CONTENTS -- PREFACE -- CONFERENCE COMMITTEES -- PART A Plenary Talks -- RELATIVE ENTROPIES AND ENTANGLEMENT MONOTONES -- 1. Introduction -- 2. Mathematical preliminaries -- 3. Definitions of min- and max-relative entropies -- 4. Properties of min- and max-relative entropies -- 5. Min- and max-relative entropies and state discrimination -- 6. The min- and max-relative entropies of entanglement -- 7. Smoothed min- and max-relative entropies of entanglement and their operational interpretations -- References -- BINDING, STABILITY, AND NON-BINDING OF MULTI-POLARON SYSTEMS -- 1. Definition and previous rigorous results -- 2. The multi-polaron problem and new results -- 2.1. Binding of multi-polaron systems -- 2.2. Thermodynamic stability of multi-polaron systems -- 3. Absence of bipolaron binding -- 4. Polarons in one dimension -- Acknowledgments -- References -- INTERACTING ELECTRONS ON THE HONEYCOMB LATTICE -- 1. Introduction -- 2. Short range interactions -- 3. Coulomb interactions -- 4. Peierls-Kekulé instability -- 5. Conclusions -- Acknowledgements -- References -- RENORMALIZATION OF DIRAC'S POLARIZED VACUUM -- 1. A nonlinear Dirac equation -- The free vacuum -- Electrons interacting with the polarized vacuum -- 2. Derivation from Quantum Electrodynamics -- 3. Existence and non existence of solutions -- Existence of solutions -- Maximum ionization -- 4. Renormalization -- Nonperturbative charge renormalization formula -- Asymptotic renormalization -- 5. Conclusion -- References -- CONVERGENCE RESULT FOR THICK GRAPHS -- 1. Introduction -- 2. Thick graphs -- 2.1. Definition of a thick graph -- 2.2. Examples of thick graphs -- 2.3. Appearance of thick graphs in Physics and Mathematics -- 3. Neumann Laplacians on thick graphs -- 3.1. Convergence results for Neumann Laplacians -- 3.2. Convergence of operators in different Hilbert spaces.

4. Dirichlet and other Laplacians on thick graphs -- 4.1. Dirichlet Laplacians on thick graphs -- 4.2. Difference between Neumann and Dirichlet case -- 4.3. Other vertex conditions in the limit -- 5. Outlook and open problems -- 5.1. Work in progress and open problems -- 5.2. Conclusion -- Acknowledgements -- References -- SPECTRAL PROPERTIES OF WIGNER MATRICES -- 1. Introduction -- 2. Density of States and the Semicircle Law -- 3. Delocalization of Eigenvectors of Wigner Matrices -- 4. Bulk Universality for Hermitian Wigner Matrices -- 5. Extensions and Applications of Universality -- References -- LIEB-ROBINSON BOUNDS AND QUASI-LOCALITY FOR THE DYNAMICS OF MANY-BODY QUANTUM SYSTEMS -- 1. Introduction -- 2. The General Set-Up -- 2.1. Collections of Quantum Systems -- 2.2. Interactions and Models -- 2.3. Observables and Support -- 2.4. From Locality to Commutators -- 3. Lieb-Robinson Bounds -- 3.1. On the Geometry of Γ -- 3.2. Assumptions on the Interaction Φ -- 3.3. The Main Result -- 4. Some Words on Generalizations and Applications -- 4.1. On Generalizations -- 4.2. On Applications -- Acknowledgments -- References -- DISORDER-INDUCED DELOCALIZATION ON TREE GRAPHS -- Summary -- References -- SEMICLASSICAL SPECTRAL BOUNDS AND BEYOND -- 1. Setting of the Problem. Lieb-Thirring bounds -- 2. Sharp Lieb-Thirring constants -- 3. Further developments -- 4. Logarithmic Lieb-Thirring estimates -- 5. Setting of the problem: Berezin-Li-Yau inequalities -- 6. Pólya-Berezin-Lieb-Li-Yau bounds -- 7. Pólya's conjecture in the presence of magnetic field -- 8. Two-term spectral bounds -- 9. Melas' bound -- 10. Improved Berezin bounds with remainder terms of correct order -- 11. A more geometric second term -- 12. Improving Melas' bound -- Acknowledgements -- References -- THE OTHER PLENARY TALK ABSTRACTS -- SHARP CONSTANTS IN INEQUALITIES ON THE HEISENBERG GROUP.

