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The hypersurface in ${ℂ}^3$ with an isolated quasi-homogeneous elliptic singularity of type ${\tilde{E}}_r,r=6,7,8$, has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type $E_r$ provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we first deform the polynomial algebra $ℂ[x_1,x_2,x_3]$ to a noncommutative algebra with generators $x_1,x_2,x_3$ and the following 3 relations labelled...

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...