The aim of the project is to determine the automorphism groups of prominent geometric structures—some of them are new, some of them relate to important long standing open problems). All geometries are related to Tits Buildings, introduced by Abel prize recipient Jacques Tits in the 60s of last century, and thus have a strong link with algebraic structures, in particular with simple algebraic groups, or, more generally, groups of Lie type. The project evolves around four main goals:
Firstly, prove the fundamental theorems for the Tits webs derived from the exceptional algebraic groups of relative isotropic rank 1. Secondly, show that the automorphism groups of a Ree unital is precisely the corresponding Ree group. Thirdly, generalise the results obtained jointly with Anneleen De Schepper about the reconstruction of the whole Tits building given only a small piece of structure from the classical to all exceptional cases. Fourthly, investigate the geometric structure and corresponding automorphism group of the new geometries defined using the recently discovered 1-parameter curves on spherical buildings of both classical and exceptional type.