Encyclopedia of Mathematical Physics, Volume 1-5: Five-Volume Set

Description

The Encyclopedia of Mathematical Physics provides a complete resource for researchers,students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information.Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, FranceGregory L. Naber, Drexel University, Philadelphia, PA, USATsou Sheung Tsun, University of Oxford, UKAlso available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit www.info.sciencedirect.com. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise* Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking. Cover Page......Page 1 Title Page......Page 3 ISBN 0125126603......Page 4 EDITORS AND EDITORIAL ADVISORY BOARD......Page 5 Foreword......Page 7 Preface......Page 9 Usage Guide......Page 11 Contributors......Page 13 Condensed Matter and Optics......Page 30 Introductory Article: Classical Mechanics, G. Gallavotti......Page 50 Introductory Article: Differential Geometry, S. Paycha......Page 82 Introductory Article: Electromagnetism, N.M.J. Woodhouse......Page 89 Introductory Article: Equilibrium Statistical Mechanics, G. Gallavotti......Page 100 Introductory Article: Functional Analysis, S. Paycha......Page 137 Introductory Article: Minkowski Spacetime and Special Relativity, G.L. Naber......Page 145 Introductory Article: Quantum Mechanics, G.F. dell'Antonio......Page 158 Introductory Article: Topology, Tsou Sheung Tsun......Page 180 Boundary Control Method and Inverse Problems of Wave Propagation, M.I. Belishev......Page 389 Constrained Systems, M. Henneaux......Page 660 Cotangent Bundle Reduction, J.-P. Ortega and T.S. Ratiu......Page 707 Gravitational N-Body Problem (Classical), D.C. Heggie......Page 1303 Hamiltonian Fluid Dynamics, P.J. Morrison......Page 1321 Hamiltonian Systems: Obstructions to Integrability, M. Irigoyen......Page 1352 Infinite-Dimensional Hamiltonian Systems, R. Schmid......Page 1494 Inverse Problem in Classical Mechanics, R.G. Novikov......Page 1613 KAM Theory and Celestial Mechanics, L. Chierchia......Page 1646 Peakons, D.D. Holm......Page 2114 Poisson Reduction, J.-P. Ortega and T.S. Ratiu......Page 2181 Stability Problems in Celestial Mechanics, A. Celletti......Page 2795 Symmetry and Symplectic Reduction, J.-P. Ortega and T.S. Ratiu......Page 2965 Topological Quantum Field Theory: Overview, J.M.F. Labastida and C. Lozano......Page 3053 AdS/CFT Correspondence, C.P. Herzog and I.R. Klebanov......Page 223 Axiomatic Approach to Topological Quantum Field Theory, C. Blanchet and V. Turaev......Page 281 BF Theories, M. Blau......Page 306 Boundary Conformal Field Theory, J. Cardy......Page 382 Chern-Simons Models: Rigorous Results, A.N. Sengupta......Page 545 Donaldson-Witten Theory, M. Mariño......Page 838 Duality in Topological Quantum Field Theory, C. Lozano and J.M.F. Labastida......Page 846 Finite-Type Invariants, D. Bar-Natan......Page 1068 Four-Manifold Invariants and Physics, C. Nash......Page 1114 Gauge Theoretic Invariants of 4-Manifolds, S. Bauer......Page 1185 h-Pseudodifferential Operators and Applications, B. Helffer......Page 1429 The Jones Polynomial......Page 1636 Knot Theory and Physics, L.H. Kauffman......Page 1677 Kontsevich Integral, S. Chmutov and S. Duzhin......Page 1688 Large-N and Topological Strings, R. Gopakumar......Page 1720 Mathai-Quillen Formalism, Siye Wu......Page 1847 Mathematical Knot Theory, L. Boi......Page 1856 Operator Product Expansion in Quantum Field Theory, H. Osborn......Page 2073 Schwarz-Type Topological Quantum Field