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ИСТИНА ЦЭМИ РАН |
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Integrable systems have been studied intensively for the last several decades interacting with representation theory, combinatorics and physics. Noncommutative extension of them have also been one of the main topics, such as, extension to matrix valued systems, to noncommutative spaces and so on. As for construction of exact solutions of the noncommutive integrable systems, quasideterminants play crucial roles. Quasideterminants are first introduced by I.M. Gelfand and V. Retakh in 1991. (For a good survey, see e.g. I. Gelfand, S. Gelfand, V. Retakh, R. Wilson, ``Quasideterminants.'') Many achievements have been made over the next 30 years, however, there are many things to be seen: especially in integrable systems, theory of noncommutative tau-functions, noncommutative Pfaffians and so on. It is time to review the developments from various viewpoints, to clarify important problems and discuss further perspectives. This workshop is held to achieve these objectives. The first week is arranged to be a school for students and non-experts on these topics and the second week is mostly devoted to research talks contributed by registered speakers. The topics cover noncommutative integrable systems (e.g. matrix valued systems, integrable systems on noncommutative spaces, noncommutative solitons and quantum integrable systems) and related mathematics and physics.