Encyclopedia of mathematical physics

Foreword
......Page 4
Preface
......Page 6
Usage Guide
......Page 8
Contributors
......Page 10
Condensed Matter and Optics......Page 27
Introductory Article: Classical Mechanics, G. Gallavotti......Page 47
Introductory Article: Differential Geometry, S. Paycha......Page 79
Introductory Article: Electromagnetism, N.M.J. Woodhouse......Page 86
Introductory Article: Equilibrium Statistical Mechanics, G. Gallavotti......Page 97
Introductory Article: Functional Analysis, S. Paycha......Page 134
Introductory Article: Minkowski Spacetime and Special Relativity, G.L. Naber......Page 142
Introductory Article: Quantum Mechanics, G.F. dell\'Antonio......Page 155
Introductory Article: Topology, Tsou Sheung Tsun......Page 177
Boundary Control Method and Inverse Problems of Wave Propagation, M.I. Belishev......Page 386
Constrained Systems, M. Henneaux......Page 657
Cotangent Bundle Reduction, J.-P. Ortega and T.S. Ratiu......Page 704
Gravitational N-Body Problem (Classical), D.C. Heggie......Page 1300
Hamiltonian Fluid Dynamics, P.J. Morrison......Page 1318
Hamiltonian Systems: Obstructions to Integrability, M. Irigoyen......Page 1349
Infinite-Dimensional Hamiltonian Systems, R. Schmid......Page 1491
Inverse Problem in Classical Mechanics, R.G. Novikov......Page 1610
KAM Theory and Celestial Mechanics, L. Chierchia......Page 1643
Peakons, D.D. Holm......Page 2111
Poisson Reduction, J.-P. Ortega and T.S. Ratiu......Page 2178
Stability Problems in Celestial Mechanics, A. Celletti......Page 2792
Symmetry and Symplectic Reduction, J.-P. Ortega and T.S. Ratiu......Page 2963
Topological Quantum Field Theory: Overview, J.M.F. Labastida and C. Lozano......Page 3051
AdS/CFT Correspondence, C.P. Herzog and I.R. Klebanov......Page 220
Axiomatic Approach to Topological Quantum Field Theory, C. Blanchet and V. Turaev......Page 278
BF Theories, M. Blau......Page 303
Boundary Conformal Field Theory, J. Cardy......Page 379
Chern-Simons Models: Rigorous Results, A.N. Sengupta......Page 542
Donaldson-Witten Theory, M. Mariño......Page 835
Duality in Topological Quantum Field Theory, C. Lozano and J.M.F. Labastida......Page 843
Finite-Type Invariants, D. Bar-Natan......Page 1065
Four-Manifold Invariants and Physics, C. Nash......Page 1111
Gauge Theoretic Invariants of 4-Manifolds, S. Bauer......Page 1182
h-Pseudodifferential Operators and Applications, B. Helffer......Page 1426
The Jones Polynomial......Page 1633
Knot Theory and Physics, L.H. Kauffman......Page 1674
Kontsevich Integral, S. Chmutov and S. Duzhin......Page 1685
Large-N and Topological Strings, R. Gopakumar......Page 1717
Mathai-Quillen Formalism, Siye Wu......Page 1844
Mathematical Knot Theory, L. Boi......Page 1853
Operator Product Expansion in Quantum Field Theory, H. Osborn......Page 2070
Schwarz-Type Topological Quantum Field Theory, R.K. Kaul, T.R. Govindarajan and P. Ramadevi......Page 2593
Solitons and Other Extended Field Configurations, R.S. Ward......Page 2701
Topological Defects and Their Homotopy Classification, T.W.B. Kibble......Page 3030
Topological Gravity, Two-Dimensional, T. Eguchi......Page 3037
Topological Knot Theory and Macroscopic Physics, L. Boi......Page 3044
Topological Sigma Models, D. Birmingham......Page 3063
Two-Dimensional Conformal Field Theory and Vertex Operator Algebras, M.R. Gaberdiel......Page 3090
WDVV Equations and Frobenius Manifolds, B. Dubrovin......Page 3211
