Separation coordinates, moduli spaces and Stasheff polytopes K. Schoebel Alexander Veselov 2134/16968 https://repository.lboro.ac.uk/articles/journal_contribution/Separation_coordinates_moduli_spaces_and_Stasheff_polytopes/9385022 We show that the orthogonal separation coordinates on the sphere S n are naturally parametrised by the real version of the Deligne–Mumford–Knudsen moduli space M¯0,n+2(R) of stable curves of genus zero with n + 2 marked points. We use the combinatorics of Stasheff polytopes tessellating M¯0,n+2(R) to classify the different canonical forms of separation coordinates and deduce an explicit construction of separation coordinates, as well as of Stäckel systems from the mosaic operad structure on M¯0,n+2(R) 2015-03-12 12:18:22 Separation of variables Stackel systems Stasheff polytopes Deligne-Mumford-Knudsen moduli spaces Quantum Mechanics Mathematical Sciences not elsewhere classified