Theory, R.K. Kaul, T.R. Govindarajan and P. Ramadevi......Page 2596 Solitons and Other Extended Field Configurations, R.S. Ward......Page 2704 Topological Defects and Their Homotopy Classification, T.W.B. Kibble......Page 3032 Topological Gravity, Two-Dimensional, T. Eguchi......Page 3039 Topological Knot Theory and Macroscopic Physics, L. Boi......Page 3046 Topological Sigma Models, D. Birmingham......Page 3065 Two-Dimensional Conformal Field Theory and Vertex Operator Algebras, M.R. Gaberdiel......Page 3092 WDVV Equations and Frobenius Manifolds, B. Dubrovin......Page 3213 Bose-Einstein Condensates, F. Dalfovo, L.P. Pitaevskii and S. Stringari......Page 361 Falicov-Kimball Model, Ch Gruber and D. Ueltschi......Page 1011 Fractional Quantum Hall Effect, J.K. Jain......Page 1130 High Tc Superconductor Theory, S.-C. Zhang......Page 1373 Hubbard Model, H. Tasaki......Page 1440 Liquid Crystals, O.D. Lavrentovich......Page 1777 Negative Refraction and Subdiffraction Imaging, S. O'Brien and S.A. Ramakrishna......Page 1940 Nuclear Magnetic Resonance, P.T. Callaghan......Page 2049 Optical Caustics, A. Joets......Page 2077 Quantum Phase Transitions, S. Sachdev......Page 2391 Quasiperiodic Systems, P. Kramer......Page 2410 Renormalization: Statistical Mechanics and Condensed Matter, M. Salmhofer......Page 2509 Short-Range Spin Glasses: The Metastate Approach, C.M. Newman and D.L. Stein......Page 2672 Fluid Dynamics......Page 31 Cellular Automata, M. Bruschi and F. Musso......Page 504 Lagrangian Dispersion (Passive Scalar), G. Falkovich......Page 1712 Mean Field Spin Glasses and Neural Networks, A. Bovier......Page 1864 Percolation Theory, V. Beffara and V. Sidoravicius......Page 2123 Random Matrix Theory in Physics, T. Guhr......Page 2440 Random Walks in Random Environments, L.V. Bogachev......Page 2455 Spin Glasses, F. Guerra......Page 2757 Stochastic Loewner Evolutions, G.F. Lawler......Page 2855 Two-Dimensional Ising Model, B.M. McCoy......Page 3097 Wulff Droplets, S. Shlosman......Page 3237 Averaging Methods, A.I. Neishtadt......Page 275 Bifurcations of Periodic Orbits, J.-P. Françoise......Page 334 Billiards in Bounded Convex Domains, S. Tabachnikov......Page 345 Central Manifolds, Normal Forms, P. Bonckaert......Page 516 Chaos and Attractors, R. Gilmore......Page 526 Diagrammatic Techniques in Perturbation Theory, G. Gentile......Page 782 Dissipative Dynamical Systems of Infinite Dimension, M. Efendiev, S. Zelik and A. Miranville......Page 829 Dynamical Systems and Thermodynamics, A. Carati, L. Galgani and A. Giorgilli......Page 853 Dynamical Systems in Mathematical Physics: An Illustration from Water Waves, O. Goubet......Page 861 Entropy and Quantitative Transversality, G. Comte......Page 965 Ergodic Theory, M. Yuri......Page 978 Fractal Dimensions in Dynamics, V. Županovic and D. Žubrinic......Page 1122 Generic Properties of Dynamical Systems, C. Bonatti......Page 1222 Hamiltonian Systems: Stability and Instability Theory, P. Bernard......Page 1359 Holomorphic Dynamics, M. Lyubich......Page 1380 Homeomorphisms and Diffeomorphisms of the Circle, A. Zumpano and A. Sarmiento......Page 1393 Homoclinic Phenomena, S.E. Newhouse......Page 1400 Hyperbolic Billiards, Maciej P. Wojtkowski......Page 1444 Hyperbolic Dynamical Systems, B. Hasselblatt......Page 1449 Isomonodromic Deformations, V.P. Kostov......Page 1630 Lyapunov Exponents and Strange Attractors, M. Viana......Page 1806 Multiscale Approaches, A. Lesne......Page 1922 Normal Forms and Semiclassical Approximation, D. Bambusi......Page 