XVI-th International Congress on Mathematical Physics

CONTENTS......Page 12
Preface......Page 6
INTERNATIONAL SCIENTIFIC COMMITTEE......Page 8
Prize Committees......Page 9
Acknowledgments......Page 10
Welcome addresses......Page 20
Henri Poincaré Prize......Page 24
LAUDATIO BY JAKOB YNGVASON......Page 27
LAUDATIO BY DOMOKOS SZÁSZ......Page 30
LAUDATIO BY JOEL LEBOWITZ......Page 33
IAMP Early Career Award and other prizes......Page 36
IUPAP YOUNG SCIENTIST PRIZE......Page 37
THE AHP DISTINGUISHED PAPER AWARD......Page 39
Part A Plenary Talks......Page 40
1. Introduction......Page 42
2.1. Quadrilateral lattices......Page 44
2.2. Discrete evolution systems: “Existence as integrability”......Page 48
3.1. Poisson structure of circular lattices......Page 50
3.2. Quantization and the tetrahedron equation......Page 52
4.1. Fock representation solution......Page 54
4.2. Modular double solution......Page 55
4.2.1. The “interaction-round-a-cube” formulation of the modular double solution......Page 56
4.3.1. Generalized form of the q-oscillator map......Page 58
4.3.2. Cyclic representations of the q-oscillator algebra......Page 59
4.3.3. Solution of the tetrahedron equation......Page 60
5. Conclusion......Page 61
References......Page 62
Keywords:......Page 64
References......Page 74
1.1. Historical perspective......Page 75
1.2. Quantum measure......Page 80
1.3. Euclidean and quantum scaling exponents......Page 81
1.4. Box formulation of Liouville quantum gravity......Page 82
1.5. Statement of KPZ......Page 85
2.1. GFF circular average......Page 86
2.3. GFF circular average and Brownian motion......Page 89
3.1. Gaussian exponential averages......Page 90
3.3. Random measure and Brownian motion with drift......Page 91
4.2. Quantum scaling......Page 92
4.3. Brownian stopping time......Page 93
4.4. Brownian martingale......Page 94
4.5. Probability distribution and GFF thick points......Page 95
5.1. Boundary quantum measure.......Page 96
5.2. Boundary scaling and KPZ......Page 97
6.1. ' = 4/ Liouville duality......Page 98
6.2. Brownian approach to duality [2]......Page 99
Acknowledgements......Page 100
References......Page 101
1. Introduction......Page 105
2. Local semicircle law, delocalization and level repulsion......Page 108
3. Sine kernel universality......Page 114
4. Dyson Brownian motion......Page 116
5. Local Relaxation Flow......Page 117
6. Proof of Theorem 5.1......Page 119
References......Page 122
1. Introduction......Page 125
2.1. Basics of free probability......Page 127
2.2. Free Brownian motion......Page 129
3. Single ring theorem......Page 131
4. Enumeration of maps......Page 134
References......Page 140
The physics of decision making: stochastic differential equations as models for neural dynamics and evidence accumulation in cortical circuits P. Holmes, P. Eckho., K.F. Wong-Lin, R. Bogacz, M. Zacksenhouse, J.D. Cohen......Page 142
2. Decision-making models and an optimal speed-accuracy tradeo......Page 143
2.1. Leaky competing accumulators and drift-diffusion processes......Page 144
2.2. A spiking neuron model and its reduction to competing accumulators......Page 145
2.3. An optimal speed-accuracy tradeo......Page 150
3. Behavioral experiments: a prevalent lack of optimality......Page 152
3.1. A preference for accuracy?......Page 153
3.2. Robust decisions in the face of uncertainty?......Page 154
3.3. Biophysical constraints?......Page 155
4. Discussion and conclusions......Page 157
References......Page 159
1. Introduction......Page 162
2. On-Shell Methods......Page 165
2.1. Integrals......Page 166
2.2. Unitarity......Page 167
