It is fair to say that Regina Starolis did not have a great first day of work.

In July of 1973, she arrived at Woodbridge Hall, the University’s main administrative building, to begin her new job as secretary to Yale’s president, Kingman Brewster. Her first official act in that capacity was to break his clock.

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The clock was an antique on loan from the Yale University Art Gallery and Starolis, who had previously been a passenger service manager for American Airlines, wound it too tightly.

“I thought, ‘This can’t be happening,’” she recalled in an interview this week. “The first thing I do is bust his clock.”

The rest of the day was not much better. When William Sloane Coffin ’49 DIV ’56, the University chaplain, walked into the president’s office and demanded to meet with Brewster, Starolis made her second mistake. She did not recognize Coffin.

“I was sitting up at the desk,” Starolis said. “And it was my first day and I didn’t know what to do. Finally he yelled out, ‘I am William Sloane Coffin, have you never heard of me?’ ”

Starolis hadn’t, of course, but that would never happen now. She has worked for each of the last six presidents of Yale and, according to Richard Levin, her current boss, “she quite literally knows everyone in this University.”

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If that’s true, it’s because she has to.

Starolis, who has short, blond hair and wears thin glasses, compares herself to an air traffic controller, deciding who and what should have the president’s attention at any one time. She answers phones for Levin and keeps his schedule, planning events as far as three years in advance and making changes to his calendar “every minute of every day.”

She keeps in touch with top administrators and their assistants so they know what is on Levin’s schedule for the day and so he knows what they are working on. When top officials walk by Woodbridge Hall, they often stop by her corner window to say hello. Alison Richard, the former provost, enjoyed Starolis so much that she would throw pebbles at the window to get her attention.

“One of the great truths at Yale,” Richard said in a phone interview from the University of Cambridge, where she is now vice-chancellor, “is that everyone loves and appreciates Regina Starolis.”

Richard added that Starolis acts as “the glue that holds Yale together.”

That’s a big job for any one person, but Starolis works harder than most. She has her office phone forward to her home in Bethany, Conn., when she’s not in Woodbridge Hall; she was chasing a bird out of her kitchen when Sam Waterston ’62, the actor of “Law and Order” fame, called to say he would accept the University’s offer of an honorary degree.

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Starolis has had no shortage of encounters with Woodbridge Hall’s most prominent visitors over the years. She has met four presidents of the United States and countless senators and governors. Legendary actor Peter O’Toole once sang the Whiffenpoof song to her on the phone.

But her standards are not that high. Starolis will take anybody’s call, even if she won’t put everybody through to Levin. In the ’70s, protesters gathered in Woodbridge Hall almost whenever they felt like it, and Starolis took it upon herself to talk to the protesters and see if they needed anything.

When Linda Lorimer, now the vice president and secretary, was a student at Yale Law School, Starolis found out she was getting married over the weekend and threw a wedding shower for Lorimer, who at the time was also working for the general counsel.

“Regina is obviously extremely attentive to trustees, fancy visitors, development prospects,” Lorimer said in an interview. “But she’s a person who would think to remember a bursary student.”

Starolis was born in Queens, the daughter of a furniture frame maker and a stay-at-home mother. After a few years of working for American Airlines, she decided she wanted to work for a nonprofit and arranged to meet with the personnel officers at Yale. At the time, just three people worked in that department, and Starolis told them she was hoping for a position at the Peabody Museum of Natural History because she had always been interested in archaeology.

There were no openings at the Peabody, though, and so Starolis was sent to Woodbridge Hall to interview for a job as the secretary to the University’s president.

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She never quite let go of her love for history, though.

In her office, she keeps dozens of photographs that show her with Yale professors and deans and dignitaries. She has an ink bottle that belonged to Brewster and all of Chief Investment Officer David Swensen’s books. She has a bobblehead doll of Harold Hongju Koh, the former dean of the Law School.

She has also, as Levin put it, “been present at every crazy thing that’s happened here.”

Starolis was the person who told Brewster that Spiro Agnew, the U.S. vice president with whom he had quarreled, had resigned; she was the one who connected President Jimmy Carter to Brewster when he called to offer him the post of ambassador to Britain. She does not forget anything and can still give the exact name of lectures that Brewster gave 30 years ago.

Each of the six presidents she’s worked for has been different, though she will not compare them except to say that Levin is “by far the easiest to work for.” Benno Schmidt tried to lure Starolis away from Yale when he left office in 1992, but she stayed and cites Levin’s inauguration as president as one of her favorite days from all her years at Yale.

The job has changed a great deal in Levin’s 16-year tenure. For starters, Starolis is now officially the executive assistant to the president. Levin and, consequently, Starolis, has much more interaction with people around the world, and now Starolis — who says she can find anything in the piles of paper on her desk — has to contend with the technology that lets Levin adjust his own schedule on his BlackBerry.

“I keep saying,” she told Marcia Duenkel, one of the other assistants in the President’s Office, “Get things on the calendar that we need to get in, because otherwise he’ll think there’s a place.”

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The one event not yet on Starolis’s calendar is her retirement.

Starolis, who is 65 and whose husband died 13 years ago, says she will stay “until Mr. Levin leaves.”

“I have no idea when that will be, but I do tell him once in a while, ‘Just give me a head’s up,’ ” Starolis said. “Because my whole life will change.”

In her mind, the office will change a great deal also.

“It’ll be a machine, finally. No papers, computers all over the place. Whoever does this will have to be much smarter than I am.”