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Title:
Homological mirror symmetry: cylinders and pairs of pants
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Abstract:
Mirror symmetry provides a general dictionary between symplectic geometry and algebraic geometry on mirror pairs of spaces. Its "homological" flavor, first conjectured by Kontsevich in 1994, relates Lagrangian submanifolds on the symplectic side to coherent sheaves on the algebraic side. We will aim to give a broad introduction to the basic ideas of homological mirror symmetry, and to recent advances in the field, by focusing on two simple examples: the cylinder and the pair of pants. Despite their simplicity, these examples illustrate key concepts in recent formulations of homological mirror symmetry (wrapped Fukaya categories, Landau-Ginzburg models, etc.) and give a representative view of the work currently being done to prove homological mirror symmetry in ever greater degrees of generality
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