Kontsevich's conjecture on derived category and symplectic geometry

Kontsevich's conjecture
Category theoretic mirror symmetry conjecture

When there exists mirror relation between X1 and X2, derived category of X1's  coherent sheaf  and derived Fukaya category defined from X2's symplectic structure become equivalence.

M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.

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[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.

References
Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009​

Homological Mirror Symmetry Conjecture by KONTSEVICH
/ Symplectic Language Theory / 26 April 2009​

Quantization of Language / Floer Homology Language / 24 June 2009

Tokyo
10 May 2016
SRFL Theory