Here is the petition in Churchill v. University of Colorado:

Churchill v Regents Cert Petition

Questions presented:

I. Does a bad faith investigation of all of a tenured professor’s writings and public speeches, undertaken by state university officials in retaliation for the exercise of constitutionally protected speech and with the stated purpose of finding grounds for termination, violate a clearly established right and create a freestanding First Amendment cause of action?

II. Should absolute, quasi-judicial immunity completely shield a state university and its board of regents’ termination decisions, even when a jury has determined that these officials fired a tenured professor in retaliation for speech protected by the First Amendment and would not have fired him but for his exercise of free speech?

Lower court materials here.