Bose-Einstein Condensates, F. Dalfovo, L.P. Pitaevskii and S. Stringari......Page 358
Falicov-Kimball Model, Ch Gruber and D. Ueltschi......Page 1008
Fractional Quantum Hall Effect, J.K. Jain......Page 1127
High Tc Superconductor Theory, S.-C. Zhang......Page 1370
Hubbard Model, H. Tasaki......Page 1437
Liquid Crystals, O.D. Lavrentovich......Page 1774
Negative Refraction and Subdiffraction Imaging, S. O\'Brien and S.A. Ramakrishna......Page 1937
Nuclear Magnetic Resonance, P.T. Callaghan......Page 2046
Optical Caustics, A. Joets......Page 2074
Quantum Phase Transitions, S. Sachdev......Page 2388
Quasiperiodic Systems, P. Kramer......Page 2407
Renormalization: Statistical Mechanics and Condensed Matter, M. Salmhofer......Page 2506
Short-Range Spin Glasses: The Metastate Approach, C.M. Newman and D.L. Stein......Page 2669
Fluid Dynamics......Page 28
Cellular Automata, M. Bruschi and F. Musso......Page 501
Lagrangian Dispersion (Passive Scalar), G. Falkovich......Page 1709
Mean Field Spin Glasses and Neural Networks, A. Bovier......Page 1861
Percolation Theory, V. Beffara and V. Sidoravicius......Page 2120
Random Matrix Theory in Physics, T. Guhr......Page 2437
Random Walks in Random Environments, L.V. Bogachev......Page 2452
Spin Glasses, F. Guerra......Page 2754
Stochastic Loewner Evolutions, G.F. Lawler......Page 2852
Two-Dimensional Ising Model, B.M. McCoy......Page 3095
Wulff Droplets, S. Shlosman......Page 3235
Averaging Methods, A.I. Neishtadt......Page 272
Bifurcations of Periodic Orbits, J.-P. Françoise......Page 331
Billiards in Bounded Convex Domains, S. Tabachnikov......Page 342
Central Manifolds, Normal Forms, P. Bonckaert......Page 513
Chaos and Attractors, R. Gilmore......Page 523
Diagrammatic Techniques in Perturbation Theory, G. Gentile......Page 779
Dissipative Dynamical Systems of Infinite Dimension, M. Efendiev, S. Zelik and A. Miranville......Page 826
Dynamical Systems and Thermodynamics, A. Carati, L. Galgani and A. Giorgilli......Page 850
Dynamical Systems in Mathematical Physics: An Illustration from Water Waves, O. Goubet......Page 858
Entropy and Quantitative Transversality, G. Comte......Page 962
Ergodic Theory, M. Yuri......Page 975
Fractal Dimensions in Dynamics, V. Županovic and D. Žubrinic......Page 1119
Generic Properties of Dynamical Systems, C. Bonatti......Page 1219
Hamiltonian Systems: Stability and Instability Theory, P. Bernard......Page 1356
Holomorphic Dynamics, M. Lyubich......Page 1377
Homeomorphisms and Diffeomorphisms of the Circle, A. Zumpano and A. Sarmiento......Page 1390
Homoclinic Phenomena, S.E. Newhouse......Page 1397
Hyperbolic Billiards, Maciej P. Wojtkowski......Page 1441
Hyperbolic Dynamical Systems, B. Hasselblatt......Page 1446
Isomonodromic Deformations, V.P. Kostov......Page 1627
Lyapunov Exponents and Strange Attractors, M. Viana......Page 1803
Multiscale Approaches, A. Lesne......Page 1919
Normal Forms and Semiclassical Approximation, D. Bambusi......Page 2032
Point-Vortex Dynamics, S. Boatto and D. Crowdy......Page 2165
Polygonal Billiards, S. Tabachnikov......Page 2183
Random Dynamical Systems, V. Araújo......Page 2429
Regularization for Dynamical ζ-Functions, V. Baladi......Page 2485
Resonances, N. Burq......Page 2514
Riemann-Hilbert Problem, V.P. Kostov......Page 2535
Semiclassical Spectra and Closed Orbits, Y.Colin de Verdière......Page 2611
