- •Preface
- •Foreword
- •The Henri Poincaré Prize
- •Contributors
- •Contents
- •Stability of Doubly Warped Product Spacetimes
- •Introduction
- •Warped Product Spacetimes
- •Asymptotic Behavior
- •Fuchsian Method
- •Velocity Dominated Equations
- •Velocity Dominated Solution
- •Stability
- •References
- •Introduction
- •The Tomonaga Model with Infrared Cutoff
- •The RG Analysis
- •The Dyson Equation
- •The First Ward Identity
- •The Second Ward Identity
- •The Euclidean Thirring Model
- •References
- •Introduction
- •Lie and Hopf Algebras of Feynman Graphs
- •From Hochschild Cohomology to Physics
- •Dyson-Schwinger Equations
- •References
- •Introduction
- •Quantum Representation and Dynamical Equations
- •Quantum Singularity Problem
- •Examples for Properties of Solutions
- •Effective Theory
- •Summary
- •Introduction
- •Results and Strategy of Proofs
- •References
- •Introduction
- •Critical Scaling Limits and SLE
- •Percolation
- •The Critical Loop Process
- •General Features
- •Construction of a Single Loop
- •The Near-Critical Scaling Limit
- •References
- •Black Hole Entropy Function and Duality
- •Introduction
- •Entropy Function and Electric/Magnetic Duality Covariance
- •Duality Invariant OSV Integral
- •References
- •Weak Turbulence for Periodic NLS
- •Introduction
- •Arnold Diffusion for the Toy Model ODE
- •References
- •Angular Momentum-Mass Inequality for Axisymmetric Black Holes
- •Introduction
- •Variational Principle for the Mass
- •References
- •Introduction
- •The Trace Map
- •Introduction
- •Notations
- •Entanglement-Assisted Quantum Error-Correcting Codes
- •The Channel Model: Discretization of Errors
- •The Entanglement-Assisted Canonical Code
- •The General Case
- •Distance
- •Generalized F4 Construction
- •Bounds on Performance
- •Conclusions
- •References
- •Particle Decay in Ising Field Theory with Magnetic Field
- •Ising Field Theory
- •Evolution of the Mass Spectrum
- •Particle Decay off the Critical Isotherm
- •Unstable Particles in Finite Volume
- •References
- •Lattice Supersymmetry from the Ground Up
- •References
- •Stable Maps are Dense in Dimensional One
- •Introduction
- •Density of Hyperbolicity
- •Quasi-Conformal Rigidity
- •How to Prove Rigidity?
- •The Strategy of the Proof of QC-Rigidity
- •Enhanced Nest Construction
- •Small Distortion of Thin Annuli
- •Approximating Non-renormalizable Complex Polynomials
- •References
- •Large Gap Asymptotics for Random Matrices
- •References
- •Introduction
- •Coupled Oscillators
- •Closure Equations
- •Introduction
- •Conservative Stochastic Dynamics
- •Diffusive Evolution: Green-Kubo Formula
- •Kinetic Limits: Phonon Boltzmann Equation
- •References
- •Introduction
- •Bethe Ansatz for Classical Lie Algebras
- •The Pseudo-Differential Equations
- •Conclusions
- •References
- •Kinetically Constrained Models
- •References
- •Introduction
- •Local Limits for Exit Measures
- •References
- •Young Researchers Symposium Plenary Lectures
- •Dynamics of Quasiperiodic Cocycles and the Spectrum of the Almost Mathieu Operator
- •Magic in Superstring Amplitudes
- •XV International Congress on Mathematical Physics Plenary Lectures
- •The Riemann-Hilbert Problem: Applications
- •Trying to Characterize Robust and Generic Dynamics
- •Cauchy Problem in General Relativity
- •Survey of Recent Mathematical Progress in the Understanding of Critical 2d Systems
- •Random Methods in Quantum Information Theory
- •Gauge Fields, Strings and Integrable Systems
- •XV International Congress on Mathematical Physics Specialized Sessions
- •Condensed Matter Physics
- •Rigorous Construction of Luttinger Liquids Through Ward Identities
- •Edge and Bulk Currents in the Integer Quantum Hall Effect
- •Dynamical Systems
- •Statistical Stability for Hénon Maps of Benedics-Carleson Type
- •Entropy and the Localization of Eigenfunctions
- •Equilibrium Statistical Mechanics
- •Short-Range Spin Glasses in a Magnetic Field
- •Non-equilibrium Statistical Mechanics
- •Current Fluctuations in Boundary Driven Interacting Particle Systems
