# Mathematical Sciences Research Institute

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# Seminar

Lorentzian geometric structures seminar: Affine crystallographic and properly discontinuous groups April 27, 2015 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: Dynamics on Moduli Spaces of Geometric Structures MSRI: Baker Board Room
Speaker(s) Grigory Soifer (Bar-Ilan University)
Description No Description
Video
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.