Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of separation coordinates on the unit sphere
in terms of geometry of Stasheff polytope.
The talk is based on joint works with L. Aguirre and G. Felder and with K.
Schoebel.