mV C-E drop will be a good fraction of the 700 mV input.  The efficiency will be quite poor, at least at low battery voltages.

I think the deciding factor is how important efficiency is.  If it is a high priority, then a more complicated drive circuit using a NFET will be necessary.  If run time isn't that important, then the NPN switch will be easier and simpler to drive.