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A senior LSE professor threatened to slap the senior vice-president of the Board of Deputies, Jonathan Arkush, following Thursday night's debate.
The incident occurred as people were leaving the auditorium where the debate had taken place.
Mr Arkush approached anthropology professor Martha Mundy, who had been watching the debate, on the top floor of the auditorium.
Professor Mundy, who is a member of BRICUP, the British Committee for the Universities of Palestine and an ardent advocate of the academic boycott, was the controversial chair for December's inflammatory LSE event where the speaker was the Arab journalist, Abdel Bari Atwan. LSE is currently investigating complaints about her chairing of that event.
When Mr Arkush, a barrister, told her that Professor Kevin Featherstone, who had chaired Thursday's debate, was a "fair" chair, Professor Mundy responded: "I want to give you a slap in the face," and accused him of "professional defamation".
Mr Arkush said after the incident: "It was enlightening to be the object of a vitriolic attack from a person who holds an academic position at LSE. I can now understand better the atmosphere which Jewish students have to suffer on campus.
"How she believes that screaming and threatening violence will help her cause is beyond me."
But Professor Mundy had a different response. She said: "I felt considerably harassed by what I perceived as organised male aggression.
"I responded to this ambush by telling the man in ironic exasperation that I could slap him for such a remark, repeating that the comparison represented professional defamation, and asking him to identify himself.
"He has turned this reaction to his aggression into an allegation of a threat by me."