Top Topologist Joins Harvard

Math students this side of Central Square just found one more reason to be excited: Michael J. Hopkins, an MIT professor of mathematics specializing in algebraic topology will join the Faculty of Arts and Sciences on July 1 as professor of mathematics.

Currently on leave from MIT and teaching a graduate-level course on algebraic topology at Harvard, Hopkins is renowned as one of today’s leaders in the field.

Topology is a branch of geometry that studies the properties of geometric objects that are preserved after bending and stretching, said Department Chair and Higgins Professor of Mathematics Joseph D. Harris.

Algebraic topology studies the associations of algebraic invariance with the geometric objects that are preserved under deformation.

Hopkins specializes primarily in homotopy theory, a branch of algebraic topology, and has previously worked with Harvard mathematicians who focus on other fields, such as number theory.

“Algebraic topology is a central field in mathematics,” Harris said. “It’s a fascinating field in its own right, but it also has a tremendous amount of connections and applications to other fields.”

Hopkins has been integral to making those connections. Whereas homotopy theory was once practiced exclusively by topologists, Harris said Hopkins’ many collaborations have “really opened up the field.”

Harris praised Hopkins for his interaction with professors from other mathematical fields.

While Hopkins will not officially join the Harvard faculty until July, he was here on sabbatical two years ago and has interacted with students in Harvard classrooms and as an adviser for senior honors theses.

“I’m excited by the students I’ve met,” Hopkins said. “They make me feel there’s a lot of opportunities to learn from students and opportunities to watch algebraic topology grow here.”

Harris described Hopkins as not only a wonderful lecturer, but also a great colleague.

“Frankly, MIT was very unhappy about letting him go,” Harris said. “He’s been a really positive force there, extremely popular as an adviser of graduate students, and a popular teacher.”

At MIT, where algebraic topology boasts a strong presence, Hopkins taught a variety of classes and also collaborated with colleague Haynes R. Miller, professor of mathematics, on an elliptic cohomology project.

Miller, who has known Hopkins for over 20 years, said Hopkins was his closest colleague at MIT, and will be his closest colleague at Harvard.

“He was just down the hall, and he’s not just down the hall anymore,” Miller said about Hopkins’ move across Cambridge.

After 15 years at MIT, Hopkins said he will miss some of the culture, but added that he will not be leaving it completely—as he will still work with research groups he knows there.

However, Hopkins does regret that he will no longer be able to participate in a sport he picked up a couple years ago.

“The MIT math department has a good intramural soccer team that I was hoping to play with, but now I won’t get the chance to,” he said wistfully.

Hopkins will also have to adapt to the differences between Harvard and MIT. A frequent joker in his lectures, Hopkins said he often teases MIT students about Star Trek.

“Someone told me I would have to replace Star Trek with Virgil,” Hopkins said. “Now, I have to quote Virgil instead of Star Trek to get laughs.”

—Staff writer Lulu Zhou can be reached at luluzhou@fas.harvard.edu