Mathematics Colloquia and Seminars

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Homological Mirror Symmetry is an equivalence of two derived categories associated to a mirror pair of Calabi-Yau manifolds. One is an enhanced version of the derived category of coherent sheaves and the other is a derived version of the Fukaya category. In this talk I will give an introduction to the latter category explaining the Fukaya category's motivation from string theory and an overview of its rigorous construction. In particular I will focus on describing the higher products that make it an A-Infinity category. The only background I'll assume is a familiarity with some basic notions in symplectic geometry (e.g. symplectic forms and Lagrangian submanifolds), homological algebra (e.g. chains complexes), and the definition of a compatible almost complex structure.