A.P. Veselov 氏 (Loughborough, UK and Tokyo, Japan)
『 From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way 』

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 integrable n-dimensional tops and separation coordinates on the unit sphere in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K. Schoebel.