Students on Thursday protested the president's attacks on Harvard, but at town hall meetings, defiance mixed with uncertainty as faculty members examined the toll of the White House's actions.
The Trump administration said it would take $2.2 billion in research funds from the school. Some small donors are doing their best to make up for the shortfall.
Demonstrators rallied on Columbia's campus and marched in Manhattan, three days after Mohsen Mahdawi was detained by immigration officials after arriving for a U.S. citizenship appointment.
The signed memorandum of understanding was thin on details, and the White House did not comment. But President Trump has said he expects to sign a full minerals deal with Kyiv soon.
The Trump administration is on course for a potential constitutional clash with the judiciary branch, which has issued several rulings countering executive orders.
Attorney General Pam Bondi moved forward aggressively and ordered prosecutors to seek the death penalty. Mangione also faces state charges in the Manhattan shooting.