Separatrix Splitting, D. Treschev......Page 2634
Stability Theory and KAM, G. Gentile......Page 2798
Symmetry and Symmetry Breaking in Dynamical Systems, I. Melbourne......Page 2957
Synchronization of Chaos, M.A. Aziz-Alaoui......Page 2986
Universality and Renormalization, M. Lyubich......Page 3116
Weakly Coupled Oscillators, E.M. Izhikevich and Y. Kuramoto......Page 3221
Bethe Ansatz, M.T. Batchelor......Page 299
Cluster Expansion, R. Kotecký......Page 577
Dimer Problems, R. Kenyon......Page 786
Eight Vertex and Hard Hexagon Models, P.A. Pearce......Page 880
Fermionic Systems, V. Mastropietro......Page 1025
Finitely Correlated States, R.F. Werner......Page 1059
Holonomic Quantum Fields, J. Palmer......Page 1385
Large Deviations in Equilibrium Statistical Mechanics, S. Shlosman......Page 1715
Metastable States, S. Shlosman......Page 1871
Phase Transitions in Continuous Systems, E. Presutti......Page 2152
Pirogov-Sinai Theory, R. Kotecký......Page 2159
Quantum Central-Limit Theorems, A.F. Verbeure......Page 2229
Quantum Spin Systems, B. Nachtergaele......Page 2394
Quantum Statistical Mechanics: Overview, L. Triolo......Page 2401
Reflection Positivity and Phase Transitions, Y. Kondratiev and Y. Kozitsky......Page 2475
Statistical Mechanics and Combinatorial Problems, R. Zecchina......Page 2822
Statistical Mechanics of Interfaces, S. Miracle-Solé......Page 2827
Superfluids, D. Einzel......Page 2887
Toeplitz Determinants and Statistical Mechanics, E.L. Basor......Page 3017
Bifurcations in Fluid Dynamics, G. Schneider......Page 327
Breaking Water Waves, A. Constantin......Page 429
Capillary Surfaces, R. Finn......Page 477
Cauchy Problem for Burgers-Type Equations, G.M. Henkin......Page 492
Compressible Flows: Mathematical Theory, G.-Q. Chen......Page 641
Fluid Mechanics: Numerical Methods, J.-L. Guermond......Page 1090
Geophysical Dynamics, M.B. Ziane......Page 1259
Incompressible Euler Equations: Mathematical Theory, D. Chae......Page 1464
Interfaces and Multicomponent Fluids, J. Kim and J. Lowengrub......Page 1589
Intermittency in Turbulence, J. Jiménez......Page 1598
Inviscid Flows, R. Robert......Page 1614
Korteweg-de Vries Equation and Other Modulation Equations, G. Schneider and E. Wayne......Page 1693
Magnetohydrodynamics, C. Le Bris......Page 1829
Newtonian Fluids and Thermohydraulics, G. Labrosse and G. Kasperski......Page 1946
Non-Newtonian Fluids, C. Guillopé......Page 2014
Partial Differential Equations: Some Examples, R. Temam......Page 2105
Stability of Flows, S. Friedlander......Page 2773
Turbulence Theories, R.M.S. Rosa......Page 3068
Variational Methods in Turbulence, F.H. Busse......Page 3124
Viscous Incompressible Fluids: Mathematical Theory, J.G. Heywood......Page 3142
Vortex Dynamics, M. Nitsche......Page 3163
Wavelets: Application to Turbulence, M. Farge and K. Schneider......Page 3181
Integrable Systems......Page 29
Abelian and Nonabelian Gauge Theories Using Differential Forms, A.C. Hirshfeld......Page 187
Abelian Higgs Vortices, J.M. Speight......Page 197
Aharonov-Bohm Effect, M. Socolovsky......Page 237
Anomalies, S.L. Adler......Page 251
BRST Quantization, M. Henneaux......Page 432
Dirac Fields in Gravitation and Nonabelian Gauge Theory, J.A. Smoller......Page 792
Effective Field Theories, G. Ecker......Page 864
Electric-Magnetic Duality, Tsou Sheung Tsun......Page 926
Electroweak Theory, K. Konishi......Page 934
