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# Mirror symmetry : [in the spring of 2000, the Clay Mathematics Institute (CMI) organized a school on Mirror Symmetry, held at Pine Manor College, Brookline, Massachusetts]

Author: Kentaro Hori; Clay Mathematics Institute (Cambridge, Mass.) Providence, R.I. : American Mathematical Society, 2003. Clay mathematics monographs, 1. Print book : EnglishView all editions and formats WorldCat Suitable for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics, and for graduate students and research mathematicians interested in  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Brookline (Mass., 2000)Kongress Book Kentaro Hori; Clay Mathematics Institute (Cambridge, Mass.) Find more information about: Kentaro Hori 0821829556 9780821829554 635000809 XX, 929 S. : graph. Darst. Part 1. Mathematical Preliminaries: Differential geometry Algebraic geometry Differential and algebraic topology Equivariant cohomology and fixed-point theorems Complex and Kahler geometry Calabi-Yau manifolds and their moduli Toric geometry for string theory Part 2. Physics Preliminaries: What is a QFT? QFT in $d=0$ QFT in dimension 1: Quantum mechanics Free quantum field theories 1 + 1 dimensions $\mathcal{N} = (2,2)$ supersymmetry Non-linear sigma models and Landau-Ginzburg models Renormalization group flow Linear sigma models Chiral rings and topological field theory Chiral rings and the geometry of the vacuum bundle BPS solitons in $\mathcal{N}=2$ Landau-Ginzburg theories D-branes Part 3. Mirror Symmetry: Physics Proof: Proof of mirror symmetry Part 4. Mirror Symmetry: Mathematics Proof: Introduction and overview Complex curves (non-singular and nodal) Moduli spaces of curves Moduli spaces $\bar{\mathcal M}_{g,n}(X,\beta)$ of stable maps Cohomology classes on $\bar{\mathcal M}_{g,n}$ and ($\bar{\mathcal M})_{g,n}(X,\beta)$ The virtual fundamental class, Gromov-Witten invariants, and descendant invariants Localization on the moduli space of maps The fundamental solution of the quantum differential equation The mirror conjecture for hypersurfaces I: The Fano case The mirror conjecture for hypersurfaces II: The Calabi-Yau case Part 5. Advanced Topics: Topological strings Topological strings and target space physics Mathematical formulation of Gopakumar-Vafa invariants Multiple covers, integrality, and Gopakumar-Vafa invariants Mirror symmetry at higher genus Some applications of mirror symmetry Aspects of mirror symmetry and D-branes More on the mathematics of D-branes: Bundles, derived categories and Lagrangians Boundary $\mathcal{N}=2$ theories References Bibliography Index. Clay mathematics monographs, 1. Kentaro Hori ... Clay Mathematics Institute.

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