273 citations · 1.3k across the 50 of their papers we have counts for
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Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces
Si Li, Bong H. Lian, Shing-Tung Yau
We study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. We construct an inhomogeneous Picard-Fuch…
Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a -field background à la Polchinski-Grothendieck Ansatz
Chien-Hao Liu, Shing-Tung Yau
In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study…
Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a co…
Gap of the First Two Eigenvalues of the Schrödinger Operator with Nonconvex Potential
Shing-Tung Yau
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The re…
An Estimate of the Gap of the First Two Eigenvalues in the Schrödinger Operator
Shing-Tung Yau
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the…
Azumaya structure on D-branes and resolution of ADE orbifold singularities revisited: Douglas-Moore vs. Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In this continuation of [L-Y1] and [L-L-S-Y], we explain how the Azumaya structure on D-branes together with a netted categorical quotient construction produces the same resolution…