Rate My Professor Shing-Tung Yau

Yau pioneered geometric analysis by applying partial differential equation techniques to differential geometry, resolving major conjectures including the Calabi conjecture in his 1978 paper 'On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I,' which introduced Calabi-Yau manifolds fundamental to string theory. With Richard Schoen, he proved the positive mass conjecture in general relativity in 1979 ('On the proof of the positive mass conjecture in general relativity'), leading to the Schoen-Yau black hole existence theorem and quasi-local mass definitions. Collaborating with Karen Uhlenbeck, he established the existence of Hermitian Yang-Mills connections. Other key works include the Strominger-Yau-Zaslow construction for mirror symmetry ('Mirror symmetry is T-duality,' 1996) and heat kernel estimates with Peter Li ('On the parabolic kernel of the Schrödinger operator,' 1986). His textbook 'Lectures on Differential Geometry' appeared in 1994. Yau's innovations have transformed understanding of geometric differential equations, impacting mathematics, theoretical physics, and general relativity. Major awards include the Fields Medal (1982), Oswald Veblen Prize (1981), MacArthur Fellowship (1984), Crafoord Prize (1994), United States National Medal of Science (1997) for fundamental contributions in mathematics and physics, and the Shaw Prize in Mathematical Sciences (2023, shared with Vladimir Drinfeld) for contributions to mathematical physics, arithmetic, differential geometry, and Kähler geometry.