2035 Point-Vortex Dynamics, S. Boatto and D. Crowdy......Page 2168 Polygonal Billiards, S. Tabachnikov......Page 2186 Random Dynamical Systems, V. Araújo......Page 2432 Regularization for Dynamical ζ-Functions, V. Baladi......Page 2488 Resonances, N. Burq......Page 2517 Riemann-Hilbert Problem, V.P. Kostov......Page 2538 Semiclassical Spectra and Closed Orbits, Y.Colin de Verdière......Page 2614 Separatrix Splitting, D. Treschev......Page 2637 Stability Theory and KAM, G. Gentile......Page 2801 Symmetry and Symmetry Breaking in Dynamical Systems, I. Melbourne......Page 2959 Synchronization of Chaos, M.A. Aziz-Alaoui......Page 2988 Universality and Renormalization, M. Lyubich......Page 3118 Weakly Coupled Oscillators, E.M. Izhikevich and Y. Kuramoto......Page 3223 Bethe Ansatz, M.T. Batchelor......Page 302 Cluster Expansion, R. Kotecký......Page 580 Dimer Problems, R. Kenyon......Page 789 Eight Vertex and Hard Hexagon Models, P.A. Pearce......Page 883 Fermionic Systems, V. Mastropietro......Page 1028 Finitely Correlated States, R.F. Werner......Page 1062 Holonomic Quantum Fields, J. Palmer......Page 1388 Large Deviations in Equilibrium Statistical Mechanics, S. Shlosman......Page 1718 Metastable States, S. Shlosman......Page 1874 Phase Transitions in Continuous Systems, E. Presutti......Page 2155 Pirogov-Sinai Theory, R. Kotecký......Page 2162 Quantum Central-Limit Theorems, A.F. Verbeure......Page 2232 Quantum Spin Systems, B. Nachtergaele......Page 2397 Quantum Statistical Mechanics: Overview, L. Triolo......Page 2404 Reflection Positivity and Phase Transitions, Y. Kondratiev and Y. Kozitsky......Page 2478 Statistical Mechanics and Combinatorial Problems, R. Zecchina......Page 2825 Statistical Mechanics of Interfaces, S. Miracle-Solé......Page 2830 Superfluids, D. Einzel......Page 2890 Toeplitz Determinants and Statistical Mechanics, E.L. Basor......Page 3019 Bifurcations in Fluid Dynamics, G. Schneider......Page 330 Breaking Water Waves, A. Constantin......Page 432 Capillary Surfaces, R. Finn......Page 480 Cauchy Problem for Burgers-Type Equations, G.M. Henkin......Page 495 Compressible Flows: Mathematical Theory, G.-Q. Chen......Page 644 Fluid Mechanics: Numerical Methods, J.-L. Guermond......Page 1093 Geophysical Dynamics, M.B. Ziane......Page 1262 Incompressible Euler Equations: Mathematical Theory, D. Chae......Page 1467 Interfaces and Multicomponent Fluids, J. Kim and J. Lowengrub......Page 1592 Intermittency in Turbulence, J. Jiménez......Page 1601 Inviscid Flows, R. Robert......Page 1617 Korteweg-de Vries Equation and Other Modulation Equations, G. Schneider and E. Wayne......Page 1696 Magnetohydrodynamics, C. Le Bris......Page 1832 Newtonian Fluids and Thermohydraulics, G. Labrosse and G. Kasperski......Page 1949 Non-Newtonian Fluids, C. Guillopé......Page 2017 Partial Differential Equations: Some Examples, R. Temam......Page 2108 Stability of Flows, S. Friedlander......Page 2776 Turbulence Theories, R.M.S. Rosa......Page 3070 Variational Methods in Turbulence, F.H. Busse......Page 3126 Viscous Incompressible Fluids: Mathematical Theory, J.G. Heywood......Page 3144 Vortex Dynamics, M. Nitsche......Page 3165 Wavelets: Application to Turbulence, M. Farge and K. Schneider......Page 3183 Integrable Systems......Page 32 Abelian and Nonabelian Gauge Theories Using Differential Forms, A.C. Hirshfeld......Page 190 Abelian Higgs Vortices, J.M. Speight......Page 200 Aharonov-Bohm Effect, M. Socolovsky......Page 240 Anomalies, S.L. Adler......Page 254 BRST Quantization, M. Henneaux......Page 