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 $\tilde{X}$

Port, Andrew. “An Introduction to Homological Mirror Symmetry and the Case of Elliptic Curves.” arXiv:1501.00730 [math], January 4, 2015. http://arxiv.org/abs/1501.00730.
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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.
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