• Octonions and the Standard Model 8 A geometrical way to see how E_{6} is connected to 10d spacetime, based on the octonionic projective plane.

• Octonions and the Standard Model 9. Duality in projective plane geometry, and how it lets us break the Lie group E_{6} into the Lorentz group, left-handed and right-handed spinors, and scalars in 10d Minkowski spacetime.

• Octonions and the Standard Model 10. Jordan algebras, their symmetry groups, their invariant structures — and how they connect quantum mechanics, special relativity and projective geometry.

• Octonions and the Standard Model 11. Particle physics on the spacetime given by the exceptional Jordan algebra: a summary of work with Greg Egan and John Huerta.

Next I’ll go back to the Standard Model!

]]>