Richard Weiss

Abstract: We give a brief introduction to the theory of buildings in which buildings appear as certain edge-colored graphs (and the number of colors is the rank of the building). Spherical buildings of rank 2 are also called generalized polygons. Those generalized polygons which arise as "residues" in spherical buildings of higher rank all satisfy the Moufang condition (a certain symmetry property). Moufang polygons have been classified (2002) by Tits and the speaker. We describe how this classification leads to a simplified proof of Tits' classification (1974) of spherical buildings of rank at least 3.   

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