cut off their goolies

apropos nothing - what sort of circumstances hypothetically trigger university disciplinary investigations?

Universities have rules that are both an improper subset of and a superset of community laws.
Generally, universities are subordinate to the laws of the jurisdiction they are in, although there are historical exemptions. Further, universities are not actually obliged to discipline their members, whether students or faculty, merely because of legal convictions, although in practise they often do.

Issues of concern to the university include internal safety - conduct that threatens the physical and intellectual community; the reputation and image of the institution - a necessary clause, but one open to abuse; and, professional misconduct and breach of intellectual ethics.

So, consider some gedankenexperiments:

• A professor is accused of sexual assault by a student.
  This ought to lead to investigation, often does, and can lead to loss of tenure.
• What if a professor is accused of sexual assault off campus?
  Should the university investigate, or wait for the outcome of any legal proceedings?
• What if a professor is the official faculty advisor to a campus group, and he advises the members of the group that they have the permission to sexually assault some sub-group of the university, and pro-actively encourages them to do so.
  Independent of the group's conduct, should this lead to an investigation?
  What if the professor knows the group did actually do such assaults and plans on more, even if the professor was not actually directly involved?
• Same case as above, but the professor advises and encourages the campus group they may sexually assault some non-university third party group.
• Same case as above, but the professor advices and encourages a non-campus group that they may sexually assault some non-university third party group.
  Acting as a professionally authoritative source on this issue, of course.
• What if the group being given the advice is a law enforcement group - eg campus police, or local city police?
  Could a law professor, acting in his capacity as a lawyer, advise campus police that they may sexually assault students in their custody.
  Could a law professor, acting in his capacity as a lawyer, advise city police that they may sexually assault students in their custody? Or advise them they may assault non-students?

  Does the university have any obligation to investigate in any case, and is there a clear line where such obligation is no longer present?