Exact Renormalization Group, P.K. Mitter......Page 997
Gauge Theories from Strings, P. Di Vecchia......Page 1188
Gauge Theory: Mathematical Applications, S.K. Donaldson......Page 1193
Instantons: Topological Aspects, M. Jardim......Page 1498
Lattice Gauge Theory, A. Di Giacomo......Page 1729
Measure on Loop Spaces, H. Airault......Page 1867
Noncommutative Geometry and the Standard Model, T. Schücker......Page 1963
Nonperturbative and Topological Aspects of Gauge Theory, R.W. Jackiw......Page 2022
Perturbative Renormalization Theory and BRST, K. Fredenhagen and M. Dütsch......Page 2140
Quantum Chromodynamics, G. Sterman......Page 2243
Quantum Electrodynamics and Its Precision Tests, S. Laporta and E. Remiddi......Page 2267
Renormalization: General Theory, J.C. Collins......Page 2498
Seiberg-Witten Theory, Siye Wu......Page 2602
Standard Model of Particle Physics, G. Altarelli......Page 2804
Supergravity, K.S. Stelle......Page 2894
Supersymmetric Particle Models, S. Pokorski......Page 2913
Symmetry Breaking in Field Theory, T.W.B. Kibble......Page 2971
Twistor Theory: Some Applications, L. Mason......Page 3076
Two-Dimensional Models, B. Schroer......Page 3101
General Relativity: Overview, R. Penrose......Page 1212
Asymptotic Structure and Conformal Infinity, J. Frauendiener......Page 267
Black Hole Mechanics, A. Ashtekar......Page 346
Boundaries for Spacetimes, S.G. Harris......Page 372
Brane Worlds, R. Maartens......Page 413
Canonical General Relativity, C. Rovelli......Page 458
Critical Phenomena in Gravitational Collapse, C. Gundlach......Page 714
Computational Methods in General Relativity: The Theory, M.W. Choptuik......Page 650
Cosmology: Mathematical Aspects, G.F.R. Ellis......Page 699
Einstein-Cartan Theory, A. Trautman......Page 914
Einstein’s Equations with Matter, Y. Choquet-Bruhat......Page 920
Einstein Equations: Exact Solutions, Jií Bicák......Page 890
Einstein Equations: Initial Value Formulation, J. Isenberg......Page 898
General Relativity: Experimental Tests, C.M. Will......Page 1206
Geometric Analysis and General Relativity, L. Andersson......Page 1227
Geometric Flows and the Penrose Inequality, H. Bray......Page 1235
Gravitational Lensing, J. Wambsganss......Page 1292
Gravitational Waves, G. González and J. Pullin......Page 1307
Hamiltonian Reduction of Einstein\'s Equations, A.E. Fischer and V. Moncrief......Page 1332
Minimal Submanifolds, T.H. Colding and W.P. Minicozzi II......Page 1874
Newtonian Limit of General Relativity, J. Ehlers......Page 1957
Quantum Field Theory in Curved Spacetime, B.S. Kay......Page 2301
Relativistic Wave Equations Including Higher Spin Fields, R. Illge and V. Wünsch......Page 2490
Shock Wave Refinement of the Friedman-Robertson-Walker Metric, B. Temple and J.A. Smoller......Page 2658
Spacetime Topology, Causal Structure and Singularities, R. Penrose......Page 2716
Spinors and Spin Coefficients, K.P. Tod......Page 2766
Stability of Minkowski Space, S. Klainerman......Page 2786
Stationary Black Holes, R. Beig and P.T. Chrusciel......Page 2810
Twistors, K.P. Tod......Page 3084
Integrable Systems: Overview, Francesco Calogero......Page 1560
Affine Quantum Groups, G.W. Delius and N. MacKay......Page 229
Bäcklund Transformations, D. Levi......Page 287
Bi-Hamiltonian Methods in Soliton Theory, M. Pedroni......Page 336
Boundary-Value Problems for Integrable Equations, B. Pelloni......Page 392
