This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich’s homological mirror symmetry conjecture, and . This is the second of two books that provide the scientific record of the school. The first book, Strings and Geometry, edited by Michael R. PDF | This monograph builds on lectures at the Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string .

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In fact one considers mirror symmetry for degenerating families for Calabi-Yau 3-folds in large volume limit which may be expressed precisely via the Gromov-Hausdorff metric. Orlov, Mirror symmetry for abelian varietiesJ.

## Dirichlet Branes and Mirror Symmetry

Looking for beautiful books? The mirror symmetry conjecture roughly claims that every Calabi-Yau 3-fold has a mirror. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book.

This monograph builds on lectures at the Clay School on Geometry and String Difichlet that sought to bridge brranes gap between the languages of string theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.

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Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality. The authors explain how Kontsevich’s conjecture is equivalent to the identification of mirrorr different categories of Dirichlet branes. Nauk 59no. Author s Product display: The narrative is organized around two principal ideas: S-dualityelectric-magnetic duality. These developments have led to a great deal of new mathematical work.

The physical existence conditions for branes are then discussed and compared in the context of mirror symmetry, culminating in Bridgeland’s definition of stability structures, and its applications to the McKay correspondence and quantum geometry.

Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes. By using our website you dirichhlet to our use of cookies. One difficulty in understanding all aspects of this work is that it requires being able to speak two different languages, the language of string theory and the language of algebraic geometry. Zaslow, Mirror symmetry is T T -duality as pages —. Computation via topological recursion in matrix models and all- genus?

### [math/] Dirichlet branes, homological mirror symmetry, and stability

A natural sequel to the first Clay monograph on Mirror Symmetry, it presents the new ideas coming out of the interactions of string theory and algebraic geometry in brxnes coherent logical context. Request a correction Enlighten Editors: Surveys 59no. The book first introduces the notion of Dirichlet brane in the symmetrj of topological quantum field theories, and then reviews the basics of string theory.

A new string revolution in the mids brought the notion of branes to the forefront. Join our email list.

## Mathematics > Algebraic Geometry

They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures. Dirichlet Branes and Mirror Symmetry.

Paul SeidelHomological mirror symmetry for the genus two curveJ. We can notify you when this item is back in stock. Maxim Kontsevich, Yan Soibelman, Homological mirror symmetry and torus fibrationsmath.

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This categorical formulation was introduced by Maxim Kontsevich in mirror the name homological mirror symmetry. Print Price 1 Label: Site tools A-Z Lists. Seidel, Homological mirror symmetry for the quartic surfacearXiv: The book continues with detailed treatments of the Strominger—Yau—Zaslow conjecture, Calabi—Yau metrics and homological mirror symmetry, and discusses more recent physical developments.

### Dirichlet Branes and Mirror Symmetry : Bennett Chow :

The topological A-model can be expressed in terms of symplectic geometry of a variety and the topological B-model can be expressed in terms of the algebraic geometry of a variety. As foreseen by Kontsevich, these turned out to have mathematical counterparts in the derived category of coherent sheaves on an algebraic variety and the Fukaya category of a symplectic manifold. Description Research in string ajd has generated a migror interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture.

The relation to T-duality was established in.