I am working on a Facebook app, but I don't think I need the default permissions from my users ("public info" and the user's email address)
I'd like to keep the permissions requested to a bare minimum, but I can't see in my app admin area on developers.facebook.com anywhere to disable these.
How can I just ask for what I want and turn these off?
You don´t need to disable those permissions, just don´t ask for them in the login process. They are only "approved", which means that you don´t need to go through a review process IF you want to use them. More information about login review: https://developers.facebook.com/docs/facebook-login/review