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Topological Field Theory, Primitive Forms and Related Topics

  • Book
  • © 1998

Overview

Editors:
  1. Masaki Kashiwara

    1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

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  2. Atsushi Matsuo

    1. Department of Mathematical Sciences, University of Tokyo, Tokyo, Japan

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  3. Kyoji Saito

    1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

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  4. Ikuo Satake

    1. Department of Mathematics, Osaka University, Toyonaka-city, Japan

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Part of the book series: Progress in Mathematics (PM, volume 160)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Degenerate Double Affine Hecke Algebra and Conformal Field Theory

    • Tomoyuki Arakawa, Takeshi Suzuki, Akihiro Tsuchiya
    Pages 1-34

  3. Vertex Algebras

    • Richard E. Borcherds
    Pages 35-77

  4. Extensions of Conformal Modules

    • Shun-Jen Cheng, Victor G. Kac, Minoru Wakimoto
    Pages 79-129

  5. String Duality and a New Description of the E 6 Singularity

    • Tohru Eguchi
    Pages 131-140

  6. A Mirror Theorem for Toric Complete Intersections

    • Alexander Givental
    Pages 141-175

  7. Precious Siegel Modular Forms of Genus Two

    • Valeri Gritsenko
    Pages 177-203

  8. Non-Abelian Conifold Transitions and N = 4 Dualities in Three Dimensions

    • Kentaro Hori, Hirosi Ooguri, Cumrun Vafa
    Pages 205-238

  9. GKZ Systems, Gröbner Fans, and Moduli Spaces of Calabi-Yau Hypersurfaces

    • Shinobu Hosono
    Pages 239-265

  10. Semisimple Holonomic D-Modules

    • Masaki Kashiwara
    Pages 267-271

  11. K3 Surfaces, Igusa Cusp Forms, and String Theory

    • Toshiya Kawai
    Pages 273-303

  12. Hodge Strings and Elements of K. Saito’s Theory of Primitive Form

    • A. Losev
    Pages 305-335

  13. Summary of the Theory of Primitive Forms

    • Atsushi Matsuo
    Pages 337-363

  14. Affine Hecke Algebras and Macdonald Polynomials

    • Masatoshi Noumi
    Pages 365-377

  15. Duality for Regular Systems of Weights: A Précis

    • Kyoji Saito
    Pages 379-426

  16. Flat Structure and the Prepotential for the Elliptic Root System of Type D4(1,1)

    • Ikuo Satake
    Pages 427-452

  17. Generalized Dynkin Diagrams and Root Systems and Their Folding

    • Jean-Bernard Zuber
    Pages 453-493
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Keywords

About this book

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures.  

The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines. 

Editors and Affiliations

  • Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Masaki Kashiwara, Kyoji Saito

  • Department of Mathematical Sciences, University of Tokyo, Tokyo, Japan

    Atsushi Matsuo

  • Department of Mathematics, Osaka University, Toyonaka-city, Japan

    Ikuo Satake

Bibliographic Information

  • Book Title: Topological Field Theory, Primitive Forms and Related Topics

  • Editors: Masaki Kashiwara, Atsushi Matsuo, Kyoji Saito, Ikuo Satake

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0705-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-8176-3975-4Published: 01 December 1998

  • Softcover ISBN: 978-1-4612-6874-1Published: 02 October 2012

  • eBook ISBN: 978-1-4612-0705-4Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 493

  • Topics: Field Theory and Polynomials, Algebraic Topology, Topology, Algebra

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