Integration of differential equations is a relevant challenge in arithmetic and a number of other methods were constructed by way of learning analytic, algebraic, and algorithmic elements of the topic. the sort of is Differential Galois idea, built by way of Kolchin and his institution, and one other originates from the Soliton thought and Inverse Spectral rework technique, which used to be born within the works of Kruskal, Zabusky, Gardner, eco-friendly and Miura. Many different ways have additionally been built, yet there has thus far been no intersection among them. This distinctive creation to the topic eventually brings them jointly, with the purpose of beginning interplay and collaboration among those quite a few mathematical groups. the gathering incorporates a LMS Invited Lecture direction by way of Michael F. Singer, including a few shorter lecture classes and evaluation articles, all dependent upon a mini-program held on the overseas Centre for Mathematical Sciences (ICMS) in Edinburgh.

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