The perspectives: applications and generalisations

Konrad Schöbel ()
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Konrad Schöbel: Friedrich-Schiller-Universität Jena

Chapter 4 in An Algebraic Geometric Approach to Separation of Variables, 2015, pp 121-130 from Springer

Abstract: Abstract We have proposed a new, purely algebraic geometric approach to the problem of separation of variables and we have demonstrated that this approach is viable by successfully carrying it out for the simplest non-trivial family of examples – that of spheres. In particular, we elucidated the natural algebro-geometric structure of the parameter space classifying equivalence classes of separation coordinates, which for a long time had only been known as a mere set, and gave a precise description of its topology. In this way we discovered that the theory of Deligne-Mumford-Knudsen moduli spaces and Stasheff polytopes provides the right framework for the classification and construction of all orthogonal separation coordinates on spheres.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-658-11408-4_5

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DOI: 10.1007/978-3-658-11408-4_5

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