Front cover image for Symplectic geometry and mirror symmetry : proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000

Symplectic geometry and mirror symmetry : proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000

In 1993, M. Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics. In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field
eBook, English, ©2001
World Scientific, River Edge, N.J., ©2001
Conference papers and proceedings
1 online resource (ix, 498 pages) : illustrations
9781281951380, 9786611951382, 9789812799821, 1281951382, 6611951385, 9812799826
646768809
Estimated transversahty in symplectic geometry and projective maps / D. Auroux
Local mirror symmetry and five-dimensional gauge theory / T. Eguchi
The Toda conjecture / E. Getzler
Examples of special Lagrangian fibrations / M. Gross
Linear models of supersymmetric D-branes / K. Hori
The connectedness of the moduli space of maps to homogeneous spaces / B. Kim and R. Pandharipande
Homological mirror symmetry and torus fibrations / M. Kontsevich and Y. Soibelman
Genus-1 Virasoro conjecture on the small phase space / X. Liu
Obstruction to and deformation of Lagrangian intersection Floer cohomology / H. Ohta
Topological open p-branes / J.-S. Park
Lagrangian torus fibration and mirror symmetry of Calabi-Yau manifolds / W.-D. Ruan
More about vanishing cycles and mutation / P. Seidel
Moment maps, monodromy and mirror manifolds / R. Thomas
English