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

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. Deriving the matrix model arXiv: Product details Format Hardback pages Dimensions 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.

The Best Books of Surveys 59no. The relation to T-duality was established in.

The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view. Last revised on April 11, at Dr Alastair Craw Deposited On: Description Research in string theory has generated a rich interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture. 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.

The mirrror symmetry conjecture roughly claims diridhlet every Calabi-Yau 3-fold has a mirror. Then the statements are: Other books in this series. 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. Mirror symmetry is related to the T-duality on each fiber of an associated Lagrangian fibration Strominger-Yau-Zaslow Clay Mathematics Monographs Volume: Discussion in the context of derived Morita equivalence includes.

Author s Product display: RR-fielddifferential K-theory. Abstract 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. They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures.

Efimov, Homological mirror symmetry for curves of higher genusInventiones Math. In this form mirror symmetry remains a conjecture, not the least because for the moment there is no complete construction of these SCFTs.

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Check out the top books of the year on our page Best Books of Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality. 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. Ordering on the AMS Bookstore is limited to individuals for personal use only.

By using our website you agree dorichlet our use of cookies. At least in some cases this can be understood as a special case of T-duality Strominger-Yau-Zaslow Skip to main content Accessibility information. A few of the relevant names: In fact one considers mirror symmetry for degenerating families for Calabi-Yau 3-folds in brznes volume limit which may be expressed precisely via the Gromov-Hausdorff metric.

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

D0-braneD2-braneD4-brane. Request a correction Enlighten Editors: Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry. D1-braneD3-braneD5-brane.

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 syymmetry work with derived categories.

Here is a list with references that give complete proofs of homological mirror symmetry on certain types of mitror. They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures. We can notify you when this item is back in stock.

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

Clay mathematics monographs 4. Dirichlet Branes and Mirror Symmetry. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more.

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