Reducible quasi-periodic solutions for the Non Linear Schr\"odinger equation

The present paper is devoted to the construction of small reducible quasi--periodic solutions for the completely resonant NLS equations on a $d$--dimensional torus \T^d. The main point is to prove that prove that the normal form is reducible, block diagonal and satisfies the second Melnikov condition block wise. From this we deduce the result by a KAM algorithm.Comment: 48 page

On the theorem of Amitsur--Levitzki

We present a proof of the Amitsur--Levitzki theorem which is a basis for a general theory of equivariant skew--symmetric maps on matrices.Comment: 3page

An algebro-geometric realization of equivariant cohomology of some Springer fibers

We give an explicit affine algebraic variety whose coordinate ring is isomorphic (as an algebra with the action of the Weyl group) with the equivariant cohomology of some Springer fibers.Comment: 5 page