Buildings: Interactions with Algebra and Geometry

Abstract

The focus of the conference was on buildings and their applications. Buildings are combinatorial structures (metric cell complexes) which may be viewed as simultaneous generalizations of trees and projective spaces. There is a rich class of groups acting on buildings; the action can often be used to obtain structural results about the group itself. On the other hand, buildings and related metric spaces — such as Riemannian symmetric spaces, p-adic symmetric spaces, metric CAT(0)-complexes - form an interesting class of geometric structures with a high degree of symmetry. In the last years, there were several new developments in the applications of buildings in arithmetic geometry, Riemannian geometry, representation theory, and geometric group theory. The workshop brought together experts from these areas whose work is related to buildings.