435 Dirac Fields in Gravitation and Nonabelian Gauge Theory, J.A. Smoller......Page 795 Effective Field Theories, G. Ecker......Page 867 Electric-Magnetic Duality, Tsou Sheung Tsun......Page 929 Electroweak Theory, K. Konishi......Page 937 Exact Renormalization Group, P.K. Mitter......Page 1000 Gauge Theories from Strings, P. Di Vecchia......Page 1191 Gauge Theory: Mathematical Applications, S.K. Donaldson......Page 1196 Instantons: Topological Aspects, M. Jardim......Page 1501 Lattice Gauge Theory, A. Di Giacomo......Page 1732 Measure on Loop Spaces, H. Airault......Page 1870 Noncommutative Geometry and the Standard Model, T. Schücker......Page 1966 Nonperturbative and Topological Aspects of Gauge Theory, R.W. Jackiw......Page 2025 Perturbative Renormalization Theory and BRST, K. Fredenhagen and M. Dütsch......Page 2143 Quantum Chromodynamics, G. Sterman......Page 2246 Quantum Electrodynamics and Its Precision Tests, S. Laporta and E. Remiddi......Page 2270 Renormalization: General Theory, J.C. Collins......Page 2501 Seiberg-Witten Theory, Siye Wu......Page 2605 Standard Model of Particle Physics, G. Altarelli......Page 2807 Supergravity, K.S. Stelle......Page 2897 Supersymmetric Particle Models, S. Pokorski......Page 2915 Symmetry Breaking in Field Theory, T.W.B. Kibble......Page 2973 Twistor Theory: Some Applications, L. Mason......Page 3078 Two-Dimensional Models, B. Schroer......Page 3103 General Relativity: Overview, R. Penrose......Page 1215 Asymptotic Structure and Conformal Infinity, J. Frauendiener......Page 270 Black Hole Mechanics, A. Ashtekar......Page 349 Boundaries for Spacetimes, S.G. Harris......Page 375 Brane Worlds, R. Maartens......Page 416 Canonical General Relativity, C. Rovelli......Page 461 Critical Phenomena in Gravitational Collapse, C. Gundlach......Page 717 Computational Methods in General Relativity: The Theory, M.W. Choptuik......Page 653 Cosmology: Mathematical Aspects, G.F.R. Ellis......Page 702 Einstein-Cartan Theory, A. Trautman......Page 917 Einstein’s Equations with Matter, Y. Choquet-Bruhat......Page 923 Einstein Equations: Exact Solutions, Jií Bicák......Page 893 Einstein Equations: Initial Value Formulation, J. Isenberg......Page 901 General Relativity: Experimental Tests, C.M. Will......Page 1209 Geometric Analysis and General Relativity, L. Andersson......Page 1230 Geometric Flows and the Penrose Inequality, H. Bray......Page 1238 Gravitational Lensing, J. Wambsganss......Page 1295 Gravitational Waves, G. González and J. Pullin......Page 1310 Hamiltonian Reduction of Einstein's Equations, A.E. Fischer and V. Moncrief......Page 1335 Minimal Submanifolds, T.H. Colding and W.P. Minicozzi II......Page 1877 Newtonian Limit of General Relativity, J. Ehlers......Page 1960 Quantum Field Theory in Curved Spacetime, B.S. Kay......Page 2304 Relativistic Wave Equations Including Higher Spin Fields, R. Illge and V. Wünsch......Page 2493 Shock Wave Refinement of the Friedman-Robertson-Walker Metric, B. Temple and J.A. Smoller......Page 2661 Spacetime Topology, Causal Structure and Singularities, R. Penrose......Page 2719 Spinors and Spin Coefficients, K.P. Tod......Page 2769 Stability of Minkowski Space, S. Klainerman......Page 2789 Stationary Black Holes, R. Beig and P.T. Chrusciel......Page 2813 Twistors, K.P. Tod......Page 3086 Integrable Systems: Overview, Francesco Calogero......Page 1563 Affine Quantum Groups, G.W. Delius and N. MacKay......Page 232 Bäcklund Transformations, D. Levi......Page 290 Bi-Hamiltonian Methods in Soliton