Generally, the University would not have an IP claim here solely based on the relationship. But, that doesn’t necessarily mean that they don’t have an IP claim that could stem out of any agreements between you and the school. For example, you could have signed an agreement that assigned rights to the University in any school-sponsored project. You would have to consult with your school on that one. However, the University would likely only have an IP claim if you voluntarily gave them one.
I think your biggest concern though is the publication of your research. If you want IP in a commercial product, you are likely seeking a patent and patents are only available on new technology. Publication of the technology means that it is no longer new, so the prior publication could defeat your patent claim.
However, there are many more factors to discuss regarding your potential intellectual property and for that reason I suggest that you speak with an intellectual property attorney to discuss more specifics about your situation.