*The classification of spherical buildings*

Richard Weiss (Tufts University, Medford, Massachusetts)

Jacques Tits gave the classification of spherical buildings of rank at least three in his famous Lecture Notes (1974). The rank two residues of a spherical building of higher rank are Moufang polygons. The classification of Moufang polygons by Tits and the speaker (which appeared in 2001) makes it possible to give a simplified proof of the classification of spherical buildings of rank at least three. We give a brief description of these developments without assuming any familiarity with the theory of buildings.