Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.

LECTURES ; 1. Quantum impurity problems in condensed matter physics ; 2. Conformal field theory and statistical mechanics ; 3. Quantum Hall effect ; 4. Topological quantum phases and quantum computation ; 5. Four lectures on computational statistical physics ; 6. Loop models ; 7. Lectures on the integrability of the 6-vertex model ; 8. Mathematical aspects of 2D phase transitions ; 9. Numerical simulations of quantum statistical mechanics models ; 10. Rapidly rotating atomic Bose gases ; 11. Quantum Hall effect ; 12. The dimer model ; 13. Boundary loop models and 2D quantum gravity ; 14. Real-space condensation in stochastic mass transport models ; 15. Quantum spin liquids ; 16. Super spin chains and super sigma models: a short introduction ; 17. Integrability and combinatorics: selected topics ; SEMINARS ; 18. A rigorous perspective on Liouville quantum gravity and KPZ ; 19. Topologically protected qubits based on Josepshon junction arrays ; 20. On some quantum Hall states with negative flux ; 21. Supersolidity and what soluble models can tell us about it

State of the art lectures in a fast growing field Written from a pedagogical perspective Presents fundamental issues in statistical mechanics Provides guidance to a new and highly challenging research field Widespread applications in different areas of science and technology

State of the art lectures in a fast growing field Written from a pedagogical perspective Presents fundamental issues in statistical mechanics Provides guidance to a new and highly challenging research field Widespread applications in different areas of science and technology