The Erwin Schr¨odinger International Boltzmanngasse 9/2 ESI Institute for Mathematical Physics A-1090 Vienna, Austria Scientific Report for the years 1993 – 2002 Impressum: Eigent¨umer, Verleger, Herausgeber: The Erwin Schr¨odinger International Institute for Math- ematical Physics, Boltzmanngasse 9, A-1090 Vienna. Redaktion: Peter W. Michor, Klaus Schmidt Supported by the Austrian Federal Ministry for Education, Science and Culture. Contents I Introduction 5 A preface by the President . ... 7 ESI and the Austrian scientific community . .... 8 Aboutthisreport....................................... ..... 9 II Scientific Report 11 Activities in 1992 preceding the official opening of the Institute 13 Conference on ‘Interfaces between mathematics and physics’ . 13 Conference ‘75 years of Radon transform’ . 13 The year 1993 15 Generalremarks ......................................... 15 Programsin1993..................................... ....... 16 Two dimensional quantum field theory . 16 Schr¨odinger operators . 19 Differentialgeometry.................................... 21 Visitorsoutsidethemainprograms. ......... 23 The year 1994 25 Generalremarks ......................................... 25 Programsin1994..................................... ....... 26 Ergodicity in non-commutative algebras . 26 Mathematicalrelativity ................................. 26 Quaternionic and hyper-K¨ahler manifolds . 28 Spinors, twistors and conformal invariants . ........ 30 Gibbsian random fields . 31 Workshops organized outside the main programs . ...... 31 Winter school in geometry and physics . 31 International symposium in honor of Boltzmann’s 150th birthday . ...... 32 The year 1995 33 Generalremarks ......................................... 33 Programsin1995..................................... ....... 33 Complexanalysis....................................... 33 Noncommutative differential geometry . 34 Field theory and differential geometry . 35 Gibbs random fields and phase transitions . 36 Reaction-diffusion equations in biological context . 37 Condensed matter physics: dynamics, geometry, and spectral theory . 38 Workshops organized outside the main programs . ...... 38 Winter school in geometry and physics . 38 1 2 CONTENTS Geometry of nonlinear partial differential equations . 39 Semi-classical limits and kinetic equations . 39 Visitorsoutsidethemainprograms. ......... 39 The year 1996 41 Generalremarks ......................................... 41 Programsin1996..................................... ....... 41 Topological, conformal and integrable field theory . ...... 41 Representation theory with applications to mathematical physics . ..... 43 Mathematical problems of quantum gravity . 45 Hyperbolic systems with singularities . ........ 46 Workshops organized outside the main programs . ...... 47 Winter school in geometry and physics. 47 Statistical mechanics as a branch of probability theory . 47 Satellite conference of the European Mathematical Congress: Aspects of spectral theory . 48 Workshop on the changing Metaphysics of Science . 50 Visitorsoutsidethemainprograms. ......... 50 The year 1997 51 Generalremarks ......................................... 51 Programsin1997..................................... ....... 51 Ergodic theory and dynamical systems . 51 Mathematicalrelativity ................................. 53 Spaces of geodesics and complex structures in general relativity and differential geometry 54 Local quantum physics . 56 Nonlinear theory of generalized functions. 60 Workshops organized outside the main programs . ...... 63 Winter school in geometry and physics . 63 Conference on formal power series and algebraic combinatorics . 64 Visitorsoutsidethemainprograms. ......... 65 The year 1998 67 Generalremarks ......................................... 67 Programsin1998..................................... ....... 67 Spectral geometry and its applications . 67 Schr¨odinger operators with magnetic fields . 69 Number theory and physics I. Convexity . 70 Number theory and physics II. Quantum field theory and the statistical distribution of primenumbers ...................................... 71 Quantization, generalized BRS cohomology, and anomalies . 73 Charged particle kinetics . 77 Workshops organized outside the main programs . ...... 79 Winter school in geometry and physics . 