I'm an undergrad living with 2 masters students and 1 lab technician who will become a masters student within a month or two, so I've gotten to know quite a few of the graduate students in my University. It is possible to hook up with one - even if they are teaching, but it is very difficult and unless you know what the hell you are doing.
I would suggest seeing if the prof goes to your schools graduate lounge and try to establish something there first. But honestly, I can't see this going anywhere.
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