Theory, M. Pedroni......Page 339 Boundary-Value Problems for Integrable Equations, B. Pelloni......Page 395 Calogero-Moser-Sutherland Systems of Nonrelativistic and Relativistic Type, S.N.M. Ruijsenaars......Page 452 ∂-Approach to Integrable Systems, P.G. Grinevich......Page 762 Eigenfunctions of Quantum Completely Integrable Systems, J.A. Toth......Page 876 Functional Equations and Integrable Systems, H.W. Braden......Page 1153 Integrability and Quantum Field Theory, T.J. Hollowood......Page 1507 Integrable Discrete Systems, O. Ragnisco......Page 1516 Integrable Systems and Algebraic Geometry, E. Previato......Page 1522 Integrable Systems and Discrete Geometry, A. Doliwa and P.M. Santini......Page 1535 Integrable Systems and Recursion Operators on Symplectic and Jacobi Manifolds, R. Caseiro and J.M. Nunes da Costa......Page 1544 Integrable Systems and the Inverse Scattering Method, A.S. Fokas......Page 1550 Integrable Systems in Random Matrix Theory, C.A. Tracy and H. Widom......Page 1559 Isochronous Systems, Francesco Calogero......Page 1623 Nonlinear Schrödinger Equations, M.J. Ablowitz and B. Prinari......Page 2009 Painlevé Equations, N. Joshi......Page 2103 Quantum Calogero-Moser Systems, R. Sasaki......Page 2225 Riemann-Hilbert Methods in Integrable Systems, D. Shepelsky......Page 2531 Sine-Gordon Equation, S.N.M. Ruijsenaars......Page 2678 Solitons and Kac-Moody Lie Algebras, E. Date......Page 2696 Toda Lattices, Y.B. Suris......Page 3010 Yang-Baxter Equations, J.H.H. Perk and H. Au-Yang......Page 3240 Quantum Field Theory......Page 33 Nonequilibrium Statistical Mechanics (Stationary): Overview, G. Gallavotti......Page 1987 Adiabatic Piston, Ch Gruber and A. Lesne......Page 209 Boltzmann Equation (Classical and Quantum), M. Pulvirenti......Page 355 Glassy Disordered Systems: Dynamical Evolution, S. Franz......Page 1281 Fourier Law, F. Bonetto and L. Rey-Bellet......Page 1102 Interacting Particle Systems and Hydrodynamic Equations, C. Landim......Page 1580 Interacting Stochastic Particle Systems, H. Spohn......Page 1587 Kinetic Equations, C. Bardos......Page 1657 Macroscopic Fluctuations and Thermodynamic Functionals, G. Jona-Lasinio......Page 1814 Nonequilibrium Statistical Mechanics: Dynamical Systems Approach, P. Buttà and C. Marchioro......Page 1997 Nonequilibrium Statistical Mechanics: Interaction between Theory and Numerical Simulations, R. Livi......Page 2001 Phase Transition Dynamics, A. Onuki......Page 2149 Stochastic Resonance, S. Herrmann and P. Imkeller......Page 2861 Quantum Field Theory: A Brief Introduction, L.H. Ryder......Page 2314 Algebraic Approach to Quantum Field Theory, R. Brunetti and K. Fredenhagen......Page 247 Axiomatic Quantum Field Theory, B. Kuckert......Page 283 Batalin-Vilkovisky Quantization, A.C. Hirshfeld......Page 296 Bosons and Fermions in External Fields, E. Langmann......Page 367 Constructive Quantum Field Theory, G. Gallavotti......Page 666 Current Algebra, G.A. Goldin......Page 723 Dirac Operator and Dirac Field, S.N.M. Ruijsenaars......Page 802 Dispersion Relations, J. Bros......Page 815 Euclidean Field Theory, F. Guerra......Page 984 Gerbes in Quantum Field Theory, J. Mickelsson......Page 1267 Hopf Algebra Structure of Renormalizable Quantum Field Theory, D. Kreimer......Page 1406 Indefinite Metric, H. Gottschalk......Page 1474 Quantum Fields with Indefinite Metric: Non-Trivial Models, S. Albeverio and H. Gottschalk......Page 2318 Perturbation Theory and Its Techniques, R.J. Szabo......Page 2130 Quantum Fields with Topological