Olivetti Club

Balazs ElekCornell University
G2 and the rolling ball

Tuesday, October 8, 2013 - 4:30pm
Malott 406

In May 1887, to his big surprise, Wilhelm Killing has discovered a previously completely unknown simple Lie algebra now known as g2. It is the smallest of the five exceptional Lie algebras, and understanding the corresponding Lie groups via their actions on simpler objects is a fascinating topic. The split real form of G2 can be realized as roughly the group of symmetries of a ball rolling on a larger ball, but only when the ratio of radii is 1:3. We will explain this realization using the fact that the same group is also the automorphism group of an 8-dimensional nonassociative algebra, the split octonions. Using the dot product and cross product of the split octonions, we will describe the incidence geometry of this rolling ball system. All of the talk is based on the paper ``G2 and the Rolling Ball'' by John Baez and John Huerta and it will be accessible to everyone who can relate to the concepts of dot product and cross product, even if they have never heard of g2 before.

Refreshments will be served in the lounge at 4:00.