S.-T. Yau

S.-T. Yau
Name	S.-T. Yau
Birth date	1949-04-04
Birth place	Chiayi, Taiwan
Nationality	Taiwanese
Fields	Differential geometry, Partial differential equation, Complex geometry
Alma mater	National Tsing Hua University; UC Berkeley
Doctoral advisor	Shiing-Shen Chern
Known for	Calabi conjecture, Calabi–Yau manifold, Yau's theorem, positive mass theorem
Awards	Fields Medal, National Medal of Science

S.-T. Yau S.-T. Yau is a Taiwanese-born mathematician noted for foundational work in differential geometry, complex manifold, and geometric analysis. His research resolved major conjectures connecting complex geometry with partial differential equation techniques and influenced developments in string theory, algebraic geometry, and global analysis. Yau has held positions at leading institutions and received numerous international honors from bodies such as the International Mathematical Union and the National Academy of Sciences.

Early life and education

Born in Chiayi, Taiwan, Yau studied at National Tsing Hua University before emigrating to the United States to pursue graduate study at the UC Berkeley. At Berkeley he completed a Ph.D. under the supervision of Shiing-Shen Chern with a dissertation touching on curvature and global properties of Riemannian manifold. During his formative years he interacted with figures such as Shiing-Shen Chern (note: advisor), Dennis Sullivan, Isadore Singer, and Michael Atiyah, situating him within a network that included John Milnor, Raoul Bott, and Kunihiko Kodaira.

Mathematical career and positions

Yau served on the faculty at UC Berkeley, followed by appointments at Harvard University, Stony Brook University, and Princeton University before accepting a long-term position at Harvard University and later at Harvard Department of Mathematics and visiting roles at institutions including Institute for Advanced Study, Mathematical Sciences Research Institute, and Tsinghua University. He cofounded centers and programs that linked differential geometry with algebraic geometry and theoretical physics, collaborating with scholars like Edward Witten, David Mumford, Pierre Deligne, and Shing-Tung Yau (see advisor lineage). Yau has advised students who became prominent mathematicians, including members of the National Academy of Sciences and fellows of the American Mathematical Society.

Major contributions and theorems

Yau proved the existence of Kähler metrics with prescribed Ricci curvature, resolving the Calabi conjecture and establishing what is commonly called Yau's theorem on the existence of Calabi–Yau manifolds, a result that linked Calabi's proposal to constructions used in string theory by physicists such as Edward Witten and Cumrun Vafa. He contributed to the proof of the positive mass theorem in general relativity, collaborating in a mathematical context related to work by Richard Schoen, and influenced results by Schoen and Yau on scalar curvature and topology, intersecting with research by Hermann Weyl and James Simons. Yau introduced analytic techniques combining nonlinear elliptic partial differential equation methods with geometric intuition, impacting the study of minimal surfaces, Einstein metrics, and moduli problems addressed by Maxwell Bergman (historical influence), Jean-Pierre Serre, and Alexander Grothendieck-era developments in algebraic geometry. His work on the structure of moduli space interacted with advances by Mumford, Deligne, Pierre Deligne, and David Mumford on stability and compactification.

Awards and honors

Yau received the Fields Medal-level recognition in major prize circles and was awarded honors including the National Medal of Science, election to the National Academy of Sciences, fellowship in the American Academy of Arts and Sciences, the Shaw Prize, and international prizes bestowed by organizations such as the International Mathematical Union, Chinese Mathematical Society, and national academies including the Academia Sinica. He has been given honorary degrees and named lectureships at institutions such as Oxford University, Cambridge University, Harvard University, and Princeton University, and has held visiting positions at the Institute for Advanced Study and Mathematical Sciences Research Institute.

Selected publications

Yau's bibliography includes influential papers and monographs on Kähler–Einstein metrics, the Calabi conjecture, and geometric analysis, appearing in journals and volumes associated with Annals of Mathematics, Communications in Mathematical Physics, Journal of Differential Geometry, and proceedings of the International Congress of Mathematicians. Notable works include expository and technical papers that have been cited alongside contributions by Shiing-Shen Chern, Calabi, Richard Schoen, Edward Witten, Pierre Deligne, and David Mumford; he has edited volumes for conferences attended by scholars from Princeton University, Harvard University, and the Institute for Advanced Study.

Influence and legacy

Yau's resolution of central problems reshaped research directions in differential geometry, complex geometry, and theoretical physics, influencing generations of mathematicians and physicists such as Edward Witten, Cumrun Vafa, Maxim Kontsevich, Kai Behrend, and Nigel Hitchin. His promotion of interdisciplinary programs connected geometry research with developments in string theory and mirror symmetry studied by researchers at Caltech, Harvard University, and Princeton University. Yau's students and collaborators occupy leadership roles across institutions including UC Berkeley, Harvard University, Princeton University, and Tsinghua University, ensuring ongoing impact on topics pioneered in his work, such as Calabi–Yau geometry, scalar curvature problems, and analytic methods in geometry.

Category:Mathematicians