  We outline the proof of a conjecture of Kontsevich on the isomorphism between
the group of polynomial symplectomorphisms in $2n$ variables and the group of
automorphisms of the $n$-th Weyl algebra over complex numbers. Our proof uses
lifting of polynomial symplectomorphisms to Weyl algebra automorphisms by means
of approximation by tame symplectomorphisms and gauging of the lifted morphism.
Approximation by tame symplectomorphisms is the symplectic version of the
well-known theorem of D. Anick and is a result of our prior work.
