### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

SEPTEMBER 19, 2014

**Speaker: **
Bill Goldman, University of Maryland

**Title: ***
Three-dimensional affine crystals
*

**Abstract:**
Crystallographers in the 19th century developed the notion of a crystallographic group to express the geometric symmetries of crystals. The classical theorems of Bieberbach gives a qualitative classification of crystallographic groups in terms of finite groups of integer matrices. In modern terms, this led to to the classification of discrete groups of isometries of Euclidean space, or, equivalently, Riemannian manifolds of zero curvature. The more general theory in affine geometry is much richer and more interesting. In this talk I will describe the recent classification in dimension three, and the intricate relationships to hyperbolic non-Euclidean geometry as well as the geometry of special relativity.

**Time:** Friday, September 19, 2014, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491