Alexander Odesski (Max-Planck-Institut für Mathematik)
odesskii@mpim-bonn.mpg.de
The talk is devoted to associative N-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincaré-Birkhoff-Witt condition (PBW-algebras). We will consider examples of such algebras depending on two continuous parameters (namely, on an elliptic curve and a point on this curve) which are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras will be described, together with their relations to integrable systems, deformation quantization, moduli spaces and other directions of modern investigations.