The Strominger-Yau-Zaslow conjecture and its impact

Abstract

This article surveys the development of the SYZ conjecture since it was proposed by Strominger, Yau and Zaslow in their famous 1996 paper, and discusses how it has been leading us to a thorough understanding of the geometry underlying mirror symmetry.

v2: minor corrections in Section 8; 22 pages. appears in "Selected Expository Works of Shing-Tung Yau with Commentary. Vol. II", 1183-1208, Adv. Lect. Math. (ALM) 29, Int. Press, Somerville, MA, 2014

References in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• Stable logarithmic maps to Deligne--Faltings pairs II
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• SYZ Mirror Symmetry of Hitchin's Moduli Spaces Near Singular Fibers I