This advice may be so ill-informed that I'll put the disclaimer up front: I'm not a lawyer, let alone an IP lawyer. That said, if the university isn't paying you, and you don't use any university resources, and you don't assign them any rights, I don't see how they can assert any rights. Looking over your work and assigning it a grade doesn't make it theirs. Otherwise they would own everything.
Now, if you were an assistant professor using university offices and labs and a certain amount of public funding to conduct work that is nigh-indistinguishable from the work your side business is doing -- to the extent that many of your grad students can't tell from moment to moment if they're doing schoolwork or startup work -- that would be a more interesting question.
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Now that is an interesting question.
This advice may be so ill-informed that I'll put the disclaimer up front: I'm not a lawyer, let alone an IP lawyer. That said, if the university isn't paying you, and you don't use any university resources, and you don't assign them any rights, I don't see how they can assert any rights. Looking over your work and assigning it a grade doesn't make it theirs. Otherwise they would own everything.
Now, if you were an assistant professor using university offices and labs and a certain amount of public funding to conduct work that is nigh-indistinguishable from the work your side business is doing -- to the extent that many of your grad students can't tell from moment to moment if they're doing schoolwork or startup work -- that would be a more interesting question.