Buildings: Skyscrapers in the Cities of Incidence Geometry and Groups
by
Hendrik Van Maldeghem
Pure Mathematics and Computer Algebra, Ghent University, B-9000 Ghent.

Buildings are geometric/group theoretic structures introduced by Jacques Tits in the early sixties. The aim of this talk is to let the audience become acquainted with this notion and with the developments since the beginning. Although we are mainly concerned about the pure theory, we will occasionally point at some applications.

In the first part of the talk, we explain the notion of a building and its diagram, and we review some highlights in the history of buildings, emphasizing classification results (spherical buildings, affine buildings, twin buildings, Moufang buildings) and the relation with groups (finite groups, groups with a BN-pair, algebraic groups, Lie groups, Kac-Moody groups). In the second part we mention some recent results, mainly concerning buildings of low rank (rank 1 and rank 2) in relation with groups (`split' BN-pairs of rank 1 and 2).

Date received: February 27, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-49.