************ Technion Geometry and Topology Seminar ************ TIME AND PLACE: Thursday, November 17, 2011, Amado 919, 15:30-16:30 SPEAKER: Jean Lecureux (Technion) TITLE: An introduction to buildings, part IV 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 future schedule of the G&T seminar see: <http://www.technion.ac.il/~sageevm/> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Michah Sageev <sageevm@math.technion.ac.il>