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Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
Chien-Hao Liu, Shing-Tung Yau
We explain how Polchinski's work on D-branes re-read from a noncommutative version of Grothendieck's equivalence of local geometries and function rings gives rise to an intrinsic p…
Heterotic Kahler/non-Kahler Transitions
Melanie Becker, Li-Sheng Tseng, Shing-Tung Yau
We show how two topologically distinct spaces - the Kahler K3 x T^2 and the non-Kahler T^2 bundle over K3 - can be smoothly connected in heterotic string theory. The transition occ…
Taming symplectic forms and the Calabi-Yau equation
Valentino Tosatti, Ben Weinkove, Shing-Tung Yau
We study the Calabi-Yau equation on symplectic manifolds. We show that Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form can be reduced to…