A major source of this international-student trend appears to be something over which campus administrators have little control. The majority of institutions—83 percent—that participated in the Institute of International Education’s 2017–18 survey cited the delay or denial of student visas as a factor contributing to the decline.

Another president at the dinner, Philip A. Glotzbach of Skidmore College, said that while his liberal-arts school in Saratoga Springs, New York, hasn’t yet experienced a decline in international students, it has had to “work a lot harder” to recruit and retain them. Barbara K. Altmann, the president of Franklin & Marshall College, said that the “latest diplomatic skirmish about visas”—combined with political tensions abroad—has compelled her school, too, to “take extraordinary measures … so international students know [they’re welcome here].” One in five students at the Lancaster, Pennsylvania, liberal-arts institution comes from outside the U.S.—most of them from China. So over the summer, Franklin & Marshall “activated a network” of Chinese nationals affiliated with the college, including upperclassmen, asking them to send reassuring messages to incoming students and their families via social media and other platforms.

Read: Should America’s universities stop taking so many international students?

Many of these visa obstacles, according to NAFSA: Association of International Educators, in part trace back to a memorandum issued in 2017 by President Donald Trump that called for the “heightened screening and vetting of applications for visas and other immigration benefits” as well as new or updated requirements for visa holders studying or working at U.S. colleges. For instance, changes implemented by the Trump administration last year made it more difficult for recent graduates with student visas to continue living in the country legally. Since then, international students’ visa issues have created unprecedented workloads for many institutions, whose international-services offices traditionally focused on supporting students with, say, workshops about setting up American bank accounts, English-tutoring services, and basic visa-application guidance.

Before the presidents’ dinner, The Atlantic reached out to numerous schools—including several members of the Ivy League and an assortment of colleges with large populations of non-Americans—to learn what it’s like behind the scenes of their international-students offices. How, if at all, have these offices’ responsibilities evolved in recent years? The 10 that responded described an increase in visa holdups for their international students since the Trump administration issued its directives, and a corresponding increase in work for schools.

“I’ve been in the field for almost 20 years,” Kristy Magner, who oversees Tulane University’s Office of International Students and Scholars, said in an email, “and the amount of immigration changes during the last three years has been exponential.” (Non-Americans make up 6 percent of incoming freshmen this fall at Tulane, a highly selective research university in New Orleans.)