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.
Author(s): Daniel Bertrand; Benjamin Enriquez; Claude Mitschi; Claude Sabbah; and Reinhard Schäfke
Series: IRMA lectures in mathematics and theoretical physics, vol.9
Edition: 1., Aufl.
Publisher: European Mathematical Society
Year: 2006
Language: English
Pages: 302
Tags: Математика;Вычислительная математика;
Preface......Page 5
Table of Contents......Page 9
Realization of irreducible monodromy by Fuchsian systems and reduction to the Birkhoff standard form(by Andrey Bolibrukh)......Page 11
The work of Andrey Bolibrukh on isomonodromic deformations......Page 19
Two notions of integrability......Page 37
Formal power series solutions of the heat equation in one spatial variable......Page 59
Multiplicity of critical points of master functions and Schubert calculus......Page 69
Some explicit solutions to the Riemann–Hilbert problem......Page 95
Galois theory of parameterized differential equations and linear differential algebraic groups......Page 123
On the reductions and classical solutions of the Schlesinger equations......Page 167
On the Riemann–Hilbert correspondence for generalized Knizhnik–Zamolodchikov equations for different root systems......Page 199
Monodromy groups of regular systemson the Riemann sphere......Page 219
Monodromy of Cherednik–Kohno–Veselov connections......Page 265
Invitation to Galois theory......Page 279
List of Participants......Page 301
