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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010292992 | QA641 M36 2010 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Author Notes
Oscar Garcia-Prada is with the Instituto de Ciencias Matematicas, Consejo Superior de Investigaciones Cientificas, Madrid, Spain. Jean Pierre Bourguignon is with the Institut des Hautes Etudes Scientifiques, France. Simon Salamon is with the Dipartimento di Matematica, Politecnico de Torino, Italy.
Table of Contents
Preface |
1 Geometry and Physics - a personal viewNigel Hitchin |
2 The Mathematical Work of Nigel HitchinMichael Atiyah |
3 The Einstein-Maxwell Equations, Extremal Kähler Metrics, and Seiberg-Witten TheoryClaude LeBrun |
4 The Nahm Transform for CaloronsBenoit Charbonneau and Jacques Hurtubise |
5 Nahm's Equations and Free Boundary ProblemsS. K. Donaldson |
6 Some Aspects of the Theory of Higgs PairsS. Ramanan |
7 Mirror Symmetry, Hitchin's Equations, and Langlands DualityEdward Witten |
8 Higgs Bundles and Geometric Structures on SurfacesWilliam M. Goldman |
9 The Locality of Holomorphic Bundles, and Locality in Quantum Field TheoryGraeme Segal |
10 Toeplitz Operators and Hitchin's Projectively Flat ConnectionJørgen Ellegaard Andersen |
11 Towards a Nonlinear Schwarz's ListPhilip Boalch |
12 An Introduction to Bundle GerbesMichael K. Murray |
13 Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part IF. Reese Harvey and H. Blaine Lawson, Jr. |
14 Skyrmions and NucleiNicholas S. Manton |
15 Mirror Symmetry of Fourier-Mukai Transformation for Elliptic Calabi-Yau ManifoldsNaichung Conan Leung and Shing Tung Yau |
16 S-duality in Hyperkähler Hodge TheoryTamás Hausel |
17 Nonembedding and Nonextension Results in Special HolonomyRobert L. Bryant |
18 Branes on Poisson VarietiesMarco Gualtieri |
19 Consistent Orientation of Moduli SpacesDaniel S. Freed and Michael J. Hopkins and Constantin Teleman |
Index |