Mirror symmetry

introduction

1994 Kontsevich
categorical equivalence of the following two categories
- derived category of bounded complexes of coherent sheaves on a smooth, complete, algebraic variety $X$ over an algebraically closed field
- Fukaya category of the symplectic manifold $\tilde{X}$

http://www.kias.re.kr/file/NewsletterNo37.pdf
Lectures on Mirror Symmetry, Derived Categories, and D-branes
Authors: Anton Kapustin, Dmitri Orlov http://arxiv.org/abs/math/0308173
Yau, Shing-Tung, ed. 1992. Essays on Mirror Manifolds. Hong Kong: International Press. http://www.ams.org/mathscinet-getitem?mr=1191418.

Candelas, Philip, Xenia C. de la Ossa, Paul S. Green, and Linda Parkes. 1991. “A Pair of Calabi-Yau Manifolds as an Exactly Soluble Superconformal Theory.” Nuclear Physics. B 359 (1): 21–74. doi:10.1016/0550-3213(91)90292-6.