Brown has two reasons to thank Richard Schoen, professor of mathematics at Stanford. In the 1980s at Berkeley, Schoen was an adviser for Nicolaos Kapouleas, professor of mathematics at Brown. Now comes Frederick Tsz-Ho Fong, the newly appointed Tamarkin Assistant Professor of Mathematics, who received his Ph.D. under Schoen’s mentorship at Stanford this spring. The Brown connection is no coincidence. Fong decided to come to Brown after he met Kapouleas, who was visiting his old adviser last year.
“He spent a year at Stanford on sabbatical and we met each other and discussed research,” Fong said. “He introduced me to who works here. So I decided to come here.”
What binds these three generations of mathematicians is an interest in geometry — the mathematics of space — and differential equations — the mathematics of change. The two are often related: Imagine the kind of math used to calculate the ever-changing curvature of a molten glass blob as it is blown from an amorphous state into a beautiful sphere that one day might hang from a chandelier.
Now consider something like that problem — a shape deforming amid intense heat — but in many more dimensions. So many dimensions, in fact, that even in so lengthy a geometry treatise as Fong’s dissertation, it was pointless to include any figures. In the big leagues of geometry, one sometimes is no longer talking about physical shapes, like spheres, or phenomena, like heat, except by analogy.
“We consider three-dimensional or four-dimensional geometry as lower-dimensional,” Fong said. “It’s impossible to draw it down on paper or the blackboard, or anything like that.”
There is, however, one very tangible and literal near-sphere on which Fong has already seen great change: Earth. Born and educated through the undergraduate level in Hong Kong, he has now made his way more than 9,800 miles across the Pacific through California and now to Rhode Island.
What has propelled Fong around the globe is collaboration. The United States in general and New England in particular offer an abundance of major research universities where a scholar can find like-minded people.
“In math, collaboration is very important,” he said. “Brown is very close to Yale, close to Havard, MIT, Princeton, and Columbia. That’s not something that Hong Kong can offer.”
The idea starts at Fong’s new home, where he looks forward to working with Kapouleas on his area of interest: minimal surfaces. As with the multidimensional spheres in Fong’s dissertation, there is a simpler physical example of the kind of math at issue in minimal surfaces. Dip a metal frame of any shape into soapy water and then take it out. The soap film that spans the frame will naturally form a minimal surface, in that it will cover the least area physically possible.
The details of this area would be new to Fong, he acknowledges, but why be in academia if not to learn.
Fong will teach three courses a year to help others learn and to gain a needed balance in his intellectual life.
“When doing research, especially in math, 99 percent of the time is getting stuck,” he said. “To spend all your day doing research is not going to be enjoyable.”
In other words, more dimensions mean more fulfillment.