XVIIth International Congress on Mathematical Physics

Preface; Congress Committees; Sponsors; CONTENTS; Prizes; PART A - PLENARY LECTURES; Integrable Combinatorics P. Di Francesco; 1. Introduction; 2. 1+1D Lorentzian gravity, integrability and trees; 2.1. 1+1D Lorentzian gravity; 2.2. Integrability; 2.3. Trees; 3. Planar maps and geodesics; 3.1. Two-dimensional quantum gravity; 3.2. Maps and trees; 3.3. Exact enumeration and integrability; 4. Alternating sign matrices; 4.1. Lambda-determinant and alternating sign matrices; 4.2. Integrabilities: six vertex, loop gas and more; 4.3. ASMs from 6V; 4.4. DPP from lattice paths.

4.5. Proof of the ASM-DPP conjecture5. Discrete integrable systems and cluster algebras; 5.1. T-system and initial data; 5.2. Cluster algebra; 5.3. Properties, applications, conjectures; 5.4. T-system as a sub-cluster algebra; 5.5. Solution and Laurent positivity; 6. Conclusion; References; Piecewise Smooth Perturbations of Integrable Systems D. Dolgopyat; 1. Introduction; 2. Examples; 2.1. Types of final motions; 2.2. Motion in periodic potential; 2.3. Billiards; 2.4. Outer billiards: approach to the boundary; 2.5. Stochastic billiards; 2.6. Outer billiards: unbounded orbits.

2.7. Ulam ping-pong3. Theory; 3.1. Normal form; 3.2. Formal perturbation theory; 4. Conclusion; References; Applications of Random Matrices to Operator Algebra Theory U. Haagerup; References; Reading in the Brain K. Hepp; 1. Introduction; 2. A microcircuit model of eye movement control of reading in thefrontal eye fields; 3. Towards connecting reading and language in brain models; 4. Conclusion; Acknowledgements; References; d = 4, N = 2 Field Theory and Physical Mathematics G.W. Moore; 1. Introduction; 2. d = 4 N = 2 field theory; 3. Wall-crossing 101; 4. Interlude: Defects in local QFT.

5. Wall crossing 1026. Reduction to three dimensions and hyperkahler geometry; 7. Theories of class S; 8. Spectral networks; 9. Conclusions; Acknowledgements; References; Microlocal Singularities and Scattering Theory for Schrodinger Equations on Manifolds S. Nakamura; 1. Very Brief Introduction to Scattering Theory; 1.1. Scattering for the Newton Particle; 1.2. Scattering in the Quantum Mechanics; 2. Scattering for the Geodesic Flow on Asymptotically Conic Manifolds; 2.1. Hamilton Flow on Asymptotically Conic Manifolds; 2.2. Nontrapping Condition and the Existence of Scattering.

2.3. Wave Operators Scattering Operators; 2.4. Euclidean Space - The Scattering Theory in the Polar Coordinate; 2.5. Scattering Matrix; 2.6. Conic Manifolds - The Geodesic Flow in the Boundary Manifold; 3. Quantization (1) - Analysis of Singularities; 3.1. Function Space and Schrodinger Operators; 3.2. Construction of Free Quantum System; 3.3. Construction of the Fundamental Solution; 3.4. Wave Front Set and the Propagation of Singularities; 3.5. The Idea of the Proof - Standard Quantization; 4. Quantization (2) - Microlocal Analysis of Scattering Matrix.

4.1. Construction of Scattering Theory - Wave Operators and the Completeness.

The International Congress on Mathematical Physics is a major conference in its field that attracts a very wide spectrum of researchers. Held every three years, it provides an overview of recent developments and achievements in mathematical physics. This volume presents the plenary lectures and invited topical session lectures from the XVIIth ICMP, which was held in Aalborg, Denmark, August 2012. It also includes additional material from the Congress. In this volume, one can find survey lectures on orthogonal polynomials, random systems, information theory in physics, several aspects of quantum.