The many facets of geometry : a tribute to Nigel Hitchin / edited by Oscar Garcia-Prada, Jean Pierre Bourguignon, Simon Salamon.

Format:

Book

Contributor:

Hitchin, N. J. (Nigel J.), 1946-

García-Prada, O. (Oscar), 1960-

Bourguignon, J.-P. (Jean-Pierre), 1947-

Salamon, Simon.

Series:

Oxford science publications.

Oxford science publications

Language:

English

Subjects (All):

Geometry, Differential.

Geometry, Algebraic.

Mathematical physics.

Physical Description:

1 online resource (453 p.)

Place of Publication:

New York : Oxford University Press, 2010.

Language Note:

English

Summary:

This title celebrates the academic career of Professor Nigel Hitchin - one of the most influential figures in the field of differential and algebraic geometry.

Contents:

CONTENTS; PREFACE; LIST OF EDITORS AND CONTRIBUTORS; 1 Geometry and physics: a personal view; 2 Mathematical work of Nigel Hitchin; 3 The Einstein-Maxwell equations, extremal Kähler metrics, and Seiberg-Witten theory; 4 The Nahm transform for calorons; 4.1 Introduction; 4.2 The work of Nye and Singer; 4.2.1 Two types of invariant self-dual gauge fields on R4; 4.2.2 The Nahm transform; 4.2.3 Involutivity of the transforms; 4.3 Twistor transform for calorons/Kac-Moody monopoles; 4.3.1 Upstairs: twistor transform for calorons; 4.3.2 Downstairs: caloron as a Kac-Moody monopole

5.4.2 Comparison with the free-boundary literature5.4.3 Degenerate case; 5.5 Relation with Nahm's equations; 6 Some aspects of the theory of Higgs pairs; 6.1 Moduli of vector bundles; 6.2 Hecke correspondence; 6.3 Moduli of Higgs pairs; 6.4 Higgs pairs and the fundamental group; 6.5 Non-abelian Hodge theory; 6.6 Hitchin morphism; 6.7 Quantization; 6.8 Hecke transformation and Hitchin discriminant; 6.9 Hitchin component; 6.10 Reductive groups and principal bundles; 6.11 Reductive groups and Higgs pairs; 6.12 Real forms; 7 Mirror symmetry, Hitchin's equations, and Langlands duality

7.1 A-model and B-model7.2 Mirror symmetry and Hitchin's equations; 7.3 Hitchin fibration; 7.3.1 A few hints; 7.4 Ramification; 7.5 Wild ramification; 7.6 Four-dimensional gauge theory and stacks; 7.6.1 Stacks; 8 Higgs bundles and geometric structures on surfaces; 8.1 Introduction; 8.2 Representations of the fundamental group; 8.2.1 Closed surface groups; 8.2.2 Representation variety; 8.2.3 Symmetries; 8.2.4 Deformation space; 8.3 Abelian groups and rank 1 Higgs bundles; 8.3.1 Symplectic vector spaces; 8.3.2 Multiplicative characters: G = C*; 8.3.3 Jacobi variety of a Riemann surface

8.4 Stable vector bundles and Higgs bundles8.5 Hyperbolic geometry: G = PSL(2, R); 8.5.1 Geometric structures; 8.5.2 Relation to the fundamental group; 8.5.3 Examples of hyperbolic structures; 8.6 Moduli of hyperbolic structures and representations; 8.6.1 Deformation spaces of geometric structures; 8.6.2 Fuchsian components of Hom(π, G)/G; 8.6.3 Characteristic classes and maximal representations; 8.6.4 Quasi-Fuchsian representations: G = PSL(2, C); 8.6.5 Teichmüller space: marked conformal structures; 8.6.6 Holomorphic vector bundles and uniformization; 8.7 Rank 2 Higgs bundles

8.7.1 Harmonic metrics

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-156757-4

1-282-76814-X

9786612768149

OCLC:

922970114