Scientists / Open questions
Shing-Tung Yau
Differential geometry; geometric analysis
1982 Fields Medal
57 questions
Affine monodromy, integrality, and uniqueness of the Loftin–Yau–Zaslow semi-flat Calabi–Yau model at the 'Y' vertex
Manifold splines without affine structure: singularity-free spline schemes for high-genus surfaces and the singularity-count versus distortion trade-off
Semicontinuity of the 4d N=2 spectrum under renormalization group flow beyond hypersurface-singularity SCFTs
The boundary between parallelizability, almost complex structure, and integrability: complex structures on compact parallelizable manifolds above dimension four, and rigidity of complex manifolds homotopy equivalent to tori
Closed-form solutions of tautological systems at maximal-unipotent-monodromy points for Calabi-Yau hypersurfaces and complete intersections in flag varieties
Existence of maximal (zero mean curvature) spacelike hypersurfaces in spacetimes under natural energy, completeness, and asymptotic hypotheses
Generators and boundary geometry of the algebra of differential Siegel modular forms DM(Γ) for genus two curves with a marked Weierstrass point
Completing the pseudonorm program for birational classification of varieties of general type: unrestricted uniform Torelli theorem, realization, computation, and canonical-metric links
Tian–Yau's conjectural identity between the equivariant alpha-invariant and normalized Lelong numbers on Fano manifolds, and the companion interior C^0 estimate for degenerate complex Monge–Ampère equations