On exceptional nilpotents in semisimple Lie algebras

Let G be a connected semisimple algebraic group defined over complex number C and let g:=Lie G, r:=rank G. It is well known that for all x from G centralizer Z(x)
has dimension bigger or equal then r. Moreover, there exists only one orbit Ge
of nilpotent elements e such that dim(z(e))=r. Such nilpotent elements are called principal ones. By Morozov-Jacobson theorem each nipotent element e can be embedded in a 3-dimensional simple subalgebra, with basis  (f,h,e) in g.

Other nilpotents are called exceptional ones. I plan to explain in my talk classification of all exceptional nilpotent elements in all semisimple Lie algebras

The talk is based on a joint paper by E.B.Vinberg, V.G.Kac, and A.G.Elashvili.