Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo
“The Octonions”
The aim of this talk is to give an overview of the Octonions and their importance in geometry. We will start by defining a normed division algebra and will then prove a theorem of Hurwitz on classification of real normed division algebras. We will then focus on the Octonions, an 8-dimensional, non-associative, real division algebra. We will give four different constructions of the Octonions - 1) using a multiplication table 2) using the Fano plane 3) by describing the Cayley-Dickson process and 4) using Clifford algebras and spinors. After proving various identities for the Octonions, we will define a generalised notion of cross product. If time permits, then we will briefly explain the theory of calibration and the relationship between the Octonions and G2 geometry.
M3-3103
Refreshments will be at 4:00pm