2.3. Factorization and On-Shell Recursion Relations......Page 170
3. N = 4 Supersymmetry: A Theoretical Laboratory......Page 172
References......Page 176
Operator algebras and noncommutative geometric aspects in conformal field theory R. Longo......Page 180
1. Introduction......Page 181
2. The periodic Lorentz gas......Page 183
3. Why “a generalization” of the linear Boltzmann equation?......Page 186
5. A limiting random flight process......Page 187
7. The space of lattices......Page 189
8. Equidistribution in the space of lattices......Page 191
10. Outlook......Page 194
References......Page 196
1. Introduction......Page 199
2. Ising, Vertex and Ashkin-Teller models......Page 201
3. Quantum spin chain and 1D Fermi systems......Page 203
4. Universal relations......Page 204
5. Renormalization Group analysis for coupled Ising models......Page 205
6. Proof of universality and anomaly non renormalization......Page 211
7. Renormalization Group for Quantum spin chain and 1D Fermi systems......Page 214
8. Universality for quantum spin chains and 1D Fermi systems......Page 215
References......Page 217
1. Introduction......Page 219
2. Spectroscopy in nonrelativistic QED......Page 221
2.1. Atoms and molecules......Page 223
2.1.1. Spectral analysis......Page 224
2.1.2. Asymptotic completeness, metastable states, and Bohr’s frequency condition.......Page 226
2.2.1. Dressed electron states......Page 229
2.2.2. Infraparticle scattering states......Page 230
Appendix A......Page 232
Appendix B......Page 235
Acknowledgments......Page 237
References......Page 238
1. Introduction......Page 241
2. The parking process......Page 242
3. The parking maneuver......Page 245
4. The measured data......Page 246
References......Page 249
1. Introduction......Page 250
1.1. The Bose Gas: A Quantum Many-Body Problem......Page 251
2.1. The Ground State Energy of Homogeneous Bose Gases......Page 252
2.2. Homogeneous Bose Gas at Positive Temperature......Page 253
2.3. Critical Temperature for BEC......Page 255
3. Trapped Bose Gases......Page 256
3.2. Ground State Energy of Dilute Trapped Gases......Page 257
3.3. BEC for Rotating Trapped Gases......Page 258
3.4. Rapid Rotation......Page 259
References......Page 261
1. Introduction......Page 265
1.1. The model......Page 266
1.2.2. Vortices and their benefit......Page 268
1.2.3. Critical fields......Page 269
2.1. The vorticity measures......Page 270
2.2. Global minimizers of G" close to Hc1......Page 271
2.3. Global minimizers in the intermediate regime......Page 272
2.4. Global minimizers in the regime n" proportional to hex......Page 273
2.5. Global minimizers in the regime |log e| « hex « e-2......Page 275
3. Next-order behavior of vortices......Page 276
3.1. Splitting of the energy and blow-up......Page 277
3.2. The “renormalized” energy......Page 278
3.3. Main result......Page 280
References......Page 282
1. Introduction......Page 284
2.1. Twisted chiral ring and quantum integrability......Page 286
2.2. Topological field theory......Page 287
2.3. Yang-Yang function and quantum spectrum......Page 288
2.4. Quantization from four dimensions......Page 289
3.1. The  -background and twisted masses......Page 290
3.1.1. Four dimensional theory on R2ε......Page 291
3.1.2. Calculation of the twisted superpotential......Page 292
4.1. The classical story......Page 294
4.1.2. Quantization......Page 295
5.1.1. The classical system......Page 296
5.1.3. The quantum system......Page 297
5.2.1. The classical system......Page 298
5.3. Hitchin system......Page 299
5.4. Relativistic systems......Page 301
