## Topology & Geometric Group Theory Seminar

## Fall 2007

### 1:30 - 2:30, Malott 253

Tuesday, September 11

**Ken Brown**,
Cornell University

*Automorphisms of buildings have infinite displacement*

Buildings were introduced by Jacques Tits in order to provide a
unified geometric framework for understanding semisimple complex Lie
groups and, later, semisimple algebraic groups over an arbitrary
field. In this talk, which describes joint work with Peter Abramenko,
I will sketch the proof of a geometric theorem about buildings, and I
will show how it yields concrete information about groups. The
geometric theorem is stated in the title. The group-theoretic
consequence is that automorphism groups of buildings typically have
trivial center.

I will try to keep the prerequisites to a minimum. In particular, the
talk will include an introduction to buildings.

Back to seminar home page.