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The perspectives: applications and generalisations

In: An Algebraic Geometric Approach to Separation of Variables

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  • Konrad Schöbel

    (Friedrich-Schiller-Universität Jena)

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.

Suggested Citation

  • Konrad Schöbel, 2015. "The perspectives: applications and generalisations," Springer Books, in: An Algebraic Geometric Approach to Separation of Variables, chapter 4, pages 121-130, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-11408-4_5
    DOI: 10.1007/978-3-658-11408-4_5
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