So, suppose you're a grad student in some academic program in the US; suppose furthermore you're employed by the university (as a teaching/research assistant, say), and you message total strangers on the internet, looking for a sexual encounter. Some of the messages may be sexually explicit/implicit.
Is it possible that, if some stranger could be offended by this, the university could act against you in some form were the stranger to contact them about it? Would the relationship of the stranger to the university matter, even if one did not know beforehand such relationship? For instance, would the situation change if the stranger is a student of the university?
Of course there is nothing illegal in the US about these actions, but universities sometimes have much stricter codes. In answering this question, please keep "large public university" in mind, not some christian college.