Facing rising infections and a new COVID-19 variant, colleges across the U.S. have once again been thwarted in seeking a move to normalcy and are starting to require booster shots, extend mask mandates, limit social gatherings and, in some cases, revert to online classes.

The threat of the omicron variant comes as a gut punch to schools that were hoping to relax safety measures this spring. Now, many are telling students to prepare for another term of masking, testing and, if cases get bad, limits around social life.

Cornell University abruptly shut down all campus activities on Tuesday and moved final exams online after more than 700 students tested positive over three days. In a campus message, President Martha Pollack said there was evidence of the omicron variant in a “significant” number of samples.

“It is obviously extremely dispiriting to have to take these steps,” Pollack wrote. “However, since the start of the pandemic, our commitment has been to follow the science and do all we can to protect the health of our faculty, staff and students.

Hours later, Princeton University moved its exams online and urged students to leave campus “at their earliest convenience” amid a rise in cases. New York University today canceled all non-academic events and encouraged professors to move finals online.

Cornell, Princeton and NYU all report student vaccination rates of more than 98%.

After a fall with few coronavirus cases, officials at Syracuse University were “feeling pretty good” about the spring term, said Kent Syverud, the upstate New York school’s chancellor.

“But omicron has changed that,” Syverud said. “It has made us go back and say, until we know more about this variant for sure, we’re going to have to reinstate some precautions.”

Last week, Syracuse announced that all eligible students and employees must get COVID-19 booster shots before the spring term. Students will also face a round of virus tests when they return, and officials are weighing whether to extend an existing mask mandate.

Much is still unknown about the omicron variant and how big of a threat it poses. In the United States and many other nations, the delta variant is currently responsible for most COVID-19 cases.

But as colleges brace for the worst, many see boosters as their best hope. More than 30 colleges have issued booster shot requirements in recent weeks, and others say they’re thinking about it. The Centers for Disease Control and Prevention is encouraging boosters for people ages 17 and older, and Pfizer last week announced that a booster of its COVID-19 vaccine might offer important protection against omicron even though the initial two doses appear less effective.

Hundreds of colleges already require COVID-19 vaccines, and some say boosters are an obvious next step.

Most booster mandates so far have come from small liberal arts colleges in the Northeast, but the list includes some as big as Boston University and NYU, and as far away as the University of Notre Dame in Indiana and the University of New Mexico.

The University of Massachusetts in Amherst was among the first to require the booster for students, saying all students must get shots unless they have medical or religious exemptions.

“The boosters are our best protection,” said Jeffrey Hescock, co-director of the university’s Public Health Promotion Center. “This demonstrates that we take public health seriously, and our students do too.”

A recent online petition arguing against the booster mandate — citing 97% of students vaccinated and few on-campus cases — has attracted a few dozen signatures. But Emily O’Brien, a freshman at UMass, said the booster shot is a reasonable demand. She was already planning on getting a booster but said the mandate will probably increase uptake among students and prevent future lockdowns.

“If the past six months have shown anything, it’s that lots of people won’t bother to get vaccines — especially younger healthy people — if they don’t have a requirement to,” said O’Brien, 18, of Bedford, New Hampshire.

UMass will also require masks at the start of spring term, and it’s sending students home with a rapid test to be taken near the end of winter break.

Many colleges are planning for potential disruption next semester even as they contend with outbreaks now.

Middlebury College in Vermont switched to remote instruction last week amid a surge in cases and urged students to leave early for winter break. Rising cases at the University of Pennsylvania led to a ban on indoor social events last Thursday.

On Friday, Tulane University in New Orleans warned that a campus spike includes probable cases of the omicron variant, confirmed in at least one student last week. In response, school officials reinstated a mask mandate and expanded virus testing.

Some other schools are already postponing the return to campus next month to avoid outbreaks. Southern New Hampshire University and DePaul University in Chicago recently said students will take classes remotely for two weeks before returning to campus after the holidays.

In a letter to students, DePaul’s president, A. Gabriel Esteban, said the school will “cautiously start winter quarter so we can sustain a robust college experience the remainder of the academic year.”

When students at Stanford University return to campus in January, they will be barred from holding parties or other big gatherings for two weeks. They’ll also be tested once a week and continue to wear masks indoors as requirements to attend in-person classes. The measures aim to limit virus transmission without going too far in limiting the college experience, said Russell Furr, associate vice provost for environmental health and safety.

“This is something we’ve grappled with throughout the pandemic — how do we get a balanced approach?” Furr said. The goal is to avoid the strict lockdowns seen early in the pandemic, when student mental health “really suffered,” he added.

At some colleges, there’s still cautious hope for a normal semester. Leaders at the University of Central Florida told professors they can require in-person attendance in the spring, which had been discouraged this fall amid a surge in delta cases.

In a campus message, interim provost Michael D. Johnson warned that if the omicron variant takes off, “we may need to change direction yet again.”

Another concern is omicron’s timing — even without a new variant, there were worries of more outbreaks as colder weather drives people indoors, said Anita Barkin, co-chair of a COVID-19 task force for the American College Health Association.

The association recently recommended that colleges focus on increasing vaccination rates to avoid a new wave of cases.

“The message in all of it is, we need to remain vigilant,” Barkin said. “There is certainly pandemic fatigue and people are tired of the pandemic — but it appears that the pandemic is not quite tired of us.”