Defects, M. Blasone, G. Vitiello and P. Jizba......Page 2323 Scattering, Asymptotic Completeness and Bound States, D. Iagolnitzer and J. Magnen......Page 2577 Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools, D. Buchholz and S.J. Summers......Page 2558 Scattering in Relativistic Quantum Field Theory: The Analytic Program, J. Bros......Page 2567 Symmetries and Conservation Laws, L.H. Ryder......Page 2941 The Jones Polynomial, V.F.R. Jones......Page 2954 Symmetries in Quantum Field Theory of Lower Spacetime Dimensions, J. Mund and K.-H. Rehren......Page 2947 Thermal Quantum Field Theory, C.D. Jäkel......Page 3002 Tomita-Takesaki Modular Theory, S.J. Summers......Page 3026 Algebraic Techniques......Page 34 Knot Invariants and Quantum Gravity, R. Gambini and J. Pullin......Page 1672 Loop Quantum Gravity, C. Rovelli......Page 1796 Quantum Cosmology, M. Bojowald......Page 2255 Quantum Dynamics in Loop Quantum Gravity, H. Sahlmann......Page 2267 Quantum Geometry and Its Applications, A. Ashtekar and J. Lewandowski......Page 2332 Spin Foams, A. Perez......Page 2747 Wheeler-De Witt Theory, J. Maharana......Page 3228 Capacities Enhanced by Entanglement, P. Hayden......Page 467 Capacity for Quantum Information, D. Kretschmann......Page 473 Channels in Quantum Information Theory, M. Keyl......Page 521 Entanglement, R.F. Werner......Page 956 Entanglement Measures, R.F. Werner......Page 961 Finite Weyl Systems, D.-M. Schlingemann......Page 1056 Optimal Cloning of Quantum States, M. Keyl......Page 2085 Quantum Channels: Classical Capacity, A.S. Holevo......Page 2244 Quantum Entropy, D. Petz......Page 2279 Quantum Error Correction and Fault Tolerance, D. Gottesman......Page 2298 Source Coding in Quantum Information Theory, N. Datta and T.C. Dorlas......Page 2711 Arithmetic Quantum Chaos, J. Marklof......Page 261 Coherent States, S.T. Ali......Page 586 Geometric Phases, P. Lévay......Page 1256 N-Particle Quantum Scattering, D.R. Yafaev......Page 2042 Quantum Ergodicity and Mixing of Eigenfunctions, S. Zelditch......Page 2285 Quantum Mechanical Scattering Theory, D.R. Yafaev......Page 2353 Quantum Mechanics: Foundations, R. Penrose......Page 2362 Quantum Mechanics: Generalizations, P. Pearle and A. Valentini......Page 2367 Quantum Mechanics: Weak Measurements, L. Diósi......Page 2378 Quantum n-Body Problem, R.G. Littlejohn......Page 2385 Schrödinger Operators, V. Bach......Page 2589 Stability of Matter, J.P. Solovej......Page 2783 Stationary Phase Approximation, J.J. Duistermaat......Page 2819 Supersymmetric Quantum Mechanics, J.-W. van Holten......Page 2920 Brane Construction of Gauge Theories, S.L. Cacciatori......Page 409 Branes and Black Hole Statistical Mechanics, S.R. Das......Page 422 Calibrated Geometry and Special Lagrangian Submanifolds, D.D. Joyce......Page 447 Compactification of Superstring Theory, M.R. Douglas......Page 635 Derived Categories, E.R. Sharpe......Page 769 Fourier-Mukai Transform in String Theory, B. Andreas......Page 1107 Large-N Dualities, A. Grassi......Page 1726 Mirror Symmetry: A Geometric Survey, R.P. Thomas......Page 1896 Noncommutative Geometry from Strings, Chong-Sun Chu......Page 1972 Random Algebraic Geometry, Attractors and Flux Vacua, M.R. Douglas......Page 2425 Riemannian Holonomy Groups and Exceptional Holonomy, D.D. Joyce......Page 2543 String Field Theory, L. Rastelli......Page 2869 String Theory: Phenomenology, A.M. Uranga......Page 2878 String Topology: Homotopy and Geometric Perspectives, R.L. Cohen......Page 2886 Superstring Theories, C. Bachas and