2023 - Research.com Mathematics in United States Leader Award
2022 - Research.com Mathematics in United States Leader Award
2013 - Fellow of the American Mathematical Society
2010 - Wolf Prize in Mathematics for his work in geometric analysis that has had a profound and dramatic impact on many areas of geometry and physics.
1997 - US President's National Medal of Science "For his fundamental contributions in mathematics and physics. Through his work, the understanding of basic geometric differential equations has been changed and he has expanded their role enormously within mathematics.", Presented by President Bill Clinton at a ceremony in Room 450, Old Executive Office Building, on Tuesday, December 17, 1997.
1993 - Fellow of the American Association for the Advancement of Science (AAAS)
1993 - Member of the National Academy of Sciences
1985 - Fellow of the MacArthur Foundation
1983 - Fellow of the American Academy of Arts and Sciences
1982 - Fields Medal of International Mathematical Union (IMU) Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge–Ampère equations.
1980 - Fellow of John Simon Guggenheim Memorial Foundation
1974 - Fellow of Alfred P. Sloan Foundation
Shing-Tung Yau mainly investigates Mathematical analysis, Pure mathematics, Scalar curvature, Mathematical physics and Topology. Shing-Tung Yau combines topics linked to Ricci curvature with his work on Mathematical analysis. The Pure mathematics study combines topics in areas such as Conformal map, Upper and lower bounds and Minkowski space.
His research investigates the connection with Scalar curvature and areas like Riemann curvature tensor which intersect with concerns in Curvature of Riemannian manifolds. His Mathematical physics research incorporates themes from Monge–Ampère equation and Spacetime. His studies deal with areas such as Topological string theory, String field theory, Genus and Non-critical string theory as well as Topology.
Pure mathematics, Mathematical analysis, Mathematical physics, Mirror symmetry and Geometry are his primary areas of study. His Pure mathematics study frequently draws connections between adjacent fields such as Algebra. In his research on the topic of Mathematical analysis, Riemann curvature tensor is strongly related with Scalar curvature.
Minkowski space is the focus of his Mathematical physics research. Specifically, his work in Curvature is concerned with the study of Sectional curvature. His work in Conformal map is not limited to one particular discipline; it also encompasses Surface.
His primary areas of study are Pure mathematics, Mathematical physics, Spacetime, Theoretical physics and Combinatorics. His research is interdisciplinary, bridging the disciplines of Curvature and Pure mathematics. His Mathematical physics study combines topics in areas such as Angular momentum, Singularity, Limit, Infinity and Null.
His study in Spacetime is interdisciplinary in nature, drawing from both Quantum, Schwarzschild radius, Minkowski space and Quantum field theory. He usually deals with Theoretical physics and limits it to topics linked to Gauge theory and Duality and Topology. Shing-Tung Yau combines subjects such as Manifold and Boundary with his study of Mirror symmetry.
His main research concerns Pure mathematics, Mathematical physics, Theoretical physics, Mathematical analysis and Coulomb. His Pure mathematics study frequently draws connections to other fields, such as Curvature. His work on General relativity as part of general Mathematical physics research is frequently linked to Algebraic stability, bridging the gap between disciplines.
His Theoretical physics research incorporates elements of Quantum field theory in curved spacetime, Quantum statistical mechanics and Quiver. His research in Mathematical analysis intersects with topics in Gaussian, Volume and Minkowski problem. Shing-Tung Yau focuses mostly in the field of String, narrowing it down to matters related to Partition function and, in some cases, Mirror symmetry and Topology.
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On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
Communications on Pure and Applied Mathematics (1978)
Mathematics and its applications
Shing Tung Yau.
international conference on control and automation (2002)
On the parabolic kernel of the Schrödinger operator
Peter Li;Shing Tung Yau.
Acta Mathematica (1986)
Mirror symmetry is T duality
Andrew Strominger;Shing Tung Yau;Eric Zaslow.
Nuclear Physics (1996)
On the proof of the positive mass conjecture in general relativity
Richard Schoen;Shing Tung Yau.
Communications in Mathematical Physics (1979)
Harmonic functions on complete riemannian manifolds
Communications on Pure and Applied Mathematics (1975)
Calabi's conjecture and some new results in algebraic geometry
Proceedings of the National Academy of Sciences of the United States of America (1977)
Lectures on Differential Geometry
Richard M. Schoen;Shing Tung Yau.
On the existence of hermitian‐yang‐mills connections in stable vector bundles
K. Uhlenbeck;S. T. Yau.
Communications on Pure and Applied Mathematics (1986)
Differential equations on riemannian manifolds and their geometric applications
S. Y. Cheng;S. T. Yau.
Communications on Pure and Applied Mathematics (1975)
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