- •Fourier Law and Random Walks in Evolving Environments
- •Exactly Solvable Systems
- •Correlation Functions and Hidden Fermionic Structure of the XYZ Spin Chain
- •Particle Decay in Ising Field Theory with Magnetic Field
- •General Relativity
- •Einstein Spaces as Attractors for the Einstein Flow
- •Loop Quantum Cosmology
- •Operator Algebras
- •From Vertex Algebras to Local Nets of von Neuman Algebras
- •Non-Commutative Manifolds and Quantum Groups
- •Partial Differential Equations
- •Weak Turbulence for Periodic NSL
- •Ginzburg-Landau Dynamics
- •Probability Theory
- •From Planar Gaussian Zeros to Gravitational Allocation
- •Quantum Mechanics
- •Recent Progress in the Spectral Theory of Quasi-Periodic Operators
- •Recent Results on Localization for Random Schrödinger Operators
- •Quantum Field Theory
- •Algebraic Aspects of Perturbative and Non-Perturbative QFT
- •Quantum Field Theory in Curved Space-Time
- •Lattice Supersymmetry From the Ground Up
- •Analytical Solution for the Effective Charging Energy of the Single Electron Box
- •Quantum Information
- •One-and-a-Half Quantum de Finetti Theorems
- •Catalytic Quantum Error Correction
- •Random Matrices
- •Probabilities of a Large Gap in the Scaled Spectrum of Random Matrices
- •Random Matrices, Asymptotic Analysis, and d-bar Problems
- •Stochastic PDE
- •Degenerately Forced Fluid Equations: Ergodicity and Solvable Models
- •Microscopic Stochastic Models for the Study of Thermal Conductivity
- •String Theory
- •Gauge Theory and Link Homologies
Contributors
Michael Aizenman Departments of Mathematics and Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, NJ 08544, USA, aizenman@princeton.edu
Nalini Anantharaman CMLS, École Polytechnique, 91128 Palaiseau, France, nalini@math.polytechnique.fr
Lars Andersson Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA; Albert Einstein Institute, Am Mühlenberg 1, 14476 Golm, Germany, larsa@math.miami.edu
Giuseppe Benfatto Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Rome, Italy, benfatto@mat.uniroma2.it
Christoph Bergbauer Institut für Mathematik II, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany; Erwin-Schrödinger-Institut, Boltzmanngasse 9, 1090 Vienna, Austria, bergbau@math.fu-berlin.de
Lorenzo Bertini Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 2, 00185 Rome, Italy, bertini@mat.uniroma1.it
Mikhail S. Birman Faculty of Physics, St. Petersburg State University, Ulyanovskaya, 3, St. Petersburg 198504, Russian Federation
Pavel M. Bleher Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA, bleher@math.iupui.edu
Martin Bojowald Institute for Gravitational Physics and Geometry, The Pennsylvania State University, 104 Davey Lab, University Park, PA 16802, USA, bojowald@gravity.psu.edu
Stella Brassesco Departamento de Matemáticas, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 20632, Caracas 1020-A, Venezuela, sbrasses@ivic.ve
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Contributors |
Todd A. Brun Communication Sciences Institute, Department of Electrical Engineering Systems, University of Southern California, 3740 McClintock Ave., EEB 502, Los Angeles, CA 90089-2565 USA, tbrun@usc.edu
Paolo Buttà Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 2, 00185 Rome, Italy, butta@mat.uniroma1.it
Jérôme Buzzi Laboratoire de Mathematique d’Orsay C.N.R.S., Université de ParisSud, Orsay Cedex, France, jerome.buzzi@math.u-psud.fr
Federico Camia Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands, fede@few.vu.nl
Nicoletta Cancrini Dip. Matematica, Univ. l’Aquila, 1-67100 L’Aquila, Italy, nicoletta.cancrini@roma1.infn.it
Gabriel Lopes Cardoso Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität München, Munich, Germany, gcardoso@theorie.physik.uni-muenchen.de
James Colliander Department of Mathematics, University of Toronto, Bahen Centre, Toronto, Ontario M5S 3G3, Canada, colliand@math.toronto.edu
Lorenzo J. Díaz Departamento de Matemática, PUC-Rio, Marquês de São Vicente 225, Gávea, Rio de Janeiro 225453-900, Brazil, lodiaz@mat.puc-rio.br