J. Troost......Page 2908 Braided and Modular Tensor Categories, V. Lyubashenko......Page 400 Clifford Algebras and Their Representations, A. Trautman......Page 567 Finite-Dimensional Algebras and Quivers, A. Savage......Page 1041 Finite Group Symmetry Breaking, G. Gaeta......Page 1050 Hopf Algebras and q-Deformation Quantum Groups, S. Majid......Page 1415 Operads, J. Stasheff......Page 2066 Low Dimensional Geometry......Page 35 Characteristic Classes, P.B. Gilkey, R. Ivanova and S. Nikcevic......Page 537 Cohomology Theories, U. Tillmann......Page 594 Equivariant Cohomology and the Cartan Model, E. Meinrenken......Page 970 Index Theorems, P.B. Gilkey, K. Kirsten, R. Ivanova and J.H. Park......Page 1480 Intersection Theory, A. Kresch......Page 1608 K-Theory, V. Mathai......Page 1703 Spectral Sequences, P. Selick......Page 2725 Knot Homologies, J. Rasmussen......Page 1665 Moduli Spaces: An Introduction, F. Kirwan......Page 1906 Quillen Determinant, S. Scott......Page 2417 Riemann Surfaces, K. Hulek......Page 2521 Several Complex Variables: Basic Geometric Theory, A. Huckleberry and T. Peternell......Page 2642 Several Complex Variables: Compact Manifolds, A. Huckleberry and T. Peternell......Page 2653 Einstein Manifolds, A.S. Dancer......Page 910 Lorentzian Geometry, P.E. Ehrlich and S.B. Kim......Page 1800 Pseudo-Riemannian Nilpotent Lie Groups, P.E. Parker......Page 2196 Singularity and Bifurcation Theory, J.-P. Françoise and C. Piquet......Page 2690 Supermanifolds, F.A. Rogers......Page 2903 Combinatorics: Overview, C. Krattenthaler......Page 602 Number Theory in Physics, M. Marcolli......Page 2057 C*-Algebras and their Classification, G.A. Elliott......Page 442 Free Probability Theory, D.-V. Voiculescu......Page 1145 Functional Integration in Quantum Physics, C. DeWitt-Morette......Page 1162 Leray-Schauder Theory and Mapping Degree, J. Mawhin......Page 1738 Ljusternik-Schnirelman Theory, J. Mawhin......Page 1785 Ordinary Special Functions, W. Van Assche......Page 2094 Positive Maps on C*-Algebras, F. Cipriani......Page 2190 Quantum Dynamical Semigroups, R. Alicki......Page 2261 Saddle Point Problems, M. Schechter......Page 2549 Spectral Theory of Linear Operators, M. Schechter......Page 2735 von Neumann Algebras: Introduction, Modular Theory, and Classification Theory, V.S. Sunder......Page 3154 von Neumann Algebras: Subfactor Theory, Y. Kawahigashi......Page 3160 Wavelets: Applications, M. Yamada......Page 3195 Wavelets: Mathematical Theory, K. Schneider and M. Farge......Page 3201 Classical Groups and Homogeneous Spaces, S. Gindikin......Page 549 Compact Groups and Their Representations, A. Kirillov and A. Kirillov, Jr.......Page 625 Lie Groups: General Theory, R. Gilmore......Page 1743 Lie Superalgebras and Their Representations, L. Frappat......Page 1762 Lie, Symplectic, and Poisson Groupoids and Their Lie Algebroids, C.-M. Marle......Page 1769 Finite-Type Invariants of 3-Manifolds, T.T.Q. Lê......Page 1076 Floer Homology, P.B. Kronheimer......Page 1084 Quantum 3-Manifold Invariants, C. Blanchet and V. Turaev......Page 2219 Singularities of the Ricci Flow, M. Anderson......Page 2686 Symplectic Geometry and Topology......Page 36 Noncommutative Tori, Yang-Mills, and String Theory, A. Konechny......Page 1981 Path Integrals in Noncommutative Geometry, R. Léandre......Page 2110 Quantum Group Differentials, Bundles and Gauge Theory, T. Brzezinski......Page 2338 Quantum Hall Effect, K. Hannabuss......Page 2346 Bifurcation Theory, M. Haragus and G. Iooss......Page 324 Elliptic Differential