This Week's Finds 8: E8 and the octonions

Here I explain the E8 root lattice and how it gives rise to the octooctonionic projective plane, a 128-dimensional manifold on which the compact Lie group called E8 acts as symmetries. I also discuss how some special root lattices give various notions of 'integer' for the real numbers, complex numbers, quaternions and octonions.
For more, read my paper "Coxeter and Dynkin diagrams" here:
math.ucr.edu/ho...
This is one of a series of lectures at the University of Edinburgh on topics drawn from my column This Week's Finds.
Cover image by Tom Ruen, CC BY-SA 4.0