ABSTRACT: I will explain how to construct all complex simple Lie algebras via elementary projective geometry and applications of this construction to algebraic geometry, representation theory and possibly knot theory.
Some of the applications are: a new proof of the Cartan-Killing classification of complex simple Lie algebras, deformation and rigidity results regarding homogeneous varieties,  a uniform method for applying  Kempf's desingularization process, enhancements and geometric interpretations of Deligne's "numerology of the exceptional groups" and Vogel's conjectured "Universal Lie algebra", and new candidates for polynomial valued
Vassiliev invariants.