2009 April