************ Technion Geometry and Topology Seminar ************
 
TIME AND PLACE: Thursday, Nov. 3, 2011, Amado 919, 15:30-16:30
 
SPEAKER: Jean Lecureux (Technion)
 
TITLE: An introduction to buildings (Part 2 of a 4 part lecture series)
 
ABSTRACT: Buildings are combinatorial and geometric object
introduced by J. Tits in the 60's. They are simplicial
complexes, or more generally cell complexes, obtained by gluing
different copies of a same tessellation, subject to incidence
axioms. One of the main feature of buildings is that they are
nonpositively curved spaces.
 
The main historical reason for studying buildings is that they
are acted upon by very interesting groups: all simple algebraic
groups act on "spherical buildings", and simple algebraic groups
over local fields act on "affine buildings". From these actions,
we can deduce properties of the groups: for example, Tits gave a
uniform proof of the abstract simplicity of simple algebraic
groups. There are also some more exotic groups acting on
buildings; the geometry of the buildings imply that they share
many interesting properties with algebraic groups.
 
After the basic definitions and the combinatorial and metric
approach to buildings, I will explain the construction of the
classical examples and also some classification and rigidity
results in these case. In the last part of the talk, I will give
a recent construction of boundaries of buildings (joint with P-E
Caprace) which is useful in particular to understand amenable
groups acting on buildings.
 
For the schedule of the Geometry and Topology Seminar, see::  
 
 <http://www.technion.ac.il/~sageevm/>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Michah Sageev   <sageevm@math.technion.ac.il>