Seminar

In 1964  L. Auslander conjectured that every crystallographic subgroup $\Gamma$ of the affine group $\text{Aff}(\mathbb R^n)$ is virtually solvable, i.e. contains a solvable subgroup of finite index. D.~Fried and W.~Goldman proved Auslander's conjecture for $n=3$ using cohomological arguments.  We (H. Abels G. Margulis, G.Soifer) proved the Auslander conjecture for $n < 7$. The proof is based mainly on dynamical arguments. The talk is divided into three parts: (1) What is proved. (2) The main ideas and methods. (3) Open problems.