Sergio Dain Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina, name@email.address
David Damanik Department of Mathematics, Rice University, Houston, TX 77005, USA, damanik@rice.edu
Gesualdo Delfino International School for Advanced Studies (SISSA), via Beirut 2-4, 34014 Trieste, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy, delfino@sissa.it
Bernard Derrida Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France, derrida@lps.ens.fr
Igor Devetak Ming Hsieh Electrical Engineering Department, University of Southern California, Los Angeles, CA 90089, USA, devetak@usc.edu
Patrick Dorey Dept. of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK, p.e.dorey@durham.ac.uk
Boris Dubrovin SISSA, via Beirut 2-4, 34014, Trieste, Italy; Steklov Mathematical Institute, Moscow, Russia, dubrovin@sissa.it
Clare Dunning IMSAS, University of Kent, Canterbury CT2 7NF, UK, t.c.dunning@kent.ac.uk
Paul Fendley Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA, fendley@rockpile.phys.virginia.edu
Contributors |
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L.R.G. Fontes Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo SP, Brasil, lrenato@ime.usp.br
François Germinet Département de Mathématiques, Univ. Cergy-Pontoise, CNRS UMR 8088, IUF, 95000 Cergy-Pontoise, France, germinet@math.u-cergy.fr
Francesco Guerra Department of Physics, Sapienza University of Rome and INFN, Section of Roma 1, Rome, Italy, francesco.guerra@roma1.infn.it
Sergei Gukov Department of Physics, University of California, Santa Barbara, CA 93106, USA, gukov@theory.caltech.edu
Min-Hsiu Hsieh Ming Hsieh Electrical Engineering Department, University of Southern California, Los Angeles, CA 90089, USA, minhsiuh@gmail.com
Arne Jensen Department of Mathematical Sciences, Aalborg University, Fr. Bajers Vej 7G, 9220 Aalborg O, Denmark, matarne@math.aau.dk
Jürg Käppeli Institut für Physik, Humboldt Universität, Berlin, Germany, kaeppeli@aei.mpg.de
Yasuyuki Kawahigashi Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan, yasuyuki@ms.u-tokyo.ac.jp
Alexander Kiselev Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA, kiselev@math.wisc.edu
Abel Klein Department of Mathematics, University of California, Irvine, CA 92697-3875, USA, aklein@uci.edu
Axel Kleinschmidt Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476 Potsdam, Germany, axel.kleinschmidt@aei.mpg.de; Present address: Service de Physique Théorique et Mathématique, Université Libre de Bruxelles & International Solvay Instititutes, Campus Plaine CP231, Boulevard du Triomphe, 1050 Bruxelles, Belgium, axel.kleinschmidt@ulb.ac.be
Herbert Koch Mathematical Institute, University of Bonn, Beringstraße 1, 53115 Bonn, Germany, koch@math.uni-bonn.de
Oleg Kozlovski Mathematics Institute Zeeman Building, University of Warwick, Coventry CV4 7AL, England, UK, oleg@maths.warwick.ac.uk
Igor Krasovsky Department of Mathematical Sciences, Brunel University West London, Uxbridge UB83PH, UK, Igor.Krasovsky@brunel.ac.uk
Dirk Kreimer CNRS at Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France; Center for Mathematical Physics, Boston University, 111 Cummington Street, Boston, MA 02215, USA, kreimer@ihes.fr
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Contributors |
Antti Kupiainen Department of Mathematics, Helsinki University, P.O. Box 4, 00014 Helsinki, Finland, ajkupiai@mappi.helsinki.fi
Giovanni Landi Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy; INFN, Sezione di Trieste, Trieste, Italy, landi@units.it
Elliot H. Lieb Departments of Mathematics and Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, NJ 08544, USA, lieb@princeton.edu
P.H.S. Lima Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo SP, Brasil, plima@ime.usp.br
Marcos Mariño Département de Physique Théorique and Section de Mathématiques, Université de Genève, 1211 Genève 4, Switzerland, marcos.marino@unige.ch
Fabio Martinelli Dip. Matematica, Univ. Roma Tre, Largo S.L. Murialdo, 00146, Rome, Italy, martin@mat.uniroma3.it
