Geometry Seminar: Huerta -- G2, Split Octonions, and the Rolling Ball

Speaker: Dr. John Huerta (ANU)

Time: Tuesday, Oct. 18, 2011, 12(NOON)--1PM

Room: Carslaw 707A 

Title: G2, split octonions, and the rolling ball

Abstract: understanding the exceptional Lie groups as 
the symmetry groups of simpler objects is a long-standing 
program in mathematics. Here, we explore one famous 
realization of the smallest exceptional Lie group, G2, 
its Lie algebra, g2, acts infinitesimally as the 
symmetries of a ball rolling on another ball, but only 
when the ratio of radii is 1:3 or 3:1. Using the split 
octonions and the "divisors-of-zero distribution" of
Agrachev, we devise a similar, but more global, picture 
of G2: it acts as the symmetries of a "fermionic ball 
rolling on a projective plane", again only when the 
ratio of radii is 1:3 or 3:1. We describe the incidence 
geometry of this system, and show how it sheds light on 
the role of this mysterious ratio, 1:3. This is joint 
work with Jim Dolan.

Lunch: we take the speaker to lunch after the talk.