Project C6: Groups, buildings, and model theory

Summary:

Buildings were invented by Jacques Tits as a uniform geometric interpretation for the (not necessarily finite) simple groups of Lie type, including the exceptional ones, over arbitrary fields. The focus of this project will be applications of the theory of spherical and affine buildings to questions arising in geometric group theory as well as in the study of algebraic groups over arbitrary fields, so there are close connections with Project C2. Methods from model theory have proven particularly useful in many of the questions studied and we want to continue our investigations. On a more applied side, the graph theoretic definition of buildings allows applications to coding theory.

Recent Preprints: