After the dissolution of the Mages Guild, who runs the Arcane University? The Synod or the College of Whispers?
To me, it sounds like the College of Whispers might have their own place (aka college) similar to the College of Winterhold.
That would mean that the Synod is in charge of the university.

Or do they both have presence in the Arcane University? Considering they are rivals, wouldn't this be very non-practical?

Even if you don't know the answer of this question, your opinion on the matter is still welcome and interesting to listen to