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Taniguchi Conference on Mathematics Nara 1998
Edited by: Masaki Maruyama, Kyoto University, Japan, and Toshikazu Sunada, Tohoku University, Japan
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
2001; 286 pp; hardcover
Volume: 31
ISBN-10: 4-931469-13-2
ISBN-13: 978-4-931469-13-6
List Price: US$66
Member Price: US$52.80
Order Code: ASPM/31
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In 1929, Mr. Toyosaburo Taniguchi established the Taniguchi Foundation with the goal of promoting research in the basic sciences in Japan and to engender mutual understanding on an international level via the exchange of ideas and research. In 1956, he instituted a division for mathematics within the Foundation and sponsored the first summer seminar. Since that time, the seminar has been held each year on various mathematical topics.

In 1974, Mr. Taniguchi promoted and sponsored an International Symposium in various fields of science on a smaller scale. His aim was to raise the level of scientific thought and research, while providing a forum where promising young scholars the world over could gather informally to exchange thoughts and to contribute their knowledge. These gatherings were held until 1999.

This volume is a collection of the research manuscripts written by the invited speakers at the final conference set up by the Taniguchi Foundation, the Taniguchi Conference on Mathematics 1998, held in Nara, Japan. The conference was aimed at gathering all previous participants of Taniguchi Symposia. The subject areas were chosen to include all important and active fields of mathematics. Hence the topics in this volume are quite diverse. The contributors are world-class mathematicians who are generally reporting on subjects for which they are well known. For example, contributions include R. E. Borcherds on vertex algebras, M. Kontsevich on non-commutative algebraic manifolds, P.-L. Lions on fluid mechnics, M. Kashiwara on micro-localization, J. Kollár on the topology of algebraic varieties, S. Mori on rational curves in algebraic varieties, and others.

Volumes in this series are freely available electronically 5 years post-publication.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.


Graduate students and research mathematicians.

Table of Contents

  • H. Arai -- Hardy spaces, Carleson measures and a gradient estimate for harmonic functions on negatively curved manifolds
  • R. E. Borcherds -- Quantum vertex algebras
  • K. Fukaya and K. Ono -- Floer homology and Gromov-Witten invariant over integer of general symplectic manifolds-Summary
  • M.-H. Giga, Y. Giga, and R. Kobayashi -- Very singular diffusion equations
  • J. Kollár -- The topology of real and complex algebraic varieties
  • S. Kusuoka -- Approximation of expectation of diffusion process and mathematical finance
  • G. Lusztig -- Representation theory in characteristic \(p\)
  • P. Malliavin -- Probability and geometry
  • S. Mochizuki -- The intrinsic Hodge theory of \(p\)-adic hyperbolic curves
  • A. Ocneanu -- Operator algebras, topology and subgroups of quantum symmetry--Construction of subgroups of quantum groups
  • S. R. S. Varadhan -- Large deviation and hydrodynamic scaling
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