There’s a lot of glass in the Pauley Ballroom at UC Berkeley, and campus officials hope it holds when the explosive provocateur Milo Yiannopoulos delivers his message to students there on Feb. 1.

He typically aims his barbs and taunts at women, people of color and anyone left of Donald Trump. But it isn’t Yiannopoulos that campus officials are so worried about. It’s the people he infuriates — and there are plenty of them — who are causing the administration to consider hiring 40 extra police officers on top of the usual seven, said UC Berkeley spokesman Dan Mogulof, who’s been bombarded with emails from students demanding that the university cancel the invitation.

Yiannopoulos, a gay conservative, is a public speaker and editor for the right-wing opinion site Breitbart News Network. He’s been making the rounds at college campuses across the country with his “Dangerous Faggot” talks, specializing in remarks meant to insult, offend and disgust those who disagree with his ideas.

A “What to Do About Milo” instruction sheet is circulating that tells critics how to express their outrage in writing and where to show up in person — including a protest at UC Davis on Jan. 13, when activists hope to shut down Yiannopoulos’ talk there. A No Milo Yiannopoulos at UC Berkeley Facebook page had been shared 1,800 times by Monday, with 529 clicks from people saying they’ll attend the protest.

That’s compared with the 500 sold-out seats to the event, hosted by the Berkeley College Republicans.

“Even if there were a specific threat (of disruption), that would not be grounds to cancel the event,” Mogulof said, adding that the students hosting the event are required to help the university pay for basic security. Their contribution is estimated at $7,500 to $10,000 for about seven officers. And although high security fees required at Yiannopoulos events have led to cancellations on some other campuses because students couldn’t afford them, Mogulof said UC Berkeley may not set fees with the intention of blocking the event and will pay for any additional officers needed. “What would be grounds to cancel would be if the speaker said, ‘I’m going to come to your campus and break the law.’”

On the contrary, Yiannopoulos has gotten a good workout exercising the law that distinguishes the United States from countries that don’t have a First Amendment, such as his native Britain.

But private companies set their own rules, and Twitter banned him in July for repeatedly breaking harassment and abuse policies.

Yiannopoulos, who has called feminists “the most easily offended group of people on the planet,” took such offense at his banning from Twitter that he devoted a speech at Florida State University in September to a “eulogy” for the company.

He also accused college students in August of “running for safe spaces at the slightest hint of a challenge to their coddled worldview,” and defended Internet trolls — perpetrators of the kind of activities for which Twitter banned him — as harmless pokers and prodders of the most vulnerable among us.

“Trolls are experts at finding soft targets,” he wrote, offering a euphemism for what is usually called bullying.

Yiannopoulos found a soft target on Dec. 13 at the University of Wisconsin in Milwaukee, where in front of 350 people in the Student Union and countless others watching on the Web, he mocked and identified by name a student who had protested a new rule requiring students in locker rooms to cover their “nonconforming genitalia.”

The rule was imposed after the student, who was making the physical transition from male to female, used the sauna in the women’s locker room last January, according to the Milwaukee Journal Sentinel.

The newspaper reported that Yiannopoulos held up the student’s photo, accused her of being a man trying to go into women’s bathrooms, and said: “The way you know he’s failed is I can still bang him.”

In September, he took a dig at people who protest the disproportionate use of excessive force by police against black people, suggesting that no such imbalance exists and that protesters should focus on weight loss instead.

“If Black Lives Matter cared about black people, in addition to their fact-free musings about police officers they would be organizing aerobics classes, not protesting the police,” he told students at Louisiana State University.

The apparent joy Yiannopoulos takes in making young adults feel bad — then mocking them for feeling bad — has prompted an array of student protests. He’s joined some of them incognito, carrying a sign that reads “Milo Sucks.”

Seven people were arrested for blocking the entrance to his speech at Michigan State University on Dec. 7, the Lansing State Journal reported. And on Dec. 15, some 40 protesters showed up at Minnesota State University chanting, “Yiannopoulos, out of Minneapolis!” reported the Minneapolis Star Tribune.

“It’s enormously good fun,” he told the paper. “All of the very worst people in the world get triggered by the mere mention of my name.”

Among those “worst people” are UC Berkeley students, including about three dozen so far who have emailed campus spokesman Mogulof with requests to cancel the speech. The “What to Do About Milo” paper also recommends contacting at least a dozen other campus leaders, from Chancellor Nicholas Dirks to Na’ilah Nasir, vice chancellor of equity and inclusion.

“Yiannopoulos’s visit would very likely pose a direct physical threat to individual students on this campus,” a student identified only as Gerard wrote Mogulof, calling the speech at the University of Wisconsin an act of sexual harassment.

Echoing the claims of other critics, Gerard urged the university to “prohibit the College Republicans from holding this event on campus property” on the ground that, in his view, harassment of that kind “is not protected free speech.”

Meanwhile, the Berkeley College Republicans have found themselves in the ironic position of championing what they call the “New Free Speech Movement” on the same campus where students of the political left gave it life a half century ago. Club members could not be reached for comment.

Mogulof has been sending out a four-paragraph response to those asking UC Berkeley to cancel the event. It says that registered students groups like the Republicans can invite speakers onto campus and that the university “has no authority to disapprove the speaker.” Nor can opponents use the “heckler’s veto” to shut down a speaker they don’t like.

“The courts have made it very clear, contrary to widely held beliefs, that there is no general exception to First Amendment protection for ‘hate’ speech or speech that is deemed to be discriminatory,” says the response, which adds that officials and campus police “will not hesitate to act” if there is a threat to security.

Some private universities have barred Yiannopoulos.

In July, DePaul University banned him from returning because his presence had created a “hostile environment” in May, when protesters took over the stage, grabbed his microphone, and hit him in the face. Campus President Dennis Holtschneider later called Yiannopoulos a “self-serving provocateur” and “unworthy” of university discourse.

NYU canceled in October, citing “physical altercations” at Yiannopoulos’ events.

At some public universities, students rescinded invitation because of costs. The College Republicans group at North Dakota State uninvited Yiannopoulos on Dec. 2, saying it didn’t have enough money for security. And “Students 4 Trump” at Iowa State canceled after the campus tacked an extra $1,900 on to the security fee.

These cancellations suggest that UC Berkeley should find a way to do the same, Lisa Hofmann-Kuroda, a doctoral student there in the department of east Asian languages and cultures, told Mogulof.

“In order to preserve student safety, I urge the university to do everything in its power to cancel this event,” she wrote. If not, “students and community members will take the initiative.”

Yiannopoulos’ schedule calls for eight campus stops before UC Berkeley, including the UC Davis event, UC Santa Barbara on Jan. 17, and Cal Poly in San Luis Obispo on Jan. 31. His tour ends at UCLA on Feb. 3.

Nanette Asimov is a San Francisco Chronicle staff writer. Email: nasimov@sfchronicle.com Twitter: @NanetteAsimov