So... plot hooks and adventure seeds for the University of Lüm... Well, I see a few possibilities.

Many of the professors (and some of the more advanced students) at the university will have experiments they want to perform and investigations they want to carry out that they may want help with, or specialized equipment and materials they may want help acquiring.

Example: Professor Lini Min of the geology department wants to carry out an expedition to a certain spot on the Abulaji Mountains where a vein of a rare ore has been discovered that she wants to study. She can't make the journey alone, however, especially since there are supposed to be dangerous creatures in that part of the mountains, so she's looking for capable people to accompany her on her expedition.

The University of Lüm may be a renowned place of learning and its students having a reputation as among the best and brightest—but they're still young people, with all that implies. Student pranks and ill-conceived attempts at cheating at classwork occasionally get out of hand, and given the levels of magic and other resources some students have access to (or can illicitly get access to), the consequences can escalate quickly.

Example: The area around one of the university dormitories has recently become infested with dangerous creatures from other planes—which have begun to spread into other neighborhoods near the university. If the PCs investigate, they may discover that a student living in the dormitories who was taking a class on interplanar studies got his hands on an item that allowed him to open a portal to a plane he was learning about and thought to use it to get ahead on his studies... but things came through the portal he hadn't anticipated, and he doesn't know how to close it. Maybe the PCs can find a way?

A university, like nearly any other large organization, can become a hotbed of politics, and sometimes those politics can turn nasty. A professor might ask for help proving that a mistrusted colleague who claims to have made a great discovery is fudging the numbers... or, conversely, a professor falsely accused of such malfeasance might want help clearing their name.

Example: A rising star in the university's economics department, Professor Eurilige Oulo claims to have carried out trials that prove that some counterintuitive economic policies would bring greater prosperity to Djarvin... and some members of the Heroes' Council that leads the nation have taken note. Another economics professor, Gqole Zoto, however, is convinced that Oulo faked those trials and that the policies she champions would lead to economic disaster. Can the PCs help him discredit Oulo's claims before the Heroes' Council adopts her perilous policies and brings the nation to economic ruin?

Much of the financing for the university is provided by the state, but some departments and professors rely on private donations to supplement their funding. For this purpose, they often invite wealthy and influential individuals to soirées where they hope to impress them enough they'll be able to ask for funding. Socially adept PCs might be asked to help with such an event or to persuade someone to attend the event—or if the PCs are already on close terms with a wealthy or powerful individual, that individual may bring them along to the event as part of their retinue. Of course, things have the potential to go wrong, especially if a rival tries to sabotage the function...

Example: Emari Laal, a wealthy dignitary from the nation of Alaghad, is visiting Djarvin, and the heads of the botany department of the University of Lüm have convinced her to stop by for a gala at the university while she's there, knowing her love of flowers and hoping they can leverage that to persuade her to give them a generous donation. Unfortunately, a political enemy of Laal's has been looking for a chance to take her out of the picture, and thought that it would be opportune to strike while she was traveling abroad and away from her usual defenses—and, finding out about the gala, and that Laal didn't plan to bring her guards there, decided that was the perfect time. The PCs have been asked to help with the gala, but didn't know that would involve stopping an attempted assassination.