In the movie Sherlock Holmes: A Game of Shadows, it is never mentioned which university Professor Moriarty teaches at. Did I miss it? Does the story have any clue?
The movie discusses nothing about the University, to which Professor Moriarty is affiliated, neither gives any hints to ascertain that.
Even in the Sherlock Holmes books, Arthur Conan Doyle has not disclosed the name of the university, but only refers to him as a mathematician, which makes him Professor of Mathematics. In The Final Problem, Doyle, briefly refers to the university as "one of our smaller universities", but never gives away the name of the university.
He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the binomial theorem which has had a European vogue. On the strength of it, he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him. But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his blood, which, instead of being modified, was increased and rendered infinitely more dangerous by his extraordinary mental powers. Dark rumors gathered round him in the University town, and eventually he was compelled to resign his chair and come down to London. He is the Napoleon of crime, Watson. He is the organizer of half that is evil and of nearly all that is undetected in this great city... —Holmes, "The Final Problem"
The smaller university was claimed to be one of the colleges, which later made University of Leeds in an article published in 1989 in New Scientist. The article needs subscription to read the entire content, and unfortunately the first paragraph which is free for access, has nothing to say about the reasoning which the author of the article uses to determine the aforementioned college.
In Sherlock Holmes: The Unauthorized Biography, which was published in 2006, and is a non-canonical Sherlock Holmes pastiche novel, the author refers to the University as Durham University. Nonetheless, this is his take. Arthur Conan Doyle, never disclosed the University.
In the film Game of Shadows, it's actually fairly obvious which University is represented in the establishing shot for the sequence where Holmes goes to 'pay his respects' to the Professor immediately after the Watson wedding. It's King's College Chapel, in Cambridge. Therefore, we can deduce that Moriarity's workplace is presented -- at least in this film -- as the University of Cambridge, not one of the other 'old stone' universities in Britain -- not Oxford, nor St. Andrew's nor Aberdeen, or any of the 'smaller' universities in Britain. But if we look at the ur-texts of Conan Doyle, it would appear that this is an invention of Guy R. and crew, for this film specifically. But the Cambridge designation is plausible, as an evil genius could thrive anywhere, and perhaps the elitist narcissist Moriarity would never settle for second-best. Have enjoyed this discussion, as I was wondering if he was a Cantabrigian in the originals, and it looks like he wasn't. All best to discussants, and I look forward to reading the complete works.