This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

"This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area."

Entropy of Eigenfunctions.- Stability of Doubly Warped Product Spacetimes.- Rigorous Construction of Luttinger Liquids Through Ward Identities.- New Algebraic Aspects of Perturbative and Non-perturbative Quantum Field Theory.- Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions.- Mathematical Issues in Loop Quantum Cosmology.- Boundary Effects on the Interface Dynamics for the Stochastic Allen-Cahn Equation.- Dimensional Entropies and Semi-Uniform Hyperbolicity.- The Scaling Limit of (Near-)Critical 2D Percolation.- Black Hole Entropy Function and Duality.- Weak Turbulence for Periodic NLS.- Angular Momentum-Mass Inequality for Axisymmetric Black Holes.- Almost Everything About the Fibonacci Operator.- Entanglement-Assisted Quantum Error-Correcting Codes.- Particle Decay in Ising Field Theory with Magnetic Field.- Fluctuations and Large Deviations in Non-equilibrium Systems.- Robust Heterodimensional Cycles and Tame Dynamics.- Hamiltonian Perturbations of Hyperbolic PDEs: from Classification Results to the Properties of Solutions.- Lattice Supersymmetry from the Ground Up.- Convergence of Symmetric Trap Models in the Hypercube.- Spontaneous Replica Symmetry Breaking in the Mean Field Spin Glass Model.- Surface Operators and Knot Homologies.- Conformal Field Theory and Operator Algebras.- Diffusion and Mixing in Fluid Flow: A Review.- Random Schrödinger Operators: Localization and Delocalization, and All That.- Unifying R-Symmetry in M-Theory.- Stable Maps are Dense in Dimensional One.- Large Gap Asymptotics for Random Matrices.- On the Derivation of Fourier's Law.- Noncommutative Manifolds and Quantum Groups.- Topological Strings on Local Curves.- Repeated Interaction Quantum Systems.- String-Localized Quantum Fields, ModularLocalization, and Gauge Theories.- Kinks and Particles in Non-integrable Quantum Field Theories.- Exponential Decay Laws in Perturbation Theory of Threshold and Embedded Eigenvalues.- Energy Diffusion and Superdiffusion in Oscillators Lattice Networks.- Trying to Characterize Robust and Generic Dynamics.- Dynamics of Bose-Einstein Condensates.- Locality Estimates for Quantum Spin Systems.- On Resolvent Identities in Gaussian Ensembles at the Edge of the Spectrum.- Energy Current Correlations for Weakly Anharmonic Lattices.- Metastates, Translation Ergodicity, and Simplicity of Thermodynamic States in Disordered Systems: an Illustration.- Random Matrices, Non-intersecting Random Walks, and Some Aspects of Universality.- Homogenization of Periodic Differential Operators as a Spectral Threshold Effect.- ABCD and ODEs.- Nonrational Conformal Field Theory.- Kinetically Constrained Models.- The Distributions of Random Matrix Theory and their Applications.- Hybrid Formalism and Topological Amplitudes.- Quantum Phases of Cold Bosons in an Optical Lattice.- Random Walks in Random Environments in the Perturbative Regime.