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Kontsevich conjecture KC_n: Is it true that the Automorphism group of the Weil algebra (the algebra of differential operators generated by $x_1, ... ,x_n, \partial x_1, ... ,\partial x_n$) is isomorphic to the polynomial symplectomorphism group of $C^{2n}$? The talk is devoted to this conjecture and its relations with the problem: is it true that $aut(aut(C^n))$ contains only inner automorphisms? We can prove that for regular ones.