The most high-profile job in the private education sector is about to be up for grabs.

On Wednesday, Harvard president Drew Faust announced she will step down in 2018 after 11 years in office. Her departure will free up the post—overseeing the oldest and most established university in America—for its 29th occupant.

Harvard has not yet commented on its criteria for Faust’s successor, but the Boston Globe notes that, given the school’s history, the new president will likely be an insider (a current Harvard dean or provost), the former leader of another top university, or a prominent Harvard alum.

If the school goes that last route, it has an abundance of worthy candidates from which to choose. One Harvard graduate who may be particularly well-suited to the job is Janet Yellen, who was an assistant professor at the university in the 1970s and is conveniently due to finish her current term as Federal Reserve chair in 2018. Another potential pick is Barack Obama—a former law school professor and Harvard Law Review president who has, of course, recently found himself unemployed.

But the list of successful Harvard students also comprises figures such as Facebook COO Sheryl Sandberg, US Supreme Court chief justice John Roberts, veteran diplomat Henry Kissinger, Yellen predecessor Ben Bernanke, Microsoft co-founder Bill Gates, New York Times op-ed columnist Nicholas D. Kristof, and television host Conan O’Brien, as well as many other slightly lesser-known leaders in business, politics, and media.

One former Harvard student who can probably be ruled out, though, is Facebook CEO Mark Zuckerberg—who never graduated (though he recently picked up an honorary degree) and may currently have a different set of presidential aspirations in mind.

There’s no guarantee the school will choose a former Harvard student, of course. Faust, a Civil War historian, has a bachelor’s degree from Bryn Mawr College and master’s and doctoral degrees from the University of Pennsylvania, where she was on the faculty for 25 years before coming to Harvard.