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 construct...
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| Sprache: | English |
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| Zusammenfassung: | 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 |
| Beschreibung: | ix, 498 p. ill |
| ISBN: | 9789812799821 |
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| 520 | |a 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 | ||
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| author_corporate | Kodung Kwahagwon (Korea) International Conference < 2000, Seoul, Korea> |
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| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
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| spelling | Kodung Kwahagwon (Korea) International Conference < 2000, Seoul, Korea> Verfasser aut 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 editors, K. Fukaya ... [et al.] Singapore World Scientific Pub. Co. c2001 ix, 498 p. ill txt rdacontent c rdamedia cr rdacarrier 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 Mirror symmetry / Congresses Symplectic groups / Congresses Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Spiegelsymmetrie (DE-588)4538605-5 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content 2\p (DE-588)1071861417 Konferenzschrift 2000 Seoul gnd-content Symplektische Geometrie (DE-588)4194232-2 s Spiegelsymmetrie (DE-588)4538605-5 s 3\p DE-604 Fukaya, Kenji 1959- Sonstige oth World Scientific (Firm) Sonstige oth Erscheint auch als Druck-Ausgabe 9789810247140 Erscheint auch als Druck-Ausgabe 9810247141 http://www.worldscientific.com/worldscibooks/10.1142/4778#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | 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 Mirror symmetry / Congresses Symplectic groups / Congresses Symplektische Geometrie (DE-588)4194232-2 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4538605-5 (DE-588)1071861417 |
| title | 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 |
| title_auth | 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 |
| title_exact_search | 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 |
| title_full | 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 editors, K. Fukaya ... [et al.] |
| title_fullStr | 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 editors, K. Fukaya ... [et al.] |
| title_full_unstemmed | 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 editors, K. Fukaya ... [et al.] |
| title_short | Symplectic geometry and mirror symmetry |
| title_sort | 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 |
| title_sub | proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000 |
| topic | Mirror symmetry / Congresses Symplectic groups / Congresses Symplektische Geometrie (DE-588)4194232-2 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| topic_facet | Mirror symmetry / Congresses Symplectic groups / Congresses Symplektische Geometrie Spiegelsymmetrie Konferenzschrift Konferenzschrift 2000 Seoul |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4778#t=toc |
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