QUADRATIC FORMS WITHOUT SEMIBOUNDEDNESS -- QUANTUM ENTANGLEMENT IN RANDOM SYSTEMS -- PART B Topical Sessions -- Session in honour of Ari Laptev -- SPECTRAL PROBLEMS IN SPACES OF CONSTANT CURVATURE -- 1. Introduction -- 2. Isoperimetric inequalities for eigenvalues of the Laplacian -- 3. Brézis-Nirenberg problem in Sn and ℍn -- Acknowledgment -- References -- TWO-TERM SPECTRAL ASYMPTOTICS FOR THE DIRICHLET LAPLACIAN ON A BOUNDED DOMAIN -- 1. Introduction and main result -- 1.1. Introduction -- 1.2. Main result -- 1.3. Strategy of the proof -- 2. Local asymptotics -- 2.1. Local asymptotics in the bulk -- 2.2. Straightening the boundary -- 2.3. Local asymptotics in half-space -- 3. Localization -- References -- ON THE ENERGY OF THE MINIMIZERS OF THE GINZBURG-LANDAU FUNCTIONAL FOR EXTERIOR MAGNETIC FIELDS BETWEEN HC2 AND HC3 -- 1. Introduction -- 2. Main results -- 3. About some techniques used in the proof -- 3.1. Reminder for the de Gennes operator -- 3.2. A virial-type result -- 3.3. Bounds on ζ -- 3.4. Proof of Theorem 2.4 -- References -- DECAY LAW FOR RESONANCES PRODUCED BY PERTURBATION OF UNSTABLE EIGENVALUES CLOSE TO A THRESHOLD -- 1. Introduction -- 2. Generalities -- 3. Heuristics -- 4. The model function, regular case -- 5. Main results -- error analysis -- 6. Crossover from exponential to non-exponential decay laws -- The exponential regime -- The bound state regime -- The non-exponential regime -- Acknowledgments -- References -- LOCALIZATION FOR THE RANDOM DISPLACEMENT MODEL -- 1. Introduction -- 2. Lifshitz tail estimates -- 3. Wegner estimate -- Acknowledgment -- References -- CONTRIBUTED TALKS -- LARGE TIME BEHAVIOR OF THE HEAT KERNEL OF TWO-DIMENSIONAL MAGNETIC SCHRÖDINGER OPERATORS AND ITS APPLICATIONS -- CALOGERO-SUTHERLAND TYPE SYSTEMS AND CONFORMAL FIELD THEORY -- Spectral theory.

EXTREMAL FUNCTIONS IN SOME INTERPOLATION INEQUALITIES: SYMMETRY, SYMMETRY BREAKING AND ESTIMATES OF THE BEST CONSTANTS -- 1. Two families of interpolation inequalities -- 2. Existence of extremals -- 3. Symmetry and symmetry breaking -- Acknowledgements -- References -- EFFECTIVE HAMILTONIANS FOR THIN DIRICHLET TUBES WITH VARYING CROSS-SECTION -- 1. The setting -- 2. Basic ideas -- 3. Results -- 4. Discussion of the results -- 5. Conclusions and outlook -- References -- OTHER TALKS -- INVITED TALK -- SPECTRAL MINIMAL PARTITIONS -- CONTRIBUTED TALKS -- HOMOGENIZATION OF THE WAVEGUIDES WITH FREQUENT ALTERNATION BOUNDARY CONDITIONS -- ABSOLUTELY CONTINUOUS SPECTRUM FOR PERIODIC MAGNETIC FIELDS -- RESONANT CYCLOTRON ACCELERATION OF PARTICLES BY A TIME PERIODIC SINGULAR FLUX TUBE -- ABSOLUTELY CONTINUOUS SPECTRUM FOR SUBSTITUTION TREES -- ADIABATIC SPECTRAL ASYMPTOTICS ON FOLIATED MANIFOLDS -- RESONANCES IN QUANTUM GRAPHS -- SPECTRAL PROPERTIES OF LEAKY STAR GRAPH -- WEAK DISORDER IN THE KRONIG-PENNEY MODEL: STABILITY OF THE ABSOLUTELY CONTINUOUS SPECTRUM AND EIGENVALUES IN GAPS -- SELF-ADJOINT EXTENSIONS OF THE AHARONOV-BOHM HAMILTONIAN ON RIEMANNIAN MANIFOLDS -- ON THE SINGULAR BEHAVIOUR OF SPECTRAL DENSITY FOR SCHRÖDINGER OPERATORS WITH WIGNER-VON NEUMANN PERTURBATION -- BOUNDARY TRIPLETS AND A RESULT OF JOST AND PAIS: AN ABSTRACT APPROACH -- ON THE DEGENERATE SPECTRAL GAPS OF THE ONE-DIMENSIONAL SCHRÖDINGER OPERATORS WITH PERIODIC POINT INTERACTIONS -- SPECTRAL PROBLEMS AND QUANTUM FEATURES OF FLUID IN NANOTUBE -- EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES AS A CONSEQUENCE OF STRONG RESOLVENT CONVERGENCE -- ON THE EIGENVALUE PROBLEM FOR A PARTICULAR CLASS OF JACOBI MATRICES -- WEYL LAW FOR LAPLACIANS WITH CONSTANT MAGNETIC FIELD ON NONCOMPACT HYPERBOLIC SURFACES WITH FINITE AREA.

