CONTENTS -- The International Solvay Institutes -- Board of Directors -- Solvay Scientific Committee for Physics -- 24th Solvay Conference on Physics -- Participants -- Auditors -- Opening Session -- Opening Address by Marc Henneaux -- Opening Address by David Gross -- Opening Address by Bertrand Halperin -- Special Session: On the Quantum Theory of Condensed Matter B. Halperin -- 1. Introduction -- 2. What is "Condensed Matter"? -- 3. Why Quantum Theory -- 4. The Solvay Tradition -- 5. Why This Subject, Now? -- 6. Focus on Collective Effects -- 7. Superconductivity -- 8. Nano-Scale Devices -- 9. Collections of Ultra-Cold Atoms -- 10. Phases and Phase Transitions -- 11. Current Technologies based on Quantum Properties of Condensed Matter Systems -- Session 1: Mesoscopic and Disordered Systems Chair: D. Loss -- Rapporteur talk: Mesoscopic and disordered systems -- Discussion -- Session 2: Exotic Phases and Quantum Phase Transitions in Model Systems Chair: A. Georges -- Rapporteur talk: Exotic phases and quantum phase transi- tions: model systems and experiments -- 1. Abstract -- 2. Introduction -- 3. Coupled Dimer Antiferromagnet -- 4. Quantum "Disordering" Magnetic Order: Spinons and Visons -- 4.1. Spinons -- 4.2. Visons -- 4.3. Solvable model -- 4.4. Field theory of spinons and visons -- 5. Spin Liquids near the Mott Transition -- 6. Exotic Metallic States -- 6.1. Fractionalized Fermi liquids -- 6.2. Algebraic charge liquids -- 7. Experiments on Mott Insulators -- 7.1. Triangular lattice -- 7.2. Kagome lattice -- 7.3. Hyperkagome lattice -- Acknowledgments -- References -- Discussion -- Prepared comment by Matthew Fishera: Spin, Bose and Non- Fermi Liquid Metals in Two-Dimensions: Accessing via Multi- leg Ladders -- 1. Challenges in Mott Materials -- 2. 2D Spin and Bose Metals -- 3. New Quasi-1D Approach to Spin and Bose Metals.

Acknowledgments -- References -- Discussion -- Prepared comment by Michael Freedman: A Topological Phase in a Quantum Gravity Model -- H described for the Dfib phase: -- References -- Discussion -- Prepared Comment by Leon Balents: Some Promising Model Systems for Exotic Phenomena -- Acknowledgements -- References -- Discussion -- Prepared Comment by Matthias Troyer: Quantum Monte Carlo Simulations: Success and Challenges -- 1. Some Applications -- 2. The Negative Sign Problem -- References -- Discussion -- Prepared Comment by Todadri Senthil: Killing the Fermi Sur- face: Towards a Theory of Non-Fermi Liquid Metals -- References -- Discussion -- Prepared Comment by Leticia Cugliandolo: Dissipative Quan- tum out of Equilibrium Dynamics -- References -- Discussion -- Session 3: Experimentally Realized Correlated-Electron Materials Chair: M. Rice -- Rapporteur talk: Experimentally Realized Correlated Elec- tron Materials: From Superconductors to Topological Insu- lators -- 1. Abstract -- 2. Introduction -- 3. Unconventional Superconductors -- 3.1. High temperature cuprate superconductors -- 3.2. Iron pnictide superconductors -- 3.3. Strontium ruthenate -- 4. Frustrated Magnets -- 5. Topological Insulators -- 6. Conclusions -- Acknowledgments -- References -- Discussion -- Prepared Comment by Patrick Lee: Comments on Recent Ad- vances in Iron Pnictides Research -- 1. Abstract -- 2. Introduction -- 3. Strong Correlations or Not? -- 4. Gap Nodes and Pairing Symmetry -- References -- Discussion -- Prepared Comment by Chandra Varma: Scholia on a Remark by C. Kallin -- References -- Discussion -- Prepared Comment by Phuan Ong: Phase Coherence, Vortex Liquid and the Nernst E ect in Cuprate Superconductors -- 1. Phase rigidity of condensate -- 2. Nernst Effect -- 3. Torque Magnetometry -- 4. Phase Diagram -- References -- Discussion.

