Ting-Wei Chao Earns the Guy C. Berry Graduate Research Award

Carnegie Mellon University’s Ting-Wei Chao is rarely satisfied, and such a quality is perfect for discrete mathematics.

Chao, a Ph.D. candidate at the Mellon College of Science’s Department of Mathematical Sciences, applied his remarkable persistence to make a meaningful contribution to extremal combinatorics, an area of mathematics that studies the counting of objects.

“Extremal means I want to find a maximum or minimum situation, such as the maximum number of certain objects,” Chao said.

Chao says he enjoys theoretical work “behind the scenes” to come up with techniques to be used by the scientific audience, such as computer scientists who want to confirm their algorithms.

He first became interested in combinatorics as a high school student competing in the International Mathematical Olympiad. He studied at National Taiwan University prior to his graduate studies at Carnegie Mellon.

“For me, combinatorics is like a puzzle that is hard to solve,” Chao said.

About three years into his graduate studies, Chao had co-written several papers. Professor Boris Bukh, Chao’s advisor, could see that he was ready to lead his own work.

“He set himself to prove the sharp bounds for the ‘joints problem,’ which is the most basic result in that area,” Bukh said. “It is not the kind of project that a sensible advisor would recommend to their Ph.D. student because the existing work was already very close to the sharp bounds; partial results would not have been particularly interesting. It was an all-or-nothing project.

“Ting-Wei and his collaborator did succeed, and in doing so they found unexpected connections to the ‘entropy method.’ The math they created is a kind of math that other mathematicians are likely to read and use. It is good math.”

Bukh described an excellent Ph.D. candidate as one who has “a persistent dissatisfaction with the state of their field and a desire to right it.”

“Ting-Wei might be excellent,” Bukh said.

Chao is the 2024 recipient of the Guy C. Berry Graduate Research Award.

The award recognizes excellence in research by MCS graduate students and was established in 2005. Guy C. Berry, emeritus university professor of chemistry, is widely recognized as a leader in rheology and light scattering of polymers. Rheology, a branch of mechanics, is the study of those properties of materials that determine their response to mechanical force. Berry has a long history of outstanding contributions to the literature in experimental fluid physics using mechanical methods and light scattering, as well as in theoretical concepts of the rheology and thermodynamics of complex fluids. His work has advanced the study of important issues in the conformation and dynamics of macromolecules.