Calogero-Moser-Sutherland Systems of Nonrelativistic and Relativistic Type, S.N.M. Ruijsenaars......Page 449
∂-Approach to Integrable Systems, P.G. Grinevich......Page 759
Eigenfunctions of Quantum Completely Integrable Systems, J.A. Toth......Page 873
Functional Equations and Integrable Systems, H.W. Braden......Page 1150
Integrability and Quantum Field Theory, T.J. Hollowood......Page 1504
Integrable Discrete Systems, O. Ragnisco......Page 1513
Integrable Systems and Algebraic Geometry, E. Previato......Page 1519
Integrable Systems and Discrete Geometry, A. Doliwa and P.M. Santini......Page 1532
Integrable Systems and Recursion Operators on Symplectic and Jacobi Manifolds, R. Caseiro and J.M. Nunes da Costa......Page 1541
Integrable Systems and the Inverse Scattering Method, A.S. Fokas......Page 1547
Integrable Systems in Random Matrix Theory, C.A. Tracy and H. Widom......Page 1556
Isochronous Systems, Francesco Calogero......Page 1620
Nonlinear Schrödinger Equations, M.J. Ablowitz and B. Prinari......Page 2006
Painlevé Equations, N. Joshi......Page 2100
Quantum Calogero-Moser Systems, R. Sasaki......Page 2222
Riemann-Hilbert Methods in Integrable Systems, D. Shepelsky......Page 2528
Sine-Gordon Equation, S.N.M. Ruijsenaars......Page 2675
Solitons and Kac-Moody Lie Algebras, E. Date......Page 2693
Toda Lattices, Y.B. Suris......Page 3008
Yang-Baxter Equations, J.H.H. Perk and H. Au-Yang......Page 3238
Quantum Field Theory......Page 30
Nonequilibrium Statistical Mechanics (Stationary): Overview, G. Gallavotti......Page 1984
Adiabatic Piston, Ch Gruber and A. Lesne......Page 206
Boltzmann Equation (Classical and Quantum), M. Pulvirenti......Page 352
Glassy Disordered Systems: Dynamical Evolution, S. Franz......Page 1278
Fourier Law, F. Bonetto and L. Rey-Bellet......Page 1099
Interacting Particle Systems and Hydrodynamic Equations, C. Landim......Page 1577
Interacting Stochastic Particle Systems, H. Spohn......Page 1584
Kinetic Equations, C. Bardos......Page 1654
Macroscopic Fluctuations and Thermodynamic Functionals, G. Jona-Lasinio......Page 1811
Nonequilibrium Statistical Mechanics: Dynamical Systems Approach, P. Buttà and C. Marchioro......Page 1994
Nonequilibrium Statistical Mechanics: Interaction between Theory and Numerical Simulations, R. Livi......Page 1998
Phase Transition Dynamics, A. Onuki......Page 2146
Stochastic Resonance, S. Herrmann and P. Imkeller......Page 2858
Quantum Field Theory: A Brief Introduction, L.H. Ryder......Page 2311
Algebraic Approach to Quantum Field Theory, R. Brunetti and K. Fredenhagen......Page 244
Axiomatic Quantum Field Theory, B. Kuckert......Page 280
Batalin-Vilkovisky Quantization, A.C. Hirshfeld......Page 293
Bosons and Fermions in External Fields, E. Langmann......Page 364
Constructive Quantum Field Theory, G. Gallavotti......Page 663
Current Algebra, G.A. Goldin......Page 720
Dirac Operator and Dirac Field, S.N.M. Ruijsenaars......Page 799
Dispersion Relations, J. Bros......Page 812
Euclidean Field Theory, F. Guerra......Page 981
Gerbes in Quantum Field Theory, J. Mickelsson......Page 1264
Hopf Algebra Structure of Renormalizable Quantum Field Theory, D. Kreimer......Page 1403
Indefinite Metric, H. Gottschalk......Page 1471
Quantum Fields with Indefinite Metric: Non-Trivial Models, S. Albeverio and H. Gottschalk......Page 2315
Perturbation Theory and Its Techniques, R.J. Szabo......Page 2127
