1. N. Anantharaman, H. Koch, S. Nonnenmacher, Entropy of Eigenfunctions 2. G. Benfatto, Rigorous construction of Luttinger liquids through Ward identities 3. C. Bergbauer, D. Kreimer, New algebraic aspects of perturbative and non-perturbative Quantum Field Theory 4. P. Bleher, Exact solution of the Six-vertex model with domain wall boundary conditions 5. M. Bojowald, mathematical issues in loop quantum cosmology 6. L. Bertini, S. Brassesco, P. Butta, Boundary effects on the interface dynamics for the stochastic Allen-Cahn equation. 7. J. Buzzi, Dimensional entropies and semi-uniform hyperbolicity 8. F. Camia, The scaling limit of (Near-) critical 2D percolation 9. G.L. Cardoso, Black hole entropy function and duality 10. J. Colliander, Weak turbulence for periodic NLS 11. S. Dain, Angular momentum-mass inequality for axisymmetric black holes 12. D. Damanik, Almost everything about the Fibonacci operator 13. I. Davetak, T. Brun, M.-H. Hsieh, Entanglement-assisted quantum error-correcting codes 14. G. Delfino, Particle decay in Ising field theory with magnetic field 15. B. Derrida, Fluctuations and large deviations in non-equilibrium systems 16. L. Diaz, Robust heterodimensional cycles and tame dynamics 17. B. Dubrovin, Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions 18. P. Fendley, K. Schoutens, Lattice supersymmetry from the ground up 19. L.R.G. Fontes, P.H.S. Lima, Convergence of symmetric trap models in the hypercube 20. F. Guerra, Spontaneous replica symmetry breaking in the mean field spin glass model 21. S. Gukov, Surface Operators and Knot Homologies 22. Y. Kawahigashi, Conformal Field Theory and Operator Algebras. 23. A. Kiselev, Diffusion and mixing in fluid flow: a review 24. F. Germinet, A. Klein, Random Schrodingeroperators: Localization and delocalization, and all that 25. A. Kleinschmidt, Unifying R-symmetry in M-theory 26. O. Kozlovski, S. van Strien, Stable maps are dense in dimension one 27. I. Krasovsky, large gap asymptotics for random matrices 28. G. Landi, Noncommutatiove manifolds and quantum groups 29. M. Marinho, Topological strings on local curves 30. M. Merkli, Repeated interaction quantum systems 31. J. Mund, String-localized quantum fields, modular localization, and gauge theories 32. G. Mussardo, Kinks and particles in non-integrable Quantum Field Theory 33. A. Jensen, G. Nenciu, Exponential decay laws in perturbation theory of threshold an embedded eigenvalues 34. S. Olla, Energy diffusion and superdiffusion in oscillators lattice networks 35. E.R. Pujals, Trying to characterize robust and generic dynamics 36. B. Schlein, Dynamics of Bose-Einstein condensates 37. B. Nachtergaele, R. Sims, Locality estimates for quantum spin systems 38. A. Soshnikov, On reseolvent identities in Gaussian ensembles at the edge of the spectrum 39. H. Spohn, Energy current correlations for weakly anharmonic lattices 40. C.M. Newman, D.L. Stein, Metastates, translation ergodicity, and simplicity of thermodynamic states in disordered systems: an illustration 41. M.Sh. Birman, T.A. Suslina, Homogenization of periodic differential operators as a spectral threshold effect 42. P. Dorey, C. Dunning, D. Masoero, J. Suzuki, R. Tateo, ABCD and ODEs 43. J. Teschner, Nonrational conformal field theory 44. C. A. Tracy, H. Widom, The distributions of random matrix theory and their applications 45. J. Kappeli, S. Theisen, P. Vanhove, Hybrid formalism and topological amplitudes 46. M. Aizenman, E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason, Quantum phases of cold bosons in an optical lattice 47. O. Zeitouni, R

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.