ON THE TWO-DIMENSIONAL COULOMB-LIKE POTENTIAL WITH A CENTRAL POINT INTERACTION -- FRACTIONAL MOMENT METHOD FOR NON-MONOTONE MODELS -- Many body quantum systems -- DIFFUSION IN HAMILTONIAN QUANTUM SYSTEMS -- 1. Model -- 2. Result -- References -- GROUND STATE PROPERTIES IN NON-RELATIVISTIC QED -- 1. Introduction -- 2. Model and analyticity of the ground state -- 3. Expansions in the fine structure constant -- References -- NON-ADIABATIC TRANSITIONS IN A SIMPLE BORN-OPPENHEIMER SCATTERING SYSTEM -- 1. Introduction -- 2. Non-Adiabatic Transitions -- 3. Comments about the Proof -- 4. Generalizations -- References -- CONTRIBUTED TALKS -- ON THE GROUND STATE ENERGY FOR MASSLESS NELSON MODEL -- ON THE IONIZATION ENERGY OF THE SEMIRELATIVISTIC PAULI-FIERZ MODEL -- COMPLETELY LOCAL INTERPRETATION OF MANY-BODY QUANTUM PHENOMENA -- ROTATING ULTRACOLD DIPOLAR GASES -- Quantum chaos -- RELATIONSHIP BETWEEN CHAOS AND THERMALIZATION IN ONE-DIMENSIONAL QUANTUM MANY-BODY SYSTEMS -- 1. Introduction -- 2. Numerical results and conclusions -- References -- QUANTIZED OPEN CHAOTIC SYSTEMS -- 1. Introduction -- 2. Transformation to nonselfadjoint spectral problems -- 2.1. Damped quantum mechanics -- 2.2. Complex scaled scattering Hamiltonian and open dynamics -- 3. Fractal Weyl laws -- 3.1. Spectral gaps -- 4. Open questions -- Acknowledgments -- References -- OTHER TALKS -- INVITED TALK -- CLASSICAL ORBIT CORRELATIONS: THE KEY FOR UNDERSTANDING UNIVERSALITY IN QUANTUM CHAOTIC SYSTEMS -- CONTRIBUTED TALKS -- MANY-PARTICLE SYSTEMS ON QUANTUM GRAPHS WITH SINGULAR INTERACTIONS -- PARAMETER-DEPENDENT SPECTRAL STATISTICS OF QUANTUM GRAPHS -- INTEGRABLE THEORY OF QUANTUM TRANSPORT IN CHAOTIC CAVITIES -- Quantum field theory -- INVITED TALKS -- RENORMALIZATION AND RESOLUTION OF SINGULARITIES -- RENORMALISATION HOPF ALGEBRAS FOR GAUGE THEORIES AND BRST SYMMETRIES.

CONTRIBUTED TALKS.