Ayers was a grad student at The New School for social Research.
He had a cousin, or sister-in-law who was a professor of Education at Barnard, Sorry I don’t remember more at this time. Been a while. Also ... the main question here is the NYC connection between Ayers (aka, “The Guy from the Neighborhood”) and Obama.
(Ayers is important to Obama, and it's possible they met in Manhattan; but there's not much to really link Ayers to Columbia itself.)
WIKI:
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After the September 11 attacks in 2001, Brzezinski was criticized for his role in the formation of the Afghan mujaheddin network. He countered that blame ought to be laid at the feet of the Soviet Union's invasion, which radicalized the relatively stable Muslim society. ...
In August 2007, Brzezinski endorsed Democratic presidential candidate Barack Obama. He stated that Obama "recognizes that the challenge is a new face, a new sense of direction, a new definition of America's role in the world."[23] also saying, "What makes Obama attractive to me is that he understands that we live in a very different world where we have to relate to a variety of cultures and people."[24] In September 2007 during a speech on the Iraq war, Obama introduced Brzezinski as "one of our most outstanding thinkers,"