Math Labs

Shing-Tung Yau

Native spelling: 丘成桐

fl. 1949, Shantou, Guangdong, China

GeometryDifferential equations and dynamical systemsMathematical physicsFields Medal 1982Crafoord Prize in Mathematics 1994Wolf Prize in Mathematics 2010Shaw Prize in Mathematical Sciences 2023

Chinese-American mathematician who proved the Calabi conjecture and the positive mass theorem; a founder of geometric analysis whose work links differential geometry to topology and mathematical physics.

Shing-Tung Yau was born on 4 April 1949 in Shantou, Guangdong, and the family moved to Hong Kong soon after. After his father's death the family lived in poverty; Yau studied mathematics at the Chinese University of Hong Kong and went to the University of California, Berkeley in 1969, where he completed his PhD under Shiing-Shen Chern in 1971. After positions at the Institute for Advanced Study, Stony Brook and Stanford, he became a professor at the University of California, San Diego in 1987 and at Harvard University the same year.

Yau's solution of the Calabi conjecture (1978) — the existence of Kähler metrics with prescribed Ricci curvature, in particular Ricci-flat Calabi–Yau metrics — created geometric analysis as a discipline in which elliptic PDE settle questions in topology and geometry. With Schoen he proved the positive mass theorem of general relativity and the positive action conjecture; with Uhlenbeck he proved the existence of minimal surfaces of higher genus; with Hamilton, Perelman's later proof of the Poincaré conjecture built on Ricci flow, a program Hamilton had launched in part inspired by Yau's program for geometric flows. Yau also drove the theory of mirror symmetry through enumerative computations on Calabi–Yau manifolds.

At Harvard he built one of the largest research groups in geometry, founded the Journal of Differential Geometry's intellectual orbit, and trained scores of students. He has organized mathematical research in China for decades — institutes in Beijing, Taiwan and Hong Kong, the S.-T. Yau High School Science Award, and the International Congress of Chinese Mathematicians. He retired from Harvard in 2022 and is now dean of the Qiuzhen College and director of the Yau Mathematical Sciences Center at Tsinghua University. His autobiography 'The Shape of a Life' appeared in 2019.

Workplaces: Harvard University, University of California, San Diego, Tsinghua University

United States, China

Award-winning work

Fields Medal 1982For contributions to differential geometry, partial differential equations and their use in general relativity and topology. In 1978 Yau proved the Calabi conjecture by solving a complex Monge–Ampère equation on compact Kähler manifolds, producing the Ricci-flat metrics now called Calabi–Yau manifolds — later the geometric heart of string compactification. With Richard Schoen he proved the positive mass theorem, confirming that the total mass of an isolated gravitational system in general relativity is non-negative, and developed the method of minimal surfaces into a tool that controlled the topology of three-manifolds. He also contributed to the theory of closed geodesics and the uniformization of Kähler manifolds.

Contributions, linked to the library

Library topicDifferential geometryFounded geometric analysis: nonlinear PDE (Monge–Ampère, minimal surfaces) used to solve problems in geometry and topology.Library topicRiemannian geometryThe Calabi conjecture and the positive mass theorem are landmarks of Riemannian and Kähler geometry.Library topicType theoryRicci flow, the tool behind the geometrization program, grew out of Yau's program of geometric flows.