Quantum Fields with Topological Defects, M. Blasone, G. Vitiello and P. Jizba......Page 2320
Scattering, Asymptotic Completeness and Bound States, D. Iagolnitzer and J. Magnen......Page 2574
Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools, D. Buchholz and S.J. Summers......Page 2555
Scattering in Relativistic Quantum Field Theory: The Analytic Program, J. Bros......Page 2564
Symmetries and Conservation Laws, L.H. Ryder......Page 2939
The Jones Polynomial, V.F.R. Jones......Page 2952
Symmetries in Quantum Field Theory of Lower Spacetime Dimensions, J. Mund and K.-H. Rehren......Page 2945
Thermal Quantum Field Theory, C.D. Jäkel......Page 3000
Tomita-Takesaki Modular Theory, S.J. Summers......Page 3024
Algebraic Techniques......Page 31
Knot Invariants and Quantum Gravity, R. Gambini and J. Pullin......Page 1669
Loop Quantum Gravity, C. Rovelli......Page 1793
Quantum Cosmology, M. Bojowald......Page 2252
Quantum Dynamics in Loop Quantum Gravity, H. Sahlmann......Page 2264
Quantum Geometry and Its Applications, A. Ashtekar and J. Lewandowski......Page 2329
Spin Foams, A. Perez......Page 2744
Wheeler-De Witt Theory, J. Maharana......Page 3226
Capacities Enhanced by Entanglement, P. Hayden......Page 464
Capacity for Quantum Information, D. Kretschmann......Page 470
Channels in Quantum Information Theory, M. Keyl......Page 518
Entanglement, R.F. Werner......Page 953
Entanglement Measures, R.F. Werner......Page 958
Finite Weyl Systems, D.-M. Schlingemann......Page 1053
Optimal Cloning of Quantum States, M. Keyl......Page 2082
Quantum Channels: Classical Capacity, A.S. Holevo......Page 2241
Quantum Entropy, D. Petz......Page 2276
Quantum Error Correction and Fault Tolerance, D. Gottesman......Page 2295
Source Coding in Quantum Information Theory, N. Datta and T.C. Dorlas......Page 2708
Arithmetic Quantum Chaos, J. Marklof......Page 258
Coherent States, S.T. Ali......Page 583
Geometric Phases, P. Lévay......Page 1253
N-Particle Quantum Scattering, D.R. Yafaev......Page 2039
Quantum Ergodicity and Mixing of Eigenfunctions, S. Zelditch......Page 2282
Quantum Mechanical Scattering Theory, D.R. Yafaev......Page 2350
Quantum Mechanics: Foundations, R. Penrose......Page 2359
Quantum Mechanics: Generalizations, P. Pearle and A. Valentini......Page 2364
Quantum Mechanics: Weak Measurements, L. Diósi......Page 2375
Quantum n-Body Problem, R.G. Littlejohn......Page 2382
Schrödinger Operators, V. Bach......Page 2586
Stability of Matter, J.P. Solovej......Page 2780
Stationary Phase Approximation, J.J. Duistermaat......Page 2816
Supersymmetric Quantum Mechanics, J.-W. van Holten......Page 2918
Brane Construction of Gauge Theories, S.L. Cacciatori......Page 406
Branes and Black Hole Statistical Mechanics, S.R. Das......Page 419
Calibrated Geometry and Special Lagrangian Submanifolds, D.D. Joyce......Page 444
Compactification of Superstring Theory, M.R. Douglas......Page 632
Derived Categories, E.R. Sharpe......Page 766
Fourier-Mukai Transform in String Theory, B. Andreas......Page 1104
Large-N Dualities, A. Grassi......Page 1723
Mirror Symmetry: A Geometric Survey, R.P. Thomas......Page 1893
Noncommutative Geometry from Strings, Chong-Sun Chu......Page 1969
Random Algebraic Geometry, Attractors and Flux Vacua, M.R. Douglas......Page 2422
Riemannian Holonomy Groups and Exceptional Holonomy, D.D. Joyce......Page 2540
String Field Theory, L. Rastelli......Page 2866
