Synopses & Reviews
Few people have proved more influential in the field of differential and algebraic geometry, and in showing how this links with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made fundamental contributions in areas as diverse as: spin geometry, instanton and monopole equations, twistor theory, symplectic geometry of moduli spaces, integrables systems, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, special Lagrangian geometry and mirror symmetry, theory of grebes, and many more.
He was previously Rouse Ball Professor of Mathematics at Cambridge University, as well as Professor of Mathematics at the University of Warwick, is a Fellow of the Royal Society and has been the President of the London Mathematical Society.
The chapters in this fascinating volume, written by some of the greats in their fields (including four Fields Medalists), show how Hitchin's ideas have impacted on a wide variety of subjects. The book grew out of the Geometry Conference in Honour of Nigel Hitchin, held in Madrid, with some additional contributions, and should be required reading for anyone seeking insights into the overlap between geometry and physics.
Table of Contents
1. Geometry and Physics - a personal view, Nigel Hitchin
2. The Mathematical Work of Nigel Hitchin, Michael Atiyah
3. The Einstein-Maxwell Equations, Extremal Kähler Metrics, and Seiberg-Witten Theory, Claude LeBrun
4. The Nahm Transform for Calorons, Benoit Charbonneau and Jacques Hurtubise
5. Nahm's Equations and Free Boundary Problems, S. K. Donaldson
6. Some Aspects of the Theory of Higgs Pairs, S. Ramanan
7. Mirror Symmetry, Hitchin's Equations, and Langlands Duality, Edward Witten
8. Higgs Bundles and Geometric Structures on Surfaces, William M. Goldman
9. The Locality of Holomorphic Bundles, and Locality in Quantum Field Theory, Graeme Segal
10. Toeplitz Operators and Hitchin's Projectively Flat Connection, Jørgen Ellegaard Andersen
11. Towards a Nonlinear Schwarz's List, Philip Boalch
12. An Introduction to Bundle Gerbes, Michael K. Murray
13. Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I, F. Reese Harvey and H. Blaine Lawson, Jr.
14. Skyrmions and Nuclei, Nicholas S. Manton
15. Mirror Symmetry of Fourier-Mukai Transformation for Elliptic Calabi-Yau Manifolds, Naichung Conan Leung and Shing Tung Yau
16. S-duality in Hyperkähler Hodge Theory, Tamás Hausel
17. Nonembedding and Nonextension Results in Special Holonomy, Robert L. Bryant
18. Branes on Poisson Varieties, Marco Gualtieri
19. Consistent Orientation of Moduli Spaces, Daniel S. Freed, Michael J. Hopkins and Constantin Teleman