William Goldman: Crooked geometry

Around 1980 Margulis proved the existence of proper affine actions of nonabelian free groups on 3-space. Later Todd Drumm found polyhedra from which one can build fundamental domains for these properly discontinuous actions. The quotients are geodesically complete flat Lorentzian 3-manifolds and intimately relate to complete hyperbolic surfaces and deformations in which every geodesic lamination infinitesimally lengthens. In this talk I will describe the geometry of these manifolds, polyhedra and group actions, and discuss the classification problem for quotients of R³ by groups of affine transformations.