Symplectic Geometry And Mirror Symmetry,: Proceedings Of The 4th Kias Annual International Conference

Symplectic Geometry and — Mirror Symmetry Proceedings of the 4th KIAS Annual International Conference Editors K. Fukaya, Y.-G. O h , K. Ono, G. Tian Symplectic Geometry and Mirror Symmetry 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 Kyoto University, Japan Y.-G. O h University of Wisconsin-Madison, USA & Korea Institute for Advanced Study, South Korea K. Ono Hokkaido University, Japan G. Tian Massachusetts Institute of Technology, USA 10 World Scientific ll New Jersey London • Singapore • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. SYMPLECTIC GEOMETRY AND MIRROR SYMMETRY Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-02-4714-1 Printed in Singapore by World Scientific Printers Speakers D. Auroux (Ecole Polytechnique), T. Eguchi (University of Tokyo), E. Getzler (Northwestern University), A. Givental (University of California-Berkeley), M. Gross (Warwick University), K. Hori (Harvard University) E. Ionel (University of Wisconsin-Madison), Bumsig Kim (Postech), Xiaobo Liu (University of Notre Dame), D. McDuff (SUNY-Stony Brook), H. Nakajima (Kyoto University), R. Pandharipande (Caltech), Jaesuk Park (Columbia University), Wei-Dong Ruan (University of Illinois-Chicago), P. Seidel (Ecole Polytechnique), R. Thomas (Imperial College) Preface 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 Aoo -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 GromovWitten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of Ax,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