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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## Mathematics > Algebraic Geometry

In this form mirror symmetry remains a conjecture, not the least because for the moment there is no complete construction of these SCFTs. We can notify you when this item mirtor back in stock. This book is suitable for graduate students and researchers with either a physics or mathematics background, who are interested in the interface between string symmetty and algebraic geometry. Zaslow, Mirror symmetry is T T -duality as pages —.

These developments have led to a great deal of new mathematical work.

### Dirichlet Branes and Mirror Symmetry

Dirichlet Branes and Mirror Symmetry. S-dualityelectric-magnetic duality. A few of the relevant names: The narrative is organized around two principal ideas: The book first introduces the notion of Dirichlet brane in the context of topological quantum field theories, and then reviews the basics of string theory. Symmetey group of distinguished mathematicians and mathematical physicists who produced this monograph worked as a team to create a unique volume.

T-dualitymirror symmetry. The appropriate definition of an appropriate version of the Fukaya category of a symplectic manifold is difficult to achieve in desired generality.

The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories of Dirichlet branes. Inthe introduction of Calabi—Yau manifolds into physics as a way to compactify ten-dimensional space-time has led to exciting cross-fertilization between physics and mathematics, especially with the discovery of mirror symmetry in Smith, Homological mirror symmetry for the four-torusDuke Math.

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.

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

Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes. See the history of this page for a list of all contributions to it. D1-braneD3-brane mlrror, D5-brane. Print Price 2 Label: This has led to exciting new work, including the Strominger—Yau—Zaslow conjecture, which used the theory of branes to propose a geometric basis for mirror symmetry, the theory of stability conditions on triangulated categories, and a physical basis for the McKay correspondence.

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 theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.

The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view. Deriving the matrix model arXiv: Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Check out the top books of the year on our page Best Books of The relation to T-duality was established in. Efimov, Homological mirror symmetry for curves of higher genusInventiones Math.

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.

This categorical formulation was introduced by Maxim Kontsevich in under the name homological mirror symmetry. Instead, theirs is a unified presentation offered in a way that both mathematicians and physicists can follow, without having all mirfor the foundations of both subjects at their immediate disposal. A new string revolution in the mids brought the notion of branes to the forefront. Algebraic Geometry, to appear, arXiv: 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.

Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality.

RR-fielddifferential K-theory. Maxim Kontsevich, Yan Soibelman, Homological mirror symmetry and torus fibrationsmath. 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.

We hope it will allow students and researchers who are familiar with the language of one of the two fields to gain acquaintance with the language of the other. Last revised on April 11, at Orlov, Mirror symmetry for abelian varietiesJ.

Looking for beautiful books? The Best Books of Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. We use cookies to give you the best possible experience.