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 IRMA Lectures in Mathematics and Theoretical Physics 2006; 302 pp; softcover Volume: 9 ISBN-10: 3-03719-020-5 ISBN-13: 978-3-03719-020-3 List Price: US$54 Member Price: US$43.20 Order Code: EMSILMTP/9 See also: Hamiltonian Systems and Their Integrability - Michele Audin This special volume is dedicated to the memory of Andrey A. Bolibrukh. It contains two expository articles devoted to some aspects of Bolibrukh's work, followed by ten refereed research articles. Topics cover complex linear and nonlinear differential equations and quantum groups: monodromy, Fuchsian linear systems, Riemann-Hilbert problem, differential Galois theory, differential algebraic groups, multisummability, isomonodromy, Painlevé equations, Schlesinger equations, integrable systems, KZ equations, complex reflection groups, and root systems. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in differential equations and quantum groups. Table of Contents Y. Ilyashenko -- Realization of irreducible monodromy by Fuchsian systems and reduction to the Birkhoff standard form (by Andrey Bolibrukh) C. Sabbah -- The work of Andrey Bolibrukh on isomonodromic deformations M. Audin -- Two notions of integrability W. Balser -- Formal power series solutions of the heat equation in one spatial variable P. Belkale, E. Mukhin, and A. Varchenko -- Multiplicity of critical points of master functions and Schubert calculus P. Boalch -- Some explicit solutions to the Riemann-Hilbert problem P. J. Cassidy and M. F. Singer -- Galois theory of parameterized differential equations and linear differential algebraic groups B. Dubrovin and M. Mazzocco -- On the reductions and classical solutions of the Schlesinger equations V. A. Golubeva -- On the Riemann-Hilbert correspondence for generalized Knizhnik-Zamolodchikov equations for different root systems V. P. Kostov -- Monodromy groups of regular systems on the Riemann sphere V. P. Leksin -- Monodromy of Cherednik-Kohno-Veselov connections H. Umemura -- Invitation to Galois theory List of Participants