6.2.1. The elliptic Calogero-Moser system......Page 302
6.2.4. The spectrum of observables......Page 303
6.2.6. More details and the origin of integral equation......Page 304
7. Discussion......Page 305
References......Page 306
Changing views of quantum field theory S. Weinberg......Page 309
Effective Field Theory: Past and Future......Page 312
References......Page 326
Part B Topical Sessions......Page 330
Dynamical Systems (including integrable systems and Hamiltonian stability)......Page 332
1. Introduction......Page 333
2. Choice of F......Page 334
3. A proof of existence of a d–dense orbit using a variational problem with constraints......Page 336
3.1. Single resonance case......Page 337
3.2. Double resonance......Page 338
References......Page 340
1. KdV equation......Page 342
2. Random dissipative perturbations: averaging......Page 343
4. The uniqueness......Page 344
5. The double limit......Page 345
References......Page 346
1. Introduction......Page 347
2. Diffusive limit of two Lorentz disks......Page 348
3. Interacting Markov chain of energies from deterministic dynamics......Page 349
References......Page 351
1. Introduction......Page 352
2. Calogero-Moser operators in infinite dimension......Page 353
3. Deformed CMS operators and classical Lie superalgebras seen from in.nity......Page 355
References......Page 356
PARTIAL HYPERBOLICITY, CHAOS AND SYMMETRY......Page 357
A RESONANCE OF THE CYCLOTRON FREQUENCY WITH A TIME-PERIODIC SINGULAR FLUX TUBE......Page 358
INTEGRABILITY ANALYSIS OF A NONLOCAL OSTROVSKY-WHITHAM FLOW......Page 359
GENERALIZED STÄCKEL TRANSFORM: INTEGRABILITY AND BEYOND......Page 360
LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR ASYMPTOTICALLY PERIODIC INITIAL CONDITIONS......Page 361
Posters......Page 362
Equilibrium Statistical Mechanics (classical and quantum)......Page 364
1. Global Dynamics of Wilson’s Renormalization Group......Page 365
2. Rigorous Results (Selection)......Page 366
4. Good Infinite Volume Coordinates......Page 367
5. Idea of The Proof......Page 368
7. Perspectives......Page 369
References......Page 370
1. Introduction......Page 371
3. Result and outline of the proof......Page 373
References......Page 375
1. Introduction......Page 376
1.1. The model......Page 377
3.1. Ward identities......Page 378
3.3. Conditional bounds......Page 379
References......Page 380
1. Introduction......Page 381
1.1. SLE and critical lattice models......Page 382
1.2. SLE and off-critical perturbations......Page 383
2.1. Loop Erased Random Walk with killing, κ = 2......Page 384
2.2. Massive Harmonic Explorer and Gaussian Free Field, κ = 4......Page 385
2.5. Critical Ising model, κ = 3......Page 386
3.1. Deriving the drift......Page 387
4. Questions......Page 388
References......Page 390
1. Random pinning/wetting models and the Harris criterion......Page 391
2. Rigorous results......Page 392
Acknowledgments......Page 394
References......Page 395
POINT GROUPS, GALOIS COVERINGS, AND THEIR APPLICATIONS TO RG ANALYSES IN TWO-DIMENSIONAL LATTICE MODELS......Page 396
ON RANDOM PERMUTATIONS WITH NONUNIFORM DISTRIBUTIONS......Page 397
Posters......Page 398
Non-Equilibrium Statistical Mechanics (including stochastic evolutions except SLE and Boltzmann equation)......Page 399
1. Coupled Maps with a conservation law......Page 400
2. Quenched diffusion......Page 402
References......Page 404
1. Introduction......Page 405
2. Main results......Page 407
References......Page 409
1. Introduction......Page 410
2. Harmonic lattice systems......Page 411
3. Anharmonic lattice systems......Page 413
