structure(with)

It would be hard not to feel somewhat intimidated while sitting across from a professor with all his or her degrees and certificates staring back at you.

Q) What is the best or some ways to interpret "with" in the above sentence.

Is it like "... a professor who has all his....?"

Or is it like "... a professor while all his or her degrees and certificates were staring back at you?"

Or is it something else?