Equations: Linear Theory, C. Amrouche, M. Krbec, Š. Necasová and B. Lucquin-Desreux......Page 944 Evolution Equations: Linear and Nonlinear, J. Escher......Page 993 Ginzburg-Landau Equation, Y. Morita......Page 1275 Image Processing: Mathematics, G. Aubert and P. Kornprobst......Page 1458 Inequalities in Sobolev Spaces, M. Vaugon......Page 1489 Localization for Quasiperiodic Potentials, S. Jitomirskaya......Page 1790 Magnetic Resonance Imaging, C.L. Epstein and F.W. Wehrli......Page 1824 Semilinear Wave Equations, P. D'Ancona......Page 2620 Separation of Variables for Differential Equations, S. Rauch-Wojciechowski and K. Marciniak......Page 2628 Symmetric Hyperbolic Systems and Shock Waves, S. Kichenassamy......Page 2935 Wave Equations and Diffraction, M.E. Taylor......Page 3176 Deformation Quantization, A.C. Hirshfeld......Page 729 Deformation Quantization and Representation Theory, S. Waldmann......Page 737 Deformation Theory, M.J. Pflaum......Page 744 Deformations of the Poisson Bracket on a Symplectic Manifold, S. Gutt and S. Waldmann......Page 752 Fedosov Quantization, N. Neumaier......Page 1019 Feynman Path Integrals, S. Mazzucchi......Page 1035 Bicrossproduct Hopf Algebras and Noncommutative Spacetime, S. Majid......Page 314 Classical r-Matrices, Lie Bialgebras, and Poisson Lie Groups, M.A. Semenov-Tian-Shansky......Page 560 q-Special Functions, T.H. Koornwinder......Page 2207 Determinantal Random Fields, A. Soshnikov......Page 775 Growth Processes in Random Matrix Theory, K. Johansson......Page 1314 Malliavin Calculus, A.B. Cruzeiro......Page 1840 Random Partitions, A. Okounkov......Page 2449 Stochastic Differential Equations, F. Russo......Page 2838 Stochastic Hydrodynamics, B. Ferrario......Page 2846 Supersymmetry Methods in Random Matrix Theory, M.R. Zirnbauer......Page 2926 Symmetry Classes in Random Matrix Theory, M.R. Zirnbauer......Page 2979 Contact Manifolds, J.B. Etnyre......Page 680 Graded Poisson Algebras, A.S. Cattaneo, D. Fiorenza and R. Longoni......Page 1288 Hamiltonian Group Actions, L.C. Jeffrey......Page 1328 Multi-Hamiltonian Systems, F. Magri and M. Pedroni......Page 1916 Recursion Operators in Classical Mechanics, F. Magri and M. Pedroni......Page 2473 Variational Techniques......Page 37 Control Problems in Mathematical Physics, B. Piccoli......Page 685 Convex Analysis and Duality Methods, G. Bouchitté......Page 691 Free Interfaces and Free Discontinuities: Variational Problems, G. Buttazzo......Page 1139 Γ-Convergence and Homogenization, G. Dal Maso......Page 1177 Geometric Measure Theory, G. Alberti......Page 1248 Hamilton-Jacobi Equations and Dynamical Systems: Variational Aspects, A. Siconolfi......Page 1364 Minimax Principle in the Calculus of Variations, A. Abbondandolo......Page 1889 Optimal Transportation, Y. Brenier......Page 2089 Variational Techniques for Ginzburg-Landau Energies, S. Serfaty......Page 3130 Variational Techniques for Microstructures, G. Dolzmann......Page 3138 B......Page 38 C......Page 39 E......Page 40 G......Page 41 I......Page 42 M......Page 43 O......Page 44 Q......Page 45 S......Page 46 St......Page 47 INDEX......Page 48 A......Page 3250 B......Page 3252 C......Page 3255 D......Page 3262 E......Page 3266 F......Page 3270 G......Page 3274 H......Page 3278 I......Page 3281 J......Page 3284 K......Page 3285 L......Page 3286 M......Page 3290 N......Page 3294 O......Page 3296 P......Page 3298 Q......Page 3302 R......Page 3305 S......Page 3308 T......Page 3318 U......Page 3321 V......Page 3322 W......Page 3323 Z......Page 3324