No, absolutely NOT federal law.
Each state determines carry in the various educational institutions.
Except for a couple of permanently closed off ones, all the streets and sidewalks at UT Knoxville are city streets; they are maintained by the city of Knoxville. What little parking actually on the street is metered, and those meters are City of Knoxville meters, not university ones.
IANAL, but would seem to me that as long as you are on only those streets or sidewalks, you are okay, ie walking through the campus from one city street to another city street, using city streets in between. Which of course doesn't help you if you need to attend classes or go to the university center, whatever.
Btw it's okay by TN statutes to leave gun in your car as long as you are an adult NON-student.
If you are an adult student, you can't.
Go figger.
- OS