String Theory: Phenomenology, A.M. Uranga......Page 2875
String Topology: Homotopy and Geometric Perspectives, R.L. Cohen......Page 2883
Superstring Theories, C. Bachas and J. Troost......Page 2906
Braided and Modular Tensor Categories, V. Lyubashenko......Page 397
Clifford Algebras and Their Representations, A. Trautman......Page 564
Finite-Dimensional Algebras and Quivers, A. Savage......Page 1038
Finite Group Symmetry Breaking, G. Gaeta......Page 1047
Hopf Algebras and q-Deformation Quantum Groups, S. Majid......Page 1412
Operads, J. Stasheff......Page 2063
Low Dimensional Geometry......Page 32
Characteristic Classes, P.B. Gilkey, R. Ivanova and S. Nikcevic......Page 534
Cohomology Theories, U. Tillmann......Page 591
Equivariant Cohomology and the Cartan Model, E. Meinrenken......Page 967
Index Theorems, P.B. Gilkey, K. Kirsten, R. Ivanova and J.H. Park......Page 1477
Intersection Theory, A. Kresch......Page 1605
K-Theory, V. Mathai......Page 1700
Spectral Sequences, P. Selick......Page 2722
Knot Homologies, J. Rasmussen......Page 1662
Moduli Spaces: An Introduction, F. Kirwan......Page 1903
Quillen Determinant, S. Scott......Page 2414
Riemann Surfaces, K. Hulek......Page 2518
Several Complex Variables: Basic Geometric Theory, A. Huckleberry and T. Peternell......Page 2639
Several Complex Variables: Compact Manifolds, A. Huckleberry and T. Peternell......Page 2650
Einstein Manifolds, A.S. Dancer......Page 907
Lorentzian Geometry, P.E. Ehrlich and S.B. Kim......Page 1797
Pseudo-Riemannian Nilpotent Lie Groups, P.E. Parker......Page 2193
Singularity and Bifurcation Theory, J.-P. Françoise and C. Piquet......Page 2687
Supermanifolds, F.A. Rogers......Page 2901
Combinatorics: Overview, C. Krattenthaler......Page 599
Number Theory in Physics, M. Marcolli......Page 2054
C*-Algebras and their Classification, G.A. Elliott......Page 439
Free Probability Theory, D.-V. Voiculescu......Page 1142
Functional Integration in Quantum Physics, C. DeWitt-Morette......Page 1159
Leray-Schauder Theory and Mapping Degree, J. Mawhin......Page 1735
Ljusternik-Schnirelman Theory, J. Mawhin......Page 1782
Ordinary Special Functions, W. Van Assche......Page 2091
Positive Maps on C*-Algebras, F. Cipriani......Page 2187
Quantum Dynamical Semigroups, R. Alicki......Page 2258
Saddle Point Problems, M. Schechter......Page 2546
Spectral Theory of Linear Operators, M. Schechter......Page 2732
von Neumann Algebras: Introduction, Modular Theory, and Classification Theory, V.S. Sunder......Page 3152
von Neumann Algebras: Subfactor Theory, Y. Kawahigashi......Page 3158
Wavelets: Applications, M. Yamada......Page 3193
Wavelets: Mathematical Theory, K. Schneider and M. Farge......Page 3199
Classical Groups and Homogeneous Spaces, S. Gindikin......Page 546
Compact Groups and Their Representations, A. Kirillov and A. Kirillov, Jr.......Page 622
Lie Groups: General Theory, R. Gilmore......Page 1740
Lie Superalgebras and Their Representations, L. Frappat......Page 1759
Lie, Symplectic, and Poisson Groupoids and Their Lie Algebroids, C.-M. Marle......Page 1766
Finite-Type Invariants of 3-Manifolds, T.T.Q. Lê......Page 1073
Floer Homology, P.B. Kronheimer......Page 1081
Quantum 3-Manifold Invariants, C. Blanchet and V. Turaev......Page 2216
Singularities of the Ricci Flow, M. Anderson......Page 2683
Symplectic Geometry and Topology......Page 33
Noncommutative Tori, Yang-Mills, and String Theory, A. Konechny......Page 1978
