The prepositional phrase is in the auditorium.
At minimum a prepositional phrase includes a preposition and a noun, pronoun, gerund, or clause as the object. Some common prepositions are at, by, in, at, to, etc... As an adverb, a prepositional phrase will answer the questions How?, When?, or Where? In this case, we can ask, "Where do the students perform?" The answer is in the auditorium.
