Title : Geometric constructions of certain exceptional buildings
Speaker: Magali Victoor
Affiliation: Ghent University
Time: 13:00 Wednesday, 28 March, 2018
Location: 303-257
Abstract
The definition of a building is very general and abstract, which does not make it easy to understand and work with. In order to understand these geometries better, we give an overview of some different perspectives to look at these geometries. By embedding these buildings in projective spaces we hope to be able to use the surrounding projective space to solve some geometric and group-theoretic problems about these objects, similarly to the situation of polar spaces. Although it was already know that buildings of type E_7 can be embedded in a 55-dimensional projective space, this construction was rather algebraic and not so easily accessible for geometric methods. We now give a geometric constuction of this embedding, as the intersection of a number of (degenerate) quadrics. To work our way up to buildings of type E_7, we start with some smaller geometries.

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