Lectures on Mirror Symmetry, Derived Categories, and D-branes

Abstract

This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to derived categories, and the reason why it is necessary to enlarge the Fukaya category with coisotropic A-branes; we discuss how to extend the definition of Floer homology to such objects and describe mirror symmetry for flat tori. The paper consists of four lectures which were given at the Institute for Pure and Applied Mathematics (Los Angeles), March 2003, as part of a program on Symplectic Geometry and Physics.

30 pages

References in corpus (1)

• Topological strings on noncommutative manifolds

Cited by in corpus (17)

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• Quantum A-infinity Structures for Open-Closed Topological Strings
• Tachyon condensation and D-branes in generalized geometries
• On higher rank coisotropic A-branes
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
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• A String Dual for Partially Topological Chern-Simons-Matter Theories
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• Some comments on the local curve (B-side)
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• Twisted Homogeneous Coordinate Rings of Abelian Surfaces via Mirror Symmetry