SMS scnews item created by Zhou Zhang at Mon 10 Oct 2011 1055
Type: Seminar
Distribution: World
Expiry: 24 Oct 2011
Calendar1: 18 Oct 2011 1200-1300
CalLoc1: Carslaw 707A
Auth: zhangou@bari.maths.usyd.edu.au

# 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.


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