The names of centers are capitalized. Remember that acronyms and initialisms commonly used within a unit may not be appropriate or necessary for an external audience.
On first reference in written publications for an external audience, preface the name of the center with “the University of Georgia” unless the full university name has been used earlier.
Centers and institutes differ in focus. A center provides an organizational base for research and a structure for extramural funding. It is not an autonomous structure and is not involved in independently offering credit courses or degree programs. An institute shares a center’s focus but has a more formalized structure, may be an autonomous unit and will offer credit courses and possibly degree programs.