The university organized an open auditorium on domestic violence. Does open auditorium make sense? thanks
No, not quite. An open auditorium is an auditorium open to the elements, and it's not something that a university would organise, though it might build one. I don't find any support for the use of auditorium to mean a meeting held in an auditorium.
I suspect you want The university organized an open meeting on domestic violence.