Asymptotic Combinatorics with Application to Mathematical Physics

Preface. Program. List of participants. Part One: Matrix Models and Graph Enumeration. Matrix Quantum Mechanics; V. Kazakov. Introduction to matrix models; E. Brézin. A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures; V. Buslaev, L. Pastur. Combinatorics and Probability of Maps; V.A. Malyshev. The Combinatorics of Alternating Tangles: from theory to computerized enumeration; J.L. Jacobsen, P. Zinn-Justin. Invariance Principles for Non-uniform Random Mappings and Trees; D. Aldous, J. Pitman. Part Two: Integrable Models (of Statistical Physics and Quantum Field Theory). Renormalization group solution of fermionic Dyson model; M.D. Missarov. Statistical Mechanics and Number Theory; H.E. Boos, V.E. Korepin. Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation; V.P. Maslov. Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D; D.S. Grebenkov. Part Three: Representation Theory. Notes on homogeneous vector bundles over complex flag manifolds; S. Igonin. Representation Theory and Doubles of Yangians of Classical Lie Superalgebras; V. Stukopin. Idempotent (asymptotic) Mathematics and the Representation theory; G.L. Litvinov, et al. A new approach to Berezin kernels and canonical representations; G. van Dijk. Theta Hypergeometric Series; V.P. Spiridonov.