This is admittedly a cold case, but I will give it a shot, given that nobody else has answered so far and the answer seems straightforward to me! (Maybe I missed something?)
I would say that you should define a context in panels, so that all the bits of the display will be able to refer to the same faculty and present the right content (this is indeed one of the major advantages of panels over blocks, which do not know what is the rest of the content on the page).
Although this is an old question - and thus you most certainly have chosen and finalised your design - from your question I wonder if you really have to use panels or if you could achieve the same result (but in a less resource-intensive way, which could be an advantage for a busy university site) by implementing a view that will present core information about the faculty and will filter linked nodes with a taxonomy (terms in the taxonomy could be "medicine", "law", "engineering"...)
Well... who knows? I hope at least the OP will see this answer to an old question lost in time... ;)