Path Integrals in Noncommutative Geometry, R. Léandre......Page 2107
Quantum Group Differentials, Bundles and Gauge Theory, T. Brzezinski......Page 2335
Quantum Hall Effect, K. Hannabuss......Page 2343
Bifurcation Theory, M. Haragus and G. Iooss......Page 321
Elliptic Differential Equations: Linear Theory, C. Amrouche, M. Krbec, Š. Necasová and B. Lucquin-Desreux......Page 941
Evolution Equations: Linear and Nonlinear, J. Escher......Page 990
Ginzburg-Landau Equation, Y. Morita......Page 1272
Image Processing: Mathematics, G. Aubert and P. Kornprobst......Page 1455
Inequalities in Sobolev Spaces, M. Vaugon......Page 1486
Localization for Quasiperiodic Potentials, S. Jitomirskaya......Page 1787
Magnetic Resonance Imaging, C.L. Epstein and F.W. Wehrli......Page 1821
Semilinear Wave Equations, P. D\'Ancona......Page 2617
Separation of Variables for Differential Equations, S. Rauch-Wojciechowski and K. Marciniak......Page 2625
Symmetric Hyperbolic Systems and Shock Waves, S. Kichenassamy......Page 2933
Wave Equations and Diffraction, M.E. Taylor......Page 3174
Deformation Quantization, A.C. Hirshfeld......Page 726
Deformation Quantization and Representation Theory, S. Waldmann......Page 734
Deformation Theory, M.J. Pflaum......Page 741
Deformations of the Poisson Bracket on a Symplectic Manifold, S. Gutt and S. Waldmann......Page 749
Fedosov Quantization, N. Neumaier......Page 1016
Feynman Path Integrals, S. Mazzucchi......Page 1032
Bicrossproduct Hopf Algebras and Noncommutative Spacetime, S. Majid......Page 311
Classical r-Matrices, Lie Bialgebras, and Poisson Lie Groups, M.A. Semenov-Tian-Shansky......Page 557
q-Special Functions, T.H. Koornwinder......Page 2204
Determinantal Random Fields, A. Soshnikov......Page 772
Growth Processes in Random Matrix Theory, K. Johansson......Page 1311
Malliavin Calculus, A.B. Cruzeiro......Page 1837
Random Partitions, A. Okounkov......Page 2446
Stochastic Differential Equations, F. Russo......Page 2835
Stochastic Hydrodynamics, B. Ferrario......Page 2843
Supersymmetry Methods in Random Matrix Theory, M.R. Zirnbauer......Page 2924
Symmetry Classes in Random Matrix Theory, M.R. Zirnbauer......Page 2977
Contact Manifolds, J.B. Etnyre......Page 677
Graded Poisson Algebras, A.S. Cattaneo, D. Fiorenza and R. Longoni......Page 1285
Hamiltonian Group Actions, L.C. Jeffrey......Page 1325
Multi-Hamiltonian Systems, F. Magri and M. Pedroni......Page 1913
Recursion Operators in Classical Mechanics, F. Magri and M. Pedroni......Page 2470
Variational Techniques......Page 34
Control Problems in Mathematical Physics, B. Piccoli......Page 682
Convex Analysis and Duality Methods, G. Bouchitté......Page 688
Free Interfaces and Free Discontinuities: Variational Problems, G. Buttazzo......Page 1136
Γ-Convergence and Homogenization, G. Dal Maso......Page 1174
Geometric Measure Theory, G. Alberti......Page 1245
Hamilton-Jacobi Equations and Dynamical Systems: Variational Aspects, A. Siconolfi......Page 1361
Minimax Principle in the Calculus of Variations, A. Abbondandolo......Page 1886
Optimal Transportation, Y. Brenier......Page 2086
Variational Techniques for Ginzburg-Landau Energies, S. Serfaty......Page 3128
Variational Techniques for Microstructures, G. Dolzmann......Page 3136
Volume 1, A-C......Page 35
Volume 2, D-H......Page 37
Volume 3, I-O......Page 39
Volume 4, P-Sp......Page 42
Volume 5, St-Z......Page 44