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The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

Many-body problem --- Civil & Environmental Engineering --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Atomic Physics --- Applied Physics --- Operations Research --- Many-body problem. --- Mathematics. --- n-body problem --- Problem of many bodies --- Problem of n-bodies --- Math --- Mathematical physics. --- Phase transformations (Statistical physics). --- Condensed materials. --- Condensed matter. --- Superconductivity. --- Superconductors. --- Mathematical Physics. --- Quantum Gases and Condensates. --- Strongly Correlated Systems, Superconductivity. --- Science --- Mechanics, Analytic --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Physical mathematics --- Materials --- Mathematics --- Vielteilchentheorie. --- Cetraro <2010> --- Quantum statistics. --- Quantum statistical mechanics --- Matrix mechanics --- Statistical mechanics --- Wave mechanics