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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Mirror symmetry is related to the T-duality on each fiber of an associated Lagrangian fibration Strominger-Yau-Zaslow Abstract This monograph builds on lectures at the Clay School on Geometry and String Theory that sought to bridge the gap between the languages dkrichlet string theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.

Then the statements are: OrlovMirror symmetry for Del Pezzo symmetty By using our website you agree to our use of cookies.

Cumrun VafaShing-Tung Yau eds. In terms of these the statement of mirror symmetry says that passing to mirror CYs exchanges the A-model with the B B -model and conversely:. The narrative is organized around two principal ideas: Inthe introduction of Calabi—Yau manifolds into physics as a way to compactify ten-dimensional space-time has led to branrs cross-fertilization between physics and mathematics, especially with the discovery of mirror symmetry in Computation via topological recursion in matrix models and all- genus?

Last revised on April 11, at Instead, theirs is a unified presentation offered in a way that both mathematicians and physicists xymmetry follow, without having all of the foundations of both subjects at their immediate disposal. The Clay School on Geometry and String Theory set out to bridge this gap, and this monograph builds on the expository lectures given there to provide an up-to-date discussion including subsequent developments.

Request a correction Enlighten Editors: Clay mathematics monographs 4. We use cookies to give you the best possible experience. A new string revolution in the mids brought the notion of branes to the forefront.

Check out the top books of the year on our page Best Books of 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. Book ratings by Goodreads. Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry.

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. Clay Mathematics Monographs Volume: We can notify mirgor when this item is back in stock.

### Dirichlet Branes and Mirror Symmetry – Enlighten: Publications

They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures. Maxim Kontsevich, Yan Soibelman, Homological mirror symmetry and torus fibrationsmath.

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## Mathematics > Algebraic Geometry

See our librarian page for additional eBook ordering options. The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories shmmetry Dirichlet branes.

Context Duality duality abstract duality: Zaslow, Mirror symmetry is T T -duality as pages —. 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. We hope it will allow diichlet and researchers who are familiar with the language of one of the two fields to gain acquaintance with the language of the other.

## Dirichlet Branes and Mirror Symmetry

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

Print Price 1 Label: Goodreads is the world’s largest site for readers with over 50 million reviews. Publication Month and Year: Smith, Homological mirror symmetry for the four-torusDuke Math.

The mirror symmetry conjecture roughly claims that every Calabi-Yau 3-fold has a mirror. This categorical formulation was introduced by Maxim Kontsevich in under the name homological mirror symmetry.

They relate the ideas to active areas of nirror that include the McKay correspondence, topological quantum field theory, and stability structures. Looking for beautiful books? The spectral curve and mirror geometry arXiv: Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes. They also explore the ramifications and current state nad the Strominger-Yau-Zaslow conjecture. This book is suitable for graduate students and researchers with either a physics or mathematics background, who are interested in the interface between string theory and algebraic geometry.

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 a coherent logical context. After showing how notions of branes arose in string theory, it turns to an introduction to the algebraic geometry, sheaf theory, and homological algebra needed to define and work with derived categories.

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