Overview

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.

Full Product Details

Author:   Ricardo Castano-Bernard ,  Fabrizio Catanese ,  Maxim Kontsevich ,  Tony Pantev
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Volume:   15
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   6.788kg
ISBN:  

9783319065137

ISBN 10:   3319065130
Pages:   436
Publication Date:   16 October 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Oren Ben-Bassat and Elizabeth Gasparim: Moduli Stacks of Bundles on Local Surfaces.- David Favero, Fabian Haiden and Ludmil Katzarkov: An orbit construction of phantoms, Orlov spectra and Knoerrer Periodicity.- Stephane Guillermou and Pierre Schapira: Microlocal theory of sheaves and Tamarkin's non displaceability theorem.- Sergei Gukov and Piotr Sulkowski: A-polynomial, B-model and Quantization.- M. Kapranov, O. Schiffmann, E. Vasserot: Spherical Hall Algebra of Spec(Z).- Maxim Kontsevich and Yan Soibelman: Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and mirror Symmetry.- Grigory Mikhalkin and Ilia Zharkov: Tropical eigen wave and intermediate Jacobians.- Andrew Neitzke: Notes on a new construction of hyperkahler metrics.- Helge Ruddat: Mirror duality of Landau-Ginzburg models via Discrete Legendre Transforms.- Nicolo Sibilla: Mirror Symmetry in dimension one and Fourier-Mukai transforms.- Alexander Soibelman: The very good property for moduli of parabolic bundles and the additive Deligne-Simpson problem.

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