What is the main conflict in Doomsday Book by Connie Willis?

James Dunworthy, a faculty member of the Oxford History Department, enters a viewing chamber where his friend, Mary Ahrens, is watching the preparations for sending a historian named Kivrin to 1320. The policy has been not to send historians to the medieval period because of the danger to the historian, but the head of the department, Mr. Basingame, is out of town and has left a faculty member named Gilchrist in charge. Gilchrist has overridden the policy to allow Kivrin to go.