Mirror Symmetry And Quantum Geometry

Abstract

Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ D-branes wrapped on torus fibers to reproduce the mirror duality itself, realizing the program of Strominger-Yau-Zaslow in a slightly different context. Floer theory of intersecting Lagrangians plays an essential role.

12 pages, ICM 2002 at Beijin

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Cited by in corpus (7)

• Generalized complex geometry and T-duality
• Homological mirror symmetry for log Calabi-Yau surfaces
• Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
• Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
• Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Open Gauged Sigma Models, Equivariant Branes, and Equivariant Homological Mirror Symmetry