Manchester Geometry Seminar 2004/2005

Consider the problem of classifying right ideals of the Weyl algebra A= C/{xy-yx=1} up to isomorphism. Then a beautiful theorem due to Berest and Wilson says that the isoclasses of ideals of A are in 1-1 correspondence with the points of some nice algebraic varieties called Calogero-Moser spaces. We give a new explicit construction of this correspondence by passing through a third space of certain strongly homotopy modules over A. The result can be viewed as a noncommutative deformation of the well-known description of the Hilbert scheme of points on the complex plane. This is our joint work with Yuri Berest (mathQA/0410194).