Prepared Comment by Steve Whitea: Pairing versus Stripes in the t-J Model -- References -- Discussion -- Prepared Comment by Zhi-Xun Shen: the Pseudogap Phe- nomena in High Temperature Superconductors -- 1. Abstract -- A. Doping Dependence [3-5] -- B. Temperature Dependence [4] -- C. Momentum Dependence [6] -- References -- Discussion -- Prepared Comment by Bernd Keimer: Perspectives in Orbital Physics -- 1. Historical Note -- 2. Some Trends in Current Research -- 3. Perspective: Oxide Heterostructures -- References -- Discussion -- Session 4: Quantum Hall Systems, and One-Dimensional Systems Chair: J. Chalker -- Rapporteur Talk by A. Stern: The Quantum Hall E ect - an Overview -- 1. Abstract -- 2. Introduction -- 3. Abelian Quantum Hall States -- 3. Abelian Quantum Hall States -- 4. Non-abelian Quantum Hall States -- 5. Quantum Hall Physics Gets Broader -- 6. Summary -- Acknowledgments -- References -- Discussion -- Prepared Comment by Jim Eisenstein: Prospects for the Quantum Hall Effect -- 1. Introduction -- 2. Opportunities -- 2.1. Anyons: Abelian and otherwise -- 2.2. Edges -- 2.3. Graphene -- 3. Challenges -- 3.1. Crystal growth -- 3.2. Low temperatures -- 4. Conclusion -- References -- Discussion -- Prepared Comment by Nick Read: Quantum Hall Fluctua- tions, Conformal Blocks and Topological Phases of Matter -- 1. Abstract -- 2. Introduction -- 3. Trial Wavefunctions and QH Phases -- 4. Adiabatic Transport -- 5. Trial Wavefunctions as Conformal Blocks -- 6. Perturbed CFTs -- 7. Topological Phases of Matter -- 8. Hall Viscosity -- 9. Conclusion -- References -- Rapporteur Talk by I. A eck: One Dimensional Quantum Condensed Matter -- 1. Introduction -- 2. Beyond the Luttinger Model -- 3. Quasi 1D Antiferromagnets -- 4. Non-Fermi Liquid Kondo E ects -- 5. Stripes in Hubbard and t-J ladders -- 6. Conclusions -- Acknowledgments -- References.

Discussion -- Session 5: Systems of Ultra-Cold Atoms, and Advanced Computational Methods Chair: P. Zoller -- Rapporteur talk by I. Bloch: Strongly Correlated Quantum Systems with Ultracold Atoms in Optical Lattices -- 1. Abstract -- 2. Introduction -- 3. Optical Lattices -- 3.1. Optical dipole force -- 3.2. Optical lattice potentials -- 4. Detection Methods -- 4.1. Time-of-flight and adiabatic mapping -- 4.2. Detection of correlations -- 5. Realizations of Strongly Correlated Phases in Optical Lattices -- 5.1. Hubbard physics -- 5.1.1. Low-Dimensional quantum systems -- 6. Outlook: Novel Systems and Detection Methods -- 6.1. Novel systems -- 6.2. Novel detection methods -- References -- Discussion -- Rapporteur Talk by S. R. White: Numerical Methods Using Matrix and Tensor Product Wavefunctions -- 1. Abstract -- 2. Introduction -- 3. Matrix Product States -- 4. Generalizations of DMRG and MPS -- 5. Two Dimensions -- 6. Conclusions -- Acknowledgments -- References -- Discussion -- Prepared Comment by Assa Auerbacha: Transport Studies of Lattice Bosons: Paradigms for Fluctuating Superconductivity -- 1. Strongly Fluctuating Superconductors -- 1.1. The Model -- 1.2. Hall conductivity -- 1.3. V-spins of vortices at half filling -- 1.4. Vortex mass, and vortex lattice melting -- References -- Discussion -- Closing Session Chair of the conference Bertrand Halperin.