79 Conference on epistemological and experimental perspectives on quantum physics . 79 Conference on the classification of filtrations of stochastic processes . ....... 80 Visitorsoutsidethemainprograms. ......... 80 The year 1999 81 Generalremarks ......................................... 81 Programsin1999..................................... ....... 81 Functional analysis . 81 Nonequilibrium statistical mechanics . 83 Holonomy Groups in Differential Geometry . 86 Complexanalysis....................................... 87 CONTENTS 3 Applications of Integrability . ..... 89 Workshops organized outside the main programs . ...... 90 Winter school in geometry and physics . 90 ESI - Workshop on Geometrical Aspects of Spectral Theory . 90 Visitorsoutsidethemainprograms. ......... 91 The year 2000 93 Generalremarks ......................................... 93 Programsin2000..................................... ....... 94 Duality, string theory and M-theory . 94 Confinement . 95 Representation theory . 97 Algebraic groups, invariant theory and applications . ...... 98 Quantum measurement and information . 100 Workshops organized outside the main programs . 102 Winter school in geometry and physics . 102 Wolfgang Pauli und die Physik des 20. Jahrhunderts . 102 Summer Session Seminar Sophus Lie . 103 Visitorsoutsidethemainprograms. .........103 The year 2001 105 Generalremarks ......................................... 105 Programsin2001..................................... .......105 Scattering theory . 105 Randomwalks .......................................... 108 MathematicalCosmology ................................. 112 Mathematical Aspects of String Theory . 114 Nonlinear Schr¨odinger and quantum-Boltzmann equations . 115 Workshops organized outside the main programs . 118 Winter school in geometry and physics . 118 75th anniversay of the Schr¨odinger equation. 118 Poissongeometry...................................... 118 Visitorsoutsidethemainprograms. .........119 The year 2002 121 Generalremarks ......................................... 121 Programsin2002..................................... .......122 Developed Turbulence . 122 Arithmetic, automata, and asymptotics . 125 Quantum field theory on curved space time . 126 Aspects of foliation theory in geometry, topology and physics . .........129 Noncommutative geometry and quantum field theory, Feynman diagrams in mathematics andphysics ........................................131 Mathematical population genetics and statistical physics . 133 Workshops organized outside the main programs . 133 Winter school in geometry and physics . 133 Arithmetic Groups and Automorphic Forms . 133 Stability matters: A symposium on mathematical physics in honor of Elliott H. Lieb . 134 Visitorsoutsidethemainprograms. .........134 4 CONTENTS Programs and workshops approved for the years 2003 – 2004 137 Theyear2003.......................................... 137 Workshop on idempotent mathematics . 137 Kakeya-related problems in analysis . 137 Penrose inequalities . 137 Gravityintwodimensions................................. 137 Moment maps and Poisson geometry . 137 Theyear2004.......................................... 138 Geometric and analytic problems related to Cartan connections . 138 Tensor categories in mathematics and physics . 138 String theory in curved backgrounds and boundary conformal field theory . 138 Many-body quantum theory . 138 Singularity formation in non-linear evolution equations . 138 Workshop on optimal transportation problems and entropy methods . 138 III Report of the Review Panel 139 Appendix A: History 151 The foundational period of the Erwin Schr¨odinger Institute . .......151 Gedanken zum ‘Erwin Schr¨odinger Institute for Mathematical Physics’ . 153 Report on the Workshop ‘Interfaces between Mathematics and Physics’ . .......155 Vertiefungsstudie . 159 Appendix B: The ESI Preprint series 165 The preprint series and its publication record . 165 ESIPreprintlist ....................................... 167 Proceedings of ESI Conferences . 204 Appendix C: List of Visitors 205 Programcodes .......................................... 205 Listofvisitors ..................................... ........206 Appendix D: Statistics 237 The budget figures 1993 – 2002 . 237 Programs, visits and visitors, and preprints in each year . .............238 Part I Introduction 5 A PREFACE.