Yes, but it is probably irrelevant.
From the connectors, at least USB is dangerous. It does not only allow many different types of possibly dangerous access like DMA, but there are also devices which, for example, emulate a keyboard and start to type malicious commands as soon as you plug them in.
But it is very unlikely that the projector uses such an attack. The projector itself is probably harmless (when it was bought), otherwise other people would already have complained. I am also not aware of any projector that had malicious firmware.
The question if it can be infected is an interesting one as many modern devices run actual operating systems. It wouldn't be that unlikely that a projector may have an Android system that allows to present slides without plugging in a computer, and such a system can be vulnerable.
But I am also not aware of a malware that first infects an Android (on the device) and then tries to infect computers that are connected to the device. It could also be possible using USB-OTG mode, but very unlikely to find in the wild.
The bottom line is, that I would trust a projector in an university not to infect my device.