As Robert Sitkoff, 32, unloads his moving boxes next fall to join the faculty at Harvard Law School from New York University School of Law, he may spot Arthur Miller, 73, toting his own belongings in the opposite direction.

Sitkoff, who just last year took a job at NYU’s law school as a tenured professor, is set to become a tenured professor at Harvard this fall. Meanwhile, Miller, who taught law school at Harvard for 36 years, will switch to NYU law school under the title of university professor.