The group started gathering on Thursday. The protest has since evolved into an encampment near 34th and Walnut on Penn's campus.
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Jameson says the encampment itself violates the university's facilities policies, along with "credible" reports of harassing and intimidating conduct.
A statue outside of College Hall was also vandalized with antisemitic graffiti, according to the university.
Jameson called it "reprehensible," and said that it would be investigated as a hate crime.
The protesters have been informed to disband the encampment immediately.
"Failure to disband the encampment immediately and to adhere to Penn's policies will result in sanctions consistent with our due process procedures as they apply to students, faculty, and staff," said Jameson.
The gathering involved students from Penn, Drexel University, Temple University and other organizations who stand in solidarity with the Palestinian people.
The groups are demanding peace in Gaza, and that schools reveal any financial ties to Israel. They also want them to cut ties with any business the group believes profits from the Israel-Hamas war.
The group is also calling for student protesters to be granted amnesty from suspension or arrest.
"These universities are always encouraging us, it's part of academic integrity and authenticity that we sit here and critically think about what's going on and that's what we're doing," said Nada Abausi, a student organizer.
Police could be seen near the Penn encampment when the protest began Thursday.
University of Pennsylvania Gaza Solidarity protest evolves into encampment on campus
However, it has not been peaceful on other campuses across the country.
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More than 90 students were arrested without incident on the campus of the University of Southern California Wednesday night.
In Boston, 108 protesters were taken into custody, and four police officers were injured when protests turned violent at Emerson College.
Locally, two graduate students at Princeton University in New Jersey were arrested and barred from campus after several dozen people gathered Thursday morning, according to school officials.
A small number of the group put up tents, which is a violation of the university's policy.
After the group was given repeated warnings to leave the area, officials said two graduate students were arrested for trespassing.
Hundreds of pro-Palestinian protesters arrested on college campuses
Subsequently, all the tents were then voluntarily taken down by the protestors, officials said.
The two Princeton students now face a disciplinary process.
Pro-Israel students told Action News that they are serving as a voice for Jewish people who are on the other side of this conflict.
"We are letting them protest for their ideology and we're going to protest for ours," said Joseph Hochberg.
Earlier this week, a similar protest was held at Swarthmore College in Delaware County.
"We remain open and willing to explore more realistic ways to find common ground and bring this latest demonstration to a peaceful conclusion," the college said in a statement.
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Read the full letter to the Penn community:
"To the Penn community,
At Penn, we pursue our academic mission guided by fundamental commitments to upholding freedom of inquiry and open expression, while maintaining a safe, inclusive, and respectful campus community.
Over the last 24 hours, we have closely monitored the protest that evolved into an encampment on College Green. We have vigilantly supported the rights of our community members to protest peacefully. Representatives from Open Expression, University Life, and faculty leadership have engaged with some of the protestors, with limited access to the broader group.
Unfortunately, blatant violations of University policies and credible reports of harassing and intimidating conduct compel us to protect the safety and security of our campus community.
The encampment itself violates the University's facilities policies. The harassing and intimidating comments and actions by some of the protesters, which were reported and documented by many in our community, violate Penn's open expression guidelines and state and federal law, including Title VI of the Civil Rights Act. All members of our community deserve to access our facilities without fear of harassment or being subjected to discriminatory comments or threats.
The vandalism of the statue in front of College Hall with antisemitic graffiti was especially reprehensible and will be investigated as a hate crime.
As we have repeatedly emphasized, we will uphold free speech and the productive exchange of ideas, but we will not allow any actions that harass, threaten, or intimidate others. We have also said that the safety of our community is paramount, and we will live up to our commitment.
I am deeply saddened and troubled that our many efforts to respectfully engage in discourse, support open expression, and create a community that is free of hate and inclusive for everyone have been ignored by those who choose to disrupt and intimidate.
We have notified the protestors of their legal and policy violations. Failure to disband the encampment immediately and to adhere to Penn's policies will result in sanctions consistent with our due process procedures as they apply to students, faculty, and staff."