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.