Davide Masoero SISSA, via Beirut 2-4, 34014 Trieste, Italy, masoero@sissa.it
Marco Merkli Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada, merkli@mun.ca
Jens Mund Departamento de Física, ICE, Univ. Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil, mund@fisica.ufjf.br
Giuseppe Mussardo International School for Advanced Studies, Via Beirut 1, 34013 Trieste, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Trieste, Italy, mussardo@sissa.it
Bruno Nachtergaele Department of Mathematics, University of California, Davis, CA 95616, USA, bxn@math.ucdavis.edu
Gheorghe Nenciu Faculty of Physics, University of Bucharest, P.O. Box MG 11, 077125 Bucharest, Romania; Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania, Georghe.Nenciu@imar.ro
Charles M. Newman Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA, newman@courant.nyu.edu
Stéphane Nonnenmacher Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, CEA/Saclay, 91191 Gif-sur-Yvette, France, snonnenmacher@cea.fr
Stefano Olla Ceremade, UMR CNRS 7534, Université de Paris Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France, olla@ceremade.dauphine.fr
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Enrique R. Pujals IMPA, Estr. Dona Castorina 110, CEP 22460-320, Rio de Janeiro, R.J., Brazil, enrique@impa.br
Cyril Roberto L.A.M.A., Univ. Marne-la-Vallée, 5 bd Descartes, 77454 Marne-la- Vallée, France, cyril.roberto@univ-mlv.fr
Benjamin Schlein DPMMS, University of Cambridge, Wilberforce Rd., Cambridge, CB3 0WB, UK
Kareljan Schoutens Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, kjs@science.uva.nl
Robert Seiringer Departments of Mathematics and Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, NJ 08544, USA, rseiring@princeton.edu
Robert Sims Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA, rsims@math.arizona.edu
Jan Philip Solovej Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark, solovej@math.ku.dk
Alexander Soshnikov Department of Mathematics, University of California at Davis, One Shields Ave., Davis, CA 95616, USA, soshniko@math.ucdavis.edu
Herbert Spohn Zentrum Mathematik and Physik Department, TU München, Boltzmannstr. 3, 85747 Garching, Germany, spohn@ma.tum.de
Daniel L. Stein Physics Department and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA, daniel.stein@nyu.edu
Sebastian van Strien Mathematics Department, University of Warwick, Coventry CV4 7AL, England, UK, strien@maths.warwick.ac.uk
Toufic M. Suidan Department of Mathematics, The University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, AZ 85721-0089, USA, tsuidan@math.arizona.edu
Tatiana A. Suslina Faculty of Physics, St. Petersburg State University, Ulyanovskaya, 3, St. Petersburg 198504, Russian Federation, suslina@list.ru
Junji Suzuki Department of Physics, Shizuoka University, Ohya 836, SURUGA, Shizuoka, Japan, sjsuzuk@ipc.shizuoka.ac.jp
Roberto Tateo Dip. di Fisica Teorica and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy, tateo@to.infn.it
Jörg Teschner DESY Theory, Notkestr. 85, 22603 Hamburg, Germany, teschner@mail.desy.de
Stefan Theisen Max-Planck-Institut für Gravitationsphysik, Albert-Einstein- Institut, Golm, Germany, theisen@aei.mpg.de
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Contributors |
Cristina Toninelli LPMA and CNRS UMR 7599, Univ. Paris VI–VII, 4, Pl. Jussieu, 75252 Paris Cedex 05, France, cristina.toninelli@upmc.fr
Craig A. Tracy Department of Mathematics, University of California, Davis, CA 95616, USA, tracy@math.ucdavis.edu
Pierre Vanhove CEA/DSM/SPhT, URA au CNRS, CEA/Saclay, 91191 Gif-sur- Yvette, France, pierre.vanhove@cea.fr
Harold Widom Department of Mathematics, University of California, Santa Cruz, CA 95064, USA, widom@ucsc.edu
Jakob Yngvason Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria; Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna, Austria, jakob.yngvason@univie.ac.at
Ofer Zeitouni Faculty of Mathematics, Weizmann Institute, Rehovot, Israel; School of Mathematics, University of Minnesota, Minneapolis, USA, zeitouni@math.umn.edu