I am in the process of applying to graduate schools this Fall 2017 (both in the US and in Europe). I do not yet know what institution I may go to nor do I know any researcher who would be willing to make such early plans. I am wondering whether or not my case matches the requirements of the NSF (Math Fellowship)? I have read the FAQs but found nothing that answers my concern.
From the description for Sponsoring Scientist, I read
The sponsoring scientist's statement is meant to show how the host and host institution will provide a vibrant and supportive environment for the Fellow's proposed research and training activities and provide a basis for the Fellow's future independent research career.
The above makes me think that this Fellowship is only appropriate for enrolled students. Is this right?
If not and it is indeed possible/appropriate for me to apply for NSF (Math Fellowship), then how should I go about finding a Sponsoring Scientist? Is it appropriate to approach/email some researchers in some schools that I will be applying to?