But Mr. Franco, who declined to be interviewed, has hardly escaped the glare of publicity. Student journalists chronicle his every move. Twitter messages breathlessly report sighting him in his habitual hoodie and shades. A student-generated blog, James Franco Has Fun, lampoons all things Franco, soliciting pictures of “James being a crazy dude.”

And the fascination is fed by Mr. Franco himself, a self-promoting — and often self-mocking — polymath who is a film director, screenwriter, painter, author, performance artist and actor, with several film projects under way. In addition to the Yale program, which could take several years, he is on track to earn a master’s degree in film from New York University this spring. (“It’s a full-time program,” an N.Y.U. spokesman said. “You can’t do it any other way.”)

Last year, Mr. Franco received a master’s degree in writing from Brooklyn College, and this semester he is co-teaching a course on film editing at Columbia College Hollywood, a private school in Los Angeles. It is called “Master Class: Editing James Franco — With James Franco.”

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Even at Yale, home of overachievers, he stands out. He has found time to undertake a multimedia musical production with about four dozen undergraduates that will open on campus in April. He is listed as a producer, but has worked with students on all aspects of the show, “The Stargazer,” including casting, making script revisions and acting in the film elements.

“We’re all really fascinated and awed,” said Cokey Cohen, the columnist at The Yale Daily News who drew Mr. Franco’s ire. “To see someone who has what we all consider to have an ideal life — with a fun, successful career — to be voluntarily doing so much schoolwork all the time is both really admirable and something I can’t even comprehend.”

Dr. Warner said the actor’s academic ambitions were impressive. “We have had experience before with students pursuing parallel degrees,” he said, “although the scale of his obligations is something that we’ve never seen before — but who has?”

Among students, attitudes run the gamut, from indifference to curiosity to full-blown obsession. Ileana Lucos, 21, an environmental studies major, said she and her friends were on high alert for news of Mr. Franco’s whereabouts.

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“Definitely, the girls are like, ‘Oh, my God, I just saw him!’ ” she said. At Yale, she explained, “you have politically famous or otherwise famous, but not like a movie star that is Hollywood famous.”

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“I don’t know,” she continued. “There’s something about him that’s mysterious.”

Others have had enough. “It doesn’t make a difference to my experience here,” said Stacey Diaz, 22, who has a double major, in international studies and African studies. “I think it’s weird that people are so wrapped up in following his every move.”

For his part, Mr. Franco strikes a balance between staying “almost under cover,” as Dr. Warner put it, and indulging his fans. This week he posted pictures online from inside his room at the Study at Yale, a boutique hotel where he stays when not commuting to his apartment in New York.

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At Atticus Bookstore Café, where he stops in a few mornings a week for coffee, the general manager, Ben Gaffney, said Mr. Franco usually took a table in the back, books in tow. “He doesn’t come in to socialize,” he said. “Girls go up and blush and giggle and say, ‘Hi.’ He just smiles and nods his head.”

Still, Mr. Franco is clearly not your average graduate student. Last semester, when he and Dr. Warner needed time to discuss a paper, Mr. Franco’s personal assistant helped arrange an unusual solution.

“The only time we could find time to talk was during a train ride from New York to New Haven,” said Dr. Warner, who splits his time between the two. “So I met him on Metro-North.”