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The Many Facets of Geometry
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The Many Facets of Geometry: A Tribute to Nigel Hitchin

Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon

Abstract

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 ... More

Keywords: Nigel Hitchin, spin geometry, istanton equations, monopole equations, twister theory, symplectic geometry, integrables systems, Higgs bundles, Einstein metrics, hyperkähler geometry

Bibliographic Information

Print publication date: 2010 Print ISBN-13: 9780199534920
Published to Oxford Scholarship Online: September 2010 DOI:10.1093/acprof:oso/9780199534920.001.0001

Authors

Affiliations are at time of print publication.

Oscar Garcia-Prada, editor
Instituto de Ciencias Matematicas, Consejo Superior de Investigaciones Cientificas, Madrid, Spain

Jean Pierre Bourguignon, editor
Institut des Hautes Etudes Scientifiques, France

Simon Salamon, editor
Dipartimento di Matematica, Politecnico de Torino, Italy

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Contents

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II Mathematical Work of Nigel Hitchin

Sir Michael Atiyah Dedicated to Nigel Hitchin

III The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

Claude LeBrun Dedicated to Nigel Hitchin on the occasion of his 60th birthday

IV The Nahm Transform for Calorons

Benoit Charbonneau and Jacques Hurtubise Dedicated to Nigel Hitchin on the occasion of his 60th birthday

V Nahm's Equations and Free‐Boundary Problems

Simon K. Donaldson Dedicated to Nigel Hitchin, with gratitude and affection

VI Some Aspects of the Theory of Higgs Pairs

S. Ramanan Dedicated to Nigel Hitchin

VII Mirror Symmetry, Hitchin's Equations, and Langlands Duality

Edward Witten Dedicated to Nigel Hitchin on the occasion of his 60th birthday

VIII Higgs Bundles and Geometric Structures on Surfaces

William M. Goldman Dedicated to Nigel Hitchin on the occasion of his 60th birthday

IX Locality of Holomorphic Bundles, and Locality in Quantum Field Theory

Graeme Segal Dedicated to Nigel Hitchin, on his 60th birthday

X Toeplitz Operators and Hitchin's Projectively Flat Connection

Jørgen Ellegaard Andersen Dedicated to Nigel Hitchin on the occasion of his 60th birthday

XI Towards a Non‐Linear Schwarz'S List

Philip Boalch Dedicated to Nigel Hitchin for his 60th birthday

XII An Introduction to Bundle Gerbes

Michael K. Murray Dedicated to Nigel Hitchin on the occasion of his 60th birthday

XIII Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I

F. Reese Harvey and H. Blaine Lawson, Jr. Dedicated to Nigel Hitchin in celebration of his 60th birthday

XIV Skyrmions and Nuclei

Nicholas S. Manton Dedicated to Nigel Hitchin on the occasion of his 60th birthday

XV Mirror Symmetry of Fourier—Mukai Transformation for Elliptic Calabi—Yau Manifolds

Naichung Conan Leung and Shing‐Tung Yau Dedicated to Nigel Hitchin on the occasion of his 60th birthday

XVI S‐Duality in HyperkäHler Hodge Theory

Tamás Hausel To Nigel Hitchin for his 60th birthday

XVII Non‐Embedding and Non‐Extension Results in Special Holonomy

Robert L. Bryant Dedicated to Nigel Hitchin with great admiration on the occasion of his 60th birthday

XVIII Branes on Poisson Varieties

Marco Gualtieri Dedicated to Nigel Hitchin on the occasion of his 60th birthday

XIX Consistent Orientation of Moduli Spaces

Daniel S. Freed, Michael J. Hopkins, and Constantin Teleman For Nigel, with admiration

End Matter