Other universities have been more open to letting professors decide for themselves what to do. “Due to these extraordinary circumstances, the university is temporarily suspending the normal requirement that teaching be done in person,” the University of Chicago said in a message to instructors on June 26.

Yale said on Wednesday that it would bring only a portion of its students back to campus for each semester: freshmen, juniors and seniors in the fall, and sophomores, juniors and seniors in the spring. “Nearly all” college courses will be taught remotely, the university said, so that all students can enroll in them.

Cornell plans to make clear to students before each semester begins which classes will be offered in person and which will be online, so they are not surprised, said Mr. Kotlikoff, the provost. He said the university environment would be safer than the outside world because students would be tested even when they did not have symptoms.

Still, campuses are not fortresses, and professors in states that have seen recent spikes in coronavirus infections are particularly worried. Hundreds of cases have been linked to universities in Southern states in recent days, including clusters among the football teams at Clemson, Auburn and Texas Tech, and outbreaks tied to fraternity rush parties in Mississippi and to the Tigerland nightlife district near the Louisiana State campus.

“We’re all holding our breath to see what the policies will be,” said Terrence Peterson, an assistant professor of history at Florida International University in Miami. Professor Peterson, 35, said he had respiratory ailments and a 6-month-old daughter at home.

Joshua Wede, 40, a psychology professor at Penn State, argued that it was not possible to maintain a meaningful level of human interaction when students are wearing masks, sitting at least six feet apart and facing straight ahead.

“The value that you have in the classroom is totally lost,” he said. “My style of teaching, I’m walking all over the room. I wouldn’t be able to do that.”