Differential Equations and Quantum Groups

This collection of papers is centred around topics of research of the late Andrei A. Bolibrukh. It starts with two short survey papers. The first one (written by Y. Ilyashenko) describes two Bolibrukh results (a sufficient condition for the solvability of the Riemann-Hilbert problem for Fuchsian systems and a discussion of the reduction to Birkhoff standard form). The second one (by C. Sabbah) contains a discussion of isomonodromic deformations and isomonodromic confluences.
Then there are ten other research contributions on various themes including a study of relations between two notions of integrability (M. Audin), formal power series solutions of the heat equation (W. Balser), master functions and the Schubert calculus on flag manifolds (P. Belkale, E. Mukhin and A. Varchenko), explicit solutions of the Riemann-Hilbert problem (P. Boalch), Galois theory for linear differential equations of a certain type (P. J. Cassidy, M. F. Singer), reductions of the Schlesinger equations (B. Dubrovin, M. Mazzocco), the Riemann-Hilbert correspondence for generalized KZ equations (V. A. Golubeva), monodromy groups of regular systems (V. P. Kostov), monodromy of Cherednik-Kohno-Veselov connections (V. P. Leksin) and finally a review of basic ideas of general differential Galois theory for ordinary differential equations (H. Umemura). The whole volume is dedicated to the memory of A. A. Bolibrukh and it gives an overview of recent results in the fields of his research interests.

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