Sarang Gopalakrishnan, California Institute of Technology/CUNY, during the workshop of during the workshop of "Many-body Cavity QED", lecture titled "Vestigial order in multimode cavities " at the Institute for Theoretical, Atomic and Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts on October 9-11, 2017.