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John Harnad is Director of the Mathematical Physics Laboratory at the Centre de Recherches Mathématiques, and Professor of Mathematics at Concordia University in Montréal. Over his career he has made numerous contributions to a variety of fields of mathematical physics, including: gauge field theory, integrable systems, random matrices, isomonodromic deformations and generating functions for graphical enumeration. He was the recipient of the 2006 Canadian Association of Physicists Prize in Theoretical and Mathematical Physics.
Preface
List of symbols
1. Examples
2. KP flows and the Sato-Segal-Wilson Grassmannian
3. The KP hierarchy and its standard reductions
4. Infinite dimensional Grassmannians
5. Fermionic representation of tau functions and Baker functions
6. Finite dimensional reductions of the infinite Grassmannian and their associated tau functions
7. Other related integrable hierarchies
8. Convolution symmetries
9. Isomonodromic deformations
10. Integrable integral operators and dual isomonodromic deformations
11. Random matrix models I. Partition functions and correlators
12. Random matrix models II. Level spacings
13. Generating functions for characters, intersection indices and Brézin-Hikami matrix models
14. Generating functions for weighted Hurwitz numbers: enumeration of branched coverings
Appendix A. Integer partitions
Appendix B. Determinantal and Pfaffian identities
Appendix C. Grassmann manifolds and flag manifolds
Appendix D. Symmetric functions
Appendix E. Finite dimensional fermions: Clifford and Grassmann algebras, spinors, isotropic Grassmannians
Appendix F. Riemann surfaces, holomorphic differentials and theta functions
Appendix G. Orthogonal polynomials
Appendix H. Solutions of selected exercises
References
Alphabetical Index.
