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

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

2003-08-18

arxiv.org/abs/math/0308173v2

Russian Math. Surveys 59 (2004), no. 5, 907--940

Mathematics

Algebraic Geometry

30 pages

Scientific paper

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.

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