Topology, Geometry and Quantum Field Theory: Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal

doi:10.1017/CBO9780511526398

The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Preface
pp ix-ix
- By Ulrike Tillmann, Oxford
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Participants
pp x-xii
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Introduction
pp 1-2
- By Sir Michael Atiyah, Edinburgh
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Part I - Contributions
pp 3-4
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1 - A variant of K-theory: K±
pp 5-17
- By Michael Atiyah, University of Edinburgh and MIT., Michael Hopkins, University of Edinburgh and MIT.
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2 - Two-vector bundles and forms of elliptic cohomology
pp 18-45
- By Nils A. Baas, NTNU, Trondheim, NTNU, Trondheim and University of Oslo, Bjørn Ian Dundas, NTNU, Trondheim, NTNU, Trondheim and University of Oslo, John Rognes, NTNU, Trondheim, NTNU, Trondheim and University of Oslo
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3 - Geometric realization of the Segal–Sugawara construction
pp 46-97
- By David Ben-Zvi, University of Chicago and University of California, Berkeley, Edward Frenkel, University of Chicago and University of California, Berkeley
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4 - Differential isomorphism and equivalence of algebraic varieties
pp 98-126
- By Yuri Berest, Cornell University and Imperial College London, George Wilson, Cornell University and Imperial College London
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5 - A polarized view of string topology
pp 127-154
- By Ralph L. Cohen, Stanford University, Véronique Godin, Stanford University
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6 - Random matrices and Calabi–Yau geometry
pp 155-172
- By Robbert Dijkgraaf, University of Amsterdam
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7 - A survey of the topological properties of symplectomorphism groups
pp 173-193
- By Dusa McDuff, State University of New York at Stony Brook
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8 - K-theory from a physical perspective
pp 194-234
- By Gregory Moore, Rutgers University
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9 - Heisenberg groups and algebraic topology
pp 235-246
- By Jack Morava
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10 - What is an elliptic object?
pp 247-343
- By Stephan Stolz, University of California at San Diego and University of Notre Dame, Peter Teichner, University of California at San Diego and University of Notre Dame
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11 - Open and closed string field theory interpreted in classical algebraic topology
pp 344-357
- By Dennis Sullivan, SUNY at Stony Brook and CUNY Graduate Center
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12 - K-theory of the moduli space of bundles on a surface and deformations of the Verlinde algebra
pp 358-378
- By Constantin Teleman, Cambridge University
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13 - Cohomology of the stable mapping class group
pp 379-404
- By Michael S. Weiss, University of Aberdeen
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14 - Conformal field theory in four and six dimensions
pp 405-420
- By Edward Witten, Institute for Advanced Study, Princeton
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Part II - The definition of conformal field theory
pp 421-422
- By Graeme Segal
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Foreword and postscript
pp 423-431
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The definition of CFT
pp 432-575
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References
pp 576-577
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Topology, Geometry and Quantum Field Theory

Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-ix

Participants
pp x-xii

Introduction
pp 1-2

Part I - Contributions
pp 3-4

1 - A variant of K-theory: K±
pp 5-17

2 - Two-vector bundles and forms of elliptic cohomology
pp 18-45

3 - Geometric realization of the Segal–Sugawara construction
pp 46-97

4 - Differential isomorphism and equivalence of algebraic varieties
pp 98-126

5 - A polarized view of string topology
pp 127-154

6 - Random matrices and Calabi–Yau geometry
pp 155-172

7 - A survey of the topological properties of symplectomorphism groups
pp 173-193

8 - K-theory from a physical perspective
pp 194-234

9 - Heisenberg groups and algebraic topology
pp 235-246

10 - What is an elliptic object?
pp 247-343

11 - Open and closed string field theory interpreted in classical algebraic topology
pp 344-357

12 - K-theory of the moduli space of bundles on a surface and deformations of the Verlinde algebra
pp 358-378

13 - Cohomology of the stable mapping class group
pp 379-404

14 - Conformal field theory in four and six dimensions
pp 405-420

Part II - The definition of conformal field theory
pp 421-422

Foreword and postscript
pp 423-431

The definition of CFT
pp 432-575

References
pp 576-577

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Topology, Geometry and Quantum Field Theory

Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal

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