It's not really an easy read, but it seems that, by default, the University wants in on anything you do in their facilities. They make this condition for students, though:

"Students are exempt from this policy for cases in which University facilities are not used and where the invention or discovery is not made in the course of the students studies at the University."

So since it's sort of "in the course of the student's studies", I might have to go after the following conditions in the policy:

" If, however, the inventor or another institution believes that the circumstances surrounding the invention, including such factors as support provided by other than the University, place where discovery was made, or lack of relevance to the regular work of the member of the faculty or staff, warrant another distribution, the inventor or the institution may request the Office of Technology Management, in consultation with the Technology Transfer Committee, to review the circumstances. After review, and upon consultation with the Office of General Counsel and the Senior Vice Chancellors, the Office of Technology Management will make recommendations to the Chancellor on the distribution of proceeds.

      The University, as determined by the Technology Transfer Committee and the Office of Technology Management, may choose to waive all rights to file a patent on a particular invention or to pursue licensing of such invention, electing instead to grant the inventor permission to proceed on his or her own in whatever manner the inventor deemsappropriate."

As luck would have it, my cofounder here used to work for them... he says that you're probably fine, but you should go to the office and double check. Or you can email Dan Bates at dbates@provost.pitt.edu, who's apparently a reasonable dude there.