In recognition of his promising early-career achievements, UC Santa Barbara mathematician Xin Zhou has received a fellowship from the Alfred P. Sloan Foundation. Each year the foundation selects fellows from a diverse group of researchers nominated by their peers.

 

The mathematics department is delighted to hear of Zhou’s fellowship. “Xin […] has already solved several significant problems about minimal surfaces […] and general relativity,” said department chair Jon McCammond, “and the ideas and tools he has created show great promise for future applications and developments.”

 

“I am very glad and honored to be selected as a Sloan fellow,” said Xin Zhou, an assistant professor of mathematics. “This is a very prestigious award for young researchers.” He said he hopes the honor will draw more attention to his field of research, especially from graduate students.

 

Zhou investigates the geometric properties of surfaces. He’s worked on topics with applications from the boundaries of black holes to the behavior of soap bubbles. “I started with general relativity when I entered graduate school,” he said. “I was trying to understand the relationship between different conserved quantities in a spacetime system, such as mass, energy, linear momentum and angular momentum.

 

“Gradually, I shifted my research focus to more pure math problems pertaining to surfaces like those that describe black holes,” Zhou added. He currently focuses on the mathematical models for soap bubbles, which involve interesting differential geometry that also applies to black holes.

 

Ideally, when we blow a soap bubble the volume inside doesn’t change, Zhou explained, and the surface tension of the soap will try to create an enclosure with the least amount of surface area. This shapes a typical soap bubble into a sphere, a shape that has the same curvature everywhere on its surface. Mathematicians call these “surfaces of constant mean curvature,” he said, and they model a class of black hole boundaries in general relativity.

 

In a flat space these surfaces are always spheres. However, general relativity tells us that the space we live in is not always flat: Matter curves it like a bowling ball on a trampoline. Zhou aims to construct these surfaces in curved spaces and investigate their properties.