Asymptotic Combinatorics with Applications to Mathematical Physics: A European Mathematical Summer School Held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 (Lecture Notes in Mathematics)

At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras. Random matrices, orthogonal polynomials and Riemann – Hilbert problem.- Asymptotic representation theory and Riemann – Hilbert problem.- Four Lectures on Random Matrix Theory.- Free Probability Theory and Random Matrices.- Algebraic geometry,symmetric functions and harmonic analysis.- A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group.- Random trees and moduli of curves.- An introduction to harmonic analysis on the infinite symmetric group.- Two lectures on the asymptotic representation theory and statistics of Young diagrams.- III Combinatorics and representation theory.- Characters of symmetric groups and free cumulants.- Algebraic length and Poincar series on reflection groups with applications to representations theory.- Mixed hook-length formula for degenerate a fine Hecke algebras.