BERKELEY, Calif. — The class is called symplectic geometry, a high-level course in mathematics that provides elite graduate students at the University of California, Berkeley, a better understanding of, among other things, planetary motion.

But symplectic geometry won’t be meeting for its scheduled Tuesday session because the professor, Katrin Wehrheim, is one of dozens of faculty members who have canceled classes ahead of a series of scheduled appearances by right-wing speakers next week in the latest round of Berkeley’s free speech wars.

“It’s just not safe to hold class,” Professor Wehrheim said. “This is not about free speech. These people are coming here to pick a fight.”

Berkeley, which has become during the Trump presidency an ideological battleground in the national debate over free speech on college campuses, is bracing for several days of disruption when a group of conservative speakers is set to appear on campus as part of an event billed “Free Speech Week.”

Invited by a small student group calling itself Berkeley Patriot, the speakers will feature Milo Yiannopoulos, the right-wing provocateur, whose appearance on campus in February was canceled when protesters attacked the venue where he was scheduled to speak.

Other speakers initially invited included Stephen K. Bannon, Ann Coulter and Mike Cernovich, a far-right blogger. However, a number of them have now said they will not appear, leaving the final lineup unclear.

Still, starting this weekend, the campus will be blanketed with hundreds of police officers carrying riot gear, a deployment that a university spokesman, Dan Mogulof, said would cost as much as $1 million. On Friday, Mr. Mogulof said he was aware of reports that the events had been canceled, but said that the university had not heard from the student group and was proceeding with security preparations.

And yet students looking to the faculty and administration for guidance on how to interpret the free speech issue are seeing deep divisions among their leaders. At Berkeley, there are both unequivocal voices championing the importance of free speech, no matter how inflammatory, and professors who say lines need to be drawn on campuses. These professors argue that the First Amendment needs to be reassessed for reasons that include the rise of internet trolling and cyberbullying and that some scientific research now shows that hateful speech can cause physical pain.

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There are faculty members who explicitly reject violence as a way to counter hateful speech, and others who say it is acceptable if used against what are perceived as fascist intruders.

“The difficulty is that there’s not any consensus among students or faculty about what to do,” said Erwin Chemerinsky, the dean of the Berkeley law school who is one of the nation’s leading First Amendment experts.

The university’s new chancellor, Carol T. Christ, has emerged as perhaps the loudest advocate of unfettered free speech, a paradox since it was the university administration in the 1960s that staunchly opposed the Free Speech Movement on campus, only changing its stance after intense pressure from students.

Ms. Christ’s administration has vowed to spend what is necessary for Free Speech Week to take place.

“Universities are fundamentally dedicated to free inquiry,” she said in an email message. “This commitment is fundamental to academic freedom.”

In some ways Ms. Christ has little choice. While private universities have more leeway in deciding whom to allow on campus, Berkeley as a public institution must adhere to the First Amendment’s broad acceptance of speech and accommodate speakers.

Critics of the administration’s stance include more than 200 professors and doctoral candidates calling for a class boycott, partly out of security concerns and partly to protest what they describe as “pro-fascist” speakers coming to campus.

“What America is not understanding about what’s happening at Berkeley is this is a community and a campus that is under a comprehensive, well-funded full assault by the alt-right,” said Michael Mark Cohen, an associate professor of American studies and African-American studies who is helping lead the boycott. “These people will not leave us alone. This has to stop unless the rest of the country is willing to let Berkeley become a battlefield.”

Mr. Cohen says he would prefer for the university to bar inflammatory right-wing speakers from coming to campus and spend the money now going to security on legal fees defending the ban.

One view shared by people on both sides of the free speech debate is that the university’s role as a sanctuary of learning is being undermined by bands of outsiders who are using Berkeley’s reputation as a liberal bastion to prove a point. This month, Ben Shapiro, a right-wing writer, spoke at Berkeley amid a heavy police presence that cost the university $600,000. He said he wanted to prove that “there are students who do want to hear different views.”

“Ninety-nine percent of us just want to go to class and study,” said Varsha Venkatasubramanian, a graduate student in history whose professors have canceled class next week. “Yes, people come here because they want to expand their experiences. But they didn’t come here for police to overtake their school and to have barriers all over the place.”

To his critics, Mr. Yiannopoulos is using the Berkeley controversy as a self-promotion exercise to sell more books.

Reached on his way to the Bay Area on Friday, Mr. Yiannopoulos said he was attending the event because “free speech is under threat like never before on college campuses.”

“Free Speech Week has been an expensive, complicated mess,” he said. “But we soldier on knowing we are on the right side of history.”

In denouncing what he calls a liberal intolerance of opposing views, Mr. Yiannopoulos is capitalizing on the large numbers of college students who believe in limiting the scope of speech on campuses beyond what is allowed by the First Amendment.

According to a survey conducted in August and made public on the Brookings Institution website, a plurality of college students polled, 44 percent, believed that hate speech was not protected by the First Amendment.

“Today’s students tend to believe in a narrower interpretation of the First Amendment than is actually true,” said the author of the study, John Villasenor, a professor at the University of California, Los Angeles. “There is this idea that what is permissible to say should be judged in large part on its impact on a listener.”

One proponent of that idea is Nancy Scheper-Hughes, an anthropology professor at Berkeley who this semester is teaching a course on the relationship between free speech and hate speech.

“Words can be like rape — they can destroy you,” Professor Scheper-Hughes said in an interview.

Professor Scheper-Hughes says sexual harassment is an example of how certain categories of speech are illegal and says there should be further changes to the country’s free speech laws.

“The Supreme Court is behind the times,” she said. “The First Amendment deserves to be re-looked at.”

Leigh Raiford, a professor of African-American Studies at Berkeley, says those who advocate free speech “absolutism” ignore the fact that minorities on campus feel especially vulnerable when adherents of the far right come to the university.

“At what point is the principle of free speech more important than community safety and the values of our city?” she said.

Watching this debate attentively but warily are the veterans of the Free Speech Movement, most of whom are now in their 70s.

Barbara Garson, an author, calls Free Speech Week a “grotesque parody” of the movement that she helped lead.

Kathleen Piper, an artist, says she and other veterans of the movement disagree with the positions of the right-wing speakers coming to campus. But she says there is a consensus among them that they should be allowed to speak.

“I think a person needs to hear stuff that they don’t agree with,” Ms. Piper said. “They need the opportunity of discovering that they are not going to melt and go down the nearest drain as a puddle if somebody says something ugly to them. I don’t think we should be protected from those experiences.”

In stark contrast to this position is Professor Wehrheim, the symplectic geometry expert, whose German heritage informs a stance that certain speech should be banned from campus.

“Americans are missing the profound analogies between present day U.S. developments and German history,” she said.

In Germany today, Professor Wehrheim said, “you will get jailed for certain speech — and I think that is absolutely the right thing.”