I'm not a teacher.
Places thought of as institutions in general rather than specific buildings are referred to without the definite article: school, church, hospital, university, etc. However, we can use the definite article to mean that somebody is in a place doing an activity, other than that for which the building was built. E.g.: She is at the church. (She is a tourist)
Colloquially, nobody answers a friend’s question like this: “Where is Luis?” “Luis is at the University of Chicago”. No, he normally says “Luis is at university”. However, when the university is referred to using the preposition “of”, the definite article is used. E.g.: the University of Wales, the University
of California at Los Angeles, etc. Many universities have both possibilities: London University/the University of London
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