Sheldon, Howard, and Raj work at the California Institute of Technology, commonly known as Caltech, in The Big Bang Theory.
Caltech is a private research university in Pasadena, California, and serves as the professional home for much of the series’ scientific cast. Sheldon is a theoretical physicist, Raj is an astrophysicist, and Howard is an aerospace engineer associated with Caltech’s Department of Applied Physics and its Jet Propulsion Laboratory connections.
The answer is often confused with the universities the characters attended. Howard studied at MIT, Leonard studied at Princeton, and Raj attended the University of Cambridge. Those are educational backgrounds, not the university where the group is primarily shown working.
Raj later takes a position connected with the Griffith Observatory, while Howard also spends time working with NASA-related projects. Even with those career developments, Caltech remains the central workplace and the canonical answer to this trivia question.