References......Page 415
1. The quest for heat equation, from the microscopic dynamics......Page 416
2. Energy Conserving Noise......Page 417
3. The weak coupling limit......Page 418
References......Page 419
1. Introduction......Page 420
2. Scaling exponent z = 3/2 for h = -log Z......Page 421
3. Weakly asymmetric simple exclusion......Page 422
4. Renormalized KPZ equation for h = -log Z......Page 423
References......Page 424
1. Introduction......Page 425
2. Mean Field Systems......Page 426
3. Dynamics of Bose-Einstein condensates......Page 428
4. Dynamical Formation of Correlations......Page 431
References......Page 434
ON THE APPROACH TO EQUILIBRIUM AND MIXING PROPERTIES IN FERMI-PASTA-ULAM MODELS......Page 436
NONEQUILIBRIUM STATISTICAL MECHANICS OF (AN)HARMONIC CHAINS WITH SELF-CONSISTENT RESERVOIRS......Page 437
POSTERS......Page 438
PDE’s (fluid dynamics, wave equation and NLSE, Boltzmann equation, general relativity, and elasticity)......Page 439
1. Introduction......Page 440
3. The Minkowski case......Page 443
4. The Schwarzschild case......Page 446
6. A general formulation and the Kerr case......Page 448
7. Discussion......Page 449
References......Page 450
1. Motivation......Page 452
2. Regularizing e.ect for scalar conservation laws......Page 453
3. The Euler system for polytropic compressible fluids......Page 455
References......Page 456
1. Introduction......Page 457
2. The Maxwell-Klein-Gordon system......Page 458
3. MKG in Lorenz and Coulomb gauges — a comparison......Page 459
4. Energy and dispersive estimates......Page 460
5. Null structure in bilinear terms of MKG......Page 461
References......Page 462
1. Introduction......Page 463
1.1. Focusing vs. Defocusing Classes of Manifolds and Solitons......Page 464
2. Main Results......Page 465
3. The o-Regularity Theorem......Page 466
3.3. Induction and Linearization......Page 467
4. Concentration vs. Dispersion Dichotomies......Page 468
References......Page 469
LANDAU DAMPING......Page 471
CRITICAL POINTS AND LEVEL SETS OF SOLUTIONS TO ELLIPTIC PDE’S......Page 472
THE HARDY INEQUALITY AND THE ASYMPTOTIC BEHAVIOUR OF THE HEAT EQUATION IN TWISTED DOMAINS......Page 473
BOUNDARY DIFFERENTIABILITY OF SOLUTIONS OF ELASTIC PLASTIC PROBLEMS WITH LINEAR HARDENING......Page 474
ON POSITIVE SOLUTIONS AND LIOUVILLE THEOREMS FOR P-LAPLACIAN-TYPE EQUATIONS......Page 475
DELTA-SHOCK WAVES AND MEDIUMS WHICH CAN BE TREATED AS PRESSURELESS CONTINUUMS......Page 476
P-ADIC PSEUDO-DIFFERENTIAL EQUATIONS AND WAVELETS......Page 477
Posters......Page 479
Probability Theory (including random matrices and SLE)......Page 482
1. Introduction......Page 483
2. Glauber dynamics for the mean-field Ising model......Page 484
3. Ising model on the Bethe Lattice......Page 485
4. Recent progress for Ising model on lattices at high temperature......Page 486
References......Page 487
1. Introduction......Page 489
2. Boltzmann distributions and maps with large faces......Page 490
3. Scaling limits......Page 491
4. Methods......Page 492
References......Page 493
2. Dynamical and near-critical percolation......Page 494
3. The Minimal Spanning Tree......Page 496
4. How do we see the MST in the scaling limit?......Page 497
6. Conformal non-invariance?......Page 498
References......Page 499
1. Dyson’s β-ensemble......Page 500
2. Scaling limits......Page 501
3. Large gaps in the β-ensemble......Page 503
References......Page 504
MAXIMUM LOCAL ROUGHNESS IN 2D BROWNIAN AND PERCOLATION MODELS......Page 505
RANDOM MATRICES WITH EXTERNAL SOURCE......Page 506
POSTERS......Page 507
Operator Algebras (including noncommutative geometry)......Page 508
