Title: The geometries of the Freudenthal-Tits magic square
Abstract: I will discuss an ongoing project (joint with H. Van Maldeghem)
to give a uniform axiomatic description of the embeddings in projective
space of the varieties corresponding with the geometries of exceptional
Lie type over arbitrary fields.
In particular, I will focus on the second row of the Freudenthal-Tits
Magic Square.
I will mainly focus on the split case, and provide a uniform (incidence)
geometric characterization of the Severi varieties over arbitrary fields.
This can be regarded as a counterpart over arbitrary fields of the
classification of smooth complex algebraic Severi varieties. The proofs
just use projective geometry.
In the remaining time, I will discuss a geometric characterization of
projective planes over quadratic alternative division algebras.