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