Deformations of operator algebras and the construction of quantum field theories G. Lechner......Page 16
1. Introduction: Wedge triples and local nets......Page 509
2. Rieffel deformations of wedge triples......Page 511
References......Page 514
1. Introduction: Superselection theory in Local Quantum Theory......Page 515
3. Categorical analysis of local extensions......Page 516
4. Connections with Rehren’s approach to modular invariants......Page 518
References......Page 520
Introduction......Page 523
1. Quantum groups......Page 524
2. Drinfeld twist......Page 525
3. Quantum Dirac operator......Page 526
References......Page 527
1. Introduction: Continuous Fields of C*-Algebras......Page 528
2. Quantization of States......Page 529
4. Positivity......Page 530
References......Page 532
TOWARDS A SPECTRAL TRIPLE FOR LQG......Page 533
PRO-C*-DYNAMICAL SYSTEMS WITH CROSSED PRODUCTS C*-ALGEBRAS......Page 534
POSTERS......Page 535
Nonrelativistic Quantum Mechanics (including quantum information)......Page 536
1. Radiationless transitions......Page 537
2. Adiabatic and superadiabatic representations......Page 538
3. The transmitted wave function......Page 540
References......Page 541
1. Introduction......Page 542
2.1. The setup......Page 543
2.2. Main results......Page 544
2.3. Inclusion of magnetic fields......Page 545
3.2. Fractional Laplacians......Page 546
3.4. Hardy–Lieb–Thirring inequalities......Page 547
4.1. Proof of Theorem 2.1 for . = 1......Page 548
4.2. Proof of Theorem 2.1 for arbitrary ω......Page 551
4.4. Proof of Corollary 2.1......Page 552
References......Page 553
1.1. Motivation: Coherent conditional execution of quantum communication protocols.......Page 555
1.2. Motivation: Non-asymptotic analysis of entanglement......Page 556
2.1. Approach: clean resource inequalities......Page 557
2.2. Approach: entanglement capacity as an interval......Page 558
References......Page 559
1. Introduction......Page 560
2. Decoupling......Page 561
3. Smooth Entropies......Page 562
4. Applications......Page 563
References......Page 564
1. Introduction......Page 565
3. Entanglement of projected and reduced density matrices......Page 566
References......Page 569
1. Introduction and model......Page 570
2.2. Boundedness of fractional moments of Green’s function......Page 571
2.3. Exponential decay of fractional moments of Green’s function......Page 572
4. Proof of Theorem 2.3......Page 573
References......Page 574
1.1. The one-particle theory......Page 575
1.2. The influence of interaction on localization: a challenge......Page 576
2.2. The main result......Page 577
2.3. Comments on the result......Page 578
3. Outline of the proof......Page 579
3.2. Eigenfunction correlator and its relation to Green function......Page 580
3.3. Inductive construction of domains of localization in parameter space......Page 581
4. Some remaining challenges......Page 583
References......Page 584
AHARONOV-BOHM ANSATZ AND TONOMURA ET AL. EXPERIMENTS: RIGOROUS PROOFS......Page 585
SIGNATURES OF NONCLASSICALITY IN MIXED-STATE QUANTUM COMPUTATION......Page 586
SPECTRAL ANALYSIS OF 1-D SCHRÖDINGER OPERATORS WITH LOCAL POINT INTERACTIONS......Page 587
ASYMPTOTIC HYPOTHESIS TESTING FOR CORRELATED QUANTUM STATES......Page 588
VERTEX COUPLINGS IN QUANTUM GRAPHS......Page 589
Posters......Page 590
String Theory and Quantum Gravity......Page 592
Keywords:......Page 593
References......Page 597
1. Introduction......Page 599
2.1. Black holes......Page 600
3. Non-vacuum spacetimes with hidden symmetries......Page 602
