Type: Seminar

Distribution: World

Expiry: 24 Oct 2011

Auth: zhangou@bari.maths.usyd.edu.au

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.