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, hyperkahler geometry, Frobenius manifolds, Painleve 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.
Preface ; 1. Geometry and Physics - a personal view ; 2. The Mathematical Work of Nigel Hitchin ; 3. The Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory ; 4. The Nahm Transform for Calorons ; 5. Nahm's Equations and Free Boundary Problems ; 6. Some Aspects of the Theory of Higgs Pairs ; 7. Mirror Symmetry, Hitchin's Equations, and Langlands Duality ; 8. Higgs Bundles and Geometric Structures on Surfaces ; 9. The Locality of Holomorphic Bundles, and Locality in Quantum Field Theory ; 10. Toeplitz Operators and Hitchin's Projectively Flat Connection ; 11. Towards a Nonlinear Schwarz's List ; 12. An Introduction to Bundle Gerbes ; 13. Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I ; 14. Skyrmions and Nuclei ; 15. Mirror Symmetry of Fourier-Mukai Transformation for Elliptic Calabi-Yau Manifolds ; 16. S-duality in Hyperkahler Hodge Theory ; 17. Nonembedding and Nonextension Results in Special Holonomy ; 18. Branes on Poisson Varieties ; 19. Consistent Orientation of Moduli Spaces ; Index