Opposition diagrams for automorphisms of spherical buildings

Abstract: The opposition relation is fundamental in Tits' theory of spherical and twin buildings. When studying automorphisms of such buildings it is of course natural to consider fixed element structures, however it is also useful to investigate the structure of the elements mapped to opposite elements by the automorphism. In this talk we discuss recent developments in this theory. This is joint work with Hendrik Van Maldeghem (Gent University).