Homological mirror symmetry and tropical geometry
Author(s)
Bibliographic Information
Homological mirror symmetry and tropical geometry
（Lecture notes of the Unione matematica italiana, 15）
Springer : UMI, c2014
Available at 16 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
C-P||Cetrano||2011200032342694
Note
Other editors: Fabrizio Catanese, Maxim Kontsevich, Tony Pantev, Yan Soibelman, Ilia Zharkov
Includes bibliographical references
Description and Table of Contents
Description
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.
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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