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://arxiv.org/abs/1412.1268
Hosono, Shinobu, and Hiromichi Takagi. “Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners.” arXiv:1410.1254 [math], October 6, 2014. http://arxiv.org/abs/1410.1254.
Chan, Kwokwai. “The Strominger-Yau-Zaslow Conjecture and Its Impact.” arXiv:1408.6062 [math], August 26, 2014. http://arxiv.org/abs/1408.6062.
Ueda, Kazushi. “Mirror Symmetry and K3 Surfaces.” arXiv:1407.1566 [math], July 6, 2014. http://arxiv.org/abs/1407.1566.
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.

Hiep, Dang Tuan. “Rational Curves on Calabi-Yau Threefolds: Verifying Mirror Symmetry Predictions.” arXiv:1409.3712 [math], September 12, 2014. http://arxiv.org/abs/1409.3712.
Polishchuk, Alexander, and Eric Zaslow. 1998. “Categorical Mirror Symmetry: The Elliptic Curve.” Advances in Theoretical and Mathematical Physics 2 (2): 443–470.
Kontsevich, Maxim. 1995. “Homological Algebra of Mirror Symmetry.” In Proceedings of the International Congress of Mathematicians, Vol.\ 1, 2 (Zürich, 1994), 120–139. Basel: Birkhäuser. http://www.ams.org/mathscinet-getitem?mr=1403918.
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.
Greene, B. R., and M. R. Plesser. 1990. “Duality in Calabi-Yau Moduli Space.” Nuclear Physics. B 338 (1): 15–37. doi:10.1016/0550-3213(90)90622-K.
Candelas, P., M. Lynker, and R. Schimmrigk. 1990. “Calabi-Yau Manifolds in Weighted $\bf P_4$.” Nuclear Physics. B 341 (2): 383–402. doi:10.1016/0550-3213(90)90185-G.