4. Generalized KY symmetries: Black hole of minimal gauged supergravity......Page 603
References......Page 605
1. Introduction......Page 607
2. Gauged supergravity......Page 608
3. Non-abelian tensor fields......Page 610
References......Page 611
SUPERCONFORMAL CHERN-SIMONS THEORIES AND ADS(4)/CFT(3) CORRESPONDENCE......Page 612
POSTERS......Page 613
Quantum Field Theory (including .eld theoretic methods in condensed matter)......Page 614
Acknowledgments......Page 615
1.2. Sub-Hopf algebras......Page 616
2. Three new results......Page 617
2.1. Generalized Witt algebras......Page 618
2.3. Kinematics as cohomology......Page 619
References......Page 620
1. Graphene - a strongly coupled, relativistic electron-hole plasma......Page 621
1.1. Anomalously strong Coulomb scattering at charge neutrality......Page 622
1.2. Graphene as a nearly perfect liquid......Page 623
2. Comparison with strongly coupled liquids solved by AdS-CFT......Page 624
References......Page 625
1. Introduction......Page 627
2. Symmetries and order-disorder dualities......Page 628
3. Orbifolds......Page 630
References......Page 632
1. Introduction......Page 633
3. Exact Representation for the Two-point Function......Page 634
4. Asymptotic Analysis of the Two-Point Function......Page 636
References......Page 637
FREE PROBABILITY MEETS SUPERSYMMETRY......Page 638
ON SINGULAR REDUCTION, QUANTIZATION AND THE OBSERVABLE ALGEBRA FOR GAUGE MODELS......Page 639
RADIATIVE CORRECTIONS TO THE MASSES OF COMPOUND PARTICLES IN THE ISING FIELD THEORY......Page 640
Posters......Page 641
Many-Body Quantum Mechanics (condensed matter, nanoscale, elasticity)......Page 643
1. Introduction......Page 644
1.1. The model......Page 645
2.2. Uniform decay in the bulk......Page 646
References......Page 647
1. Introduction......Page 649
2. The model......Page 651
2.1. The non interacting case......Page 652
References......Page 653
1. Introduction......Page 654
2. Square lattice......Page 656
References......Page 658
THE LEE-HUANG-YANG FORMULA FOR DILUTE BOSE GASES......Page 659
TWO INTEGRABLE QUANTUM IMPURITY MODELS......Page 660
TOPOLOGICAL ORDER IN QUANTUM LATTICE MODELS......Page 661
POSTERS......Page 662
New Frontiers in Mathematical Physics......Page 663
2. Cosmological evolution......Page 664
3. Inflation......Page 665
4. Cosmological perturbations......Page 666
5. Beyond the simplest models......Page 667
References......Page 669
1. Invasions in Cyclic Predator-Prey Systems......Page 670
2. Amplitude Equation and Band Width Calculation......Page 672
3. Band Width Sensitivity and Ecological Implications......Page 673
References......Page 674
QUANTUM QUENCHES: CURRENT SURVIVAL AND OTHER PROBLEMS......Page 675
CLOAKING AND TRANSFORMATION OPTICS......Page 676
SPECTRAL SINGULARITIES AND THEIR PHYSICAL APPLICATIONS......Page 677
GEOMETRIC FOURIER ANALYSIS IN COGNITIVE VISION......Page 678
Posters......Page 680
Part C Supplementary Programme......Page 682
Young Researcher Symposium......Page 684
ANALYTICAL FOUNDATIONS OF SYMPLECTIC FIELD THEORY......Page 685
RESONANT PERTURBATIONS OF HAMILTONIAN SYSTEMS IN INFINITE DIMENSIONS......Page 686
TOWARDS A QUANTUM CHURCH-TURING THEOREM......Page 687
YRS seminar talks......Page 688
Round Table “Mathematical Physics: Future Challenges”......Page 690
FAST SCRAMBLERS......Page 691
Human Rights and Social Responsibility......Page 693
FREEDOM AND DEMOCRACY ARE NOT SELF-EVIDENT......Page 694
Satellite Meetings......Page 695
XVII INTERNATIONAL FALL WORKSHOP IN GEOMETRY AND PHYSICS......Page 696
LIST OF REGISTERED PARTICIPANTS......Page 697
Speaker Index......Page 708