922 citations · 7.2k across the 348 of their papers we have counts for
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Mirror of Atiyah flop in symplectic geometry and stability conditions
Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau +1
We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct…
D-branes and synthetic/-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds
Chien-Hao Liu, Shing-Tung Yau
We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth man…
Cohomology and Hodge Theory on Symplectic Manifolds: III
Chung-Jun Tsai, Li-Sheng Tseng, Shing-Tung Yau
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered…
D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya -manifolds with a fundamental module and morphisms therefrom to a complex manifold. In t…
Cohomology and Hodge Theory on Symplectic Manifolds: II
Li-Sheng Tseng, Shing-Tung Yau
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in c…
D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
Chien-Hao Liu, Shing-Tung Yau
We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as backgroun…