نظریه تغییر شکل، جبر همولوژیک و تقارن آینه‌ای

## Contents Contents 0.1 Introduction. 1 Classical Deformation theory 1.1 Holomorphic structure on vector bundles. 1.2 Family of holomorphic structures on vector bundle. 1.3 Cohomology and Deformation. 1.4 Bundle valued Harmonic forms. 1.5 Construction of versal family and Feynman diagram. 1.6 Kuranishi family. 1.7 Formal deformation. 2 Homological algebra and Deformation theory 2.1 Homotopy theory of A ∞ and L ∞ algebras. 2.2 Maurer-Cartan equation and moduli functor. 2.3 Canonical model, Kuranishi map, and moduli space. 2.4 Super space and odd vector field -an alternative formulation of L ∞ algebra -3 Application to Mirror symmetry 3.1 Novikov ring and filtered A ∞ , L ∞ algebras. 3.2 Review of a part of global symplectic geometry. 3.3 From Lagrangian submanifold to A ∞ algebra. 3.4 Maurer-Cartan equation for filtered A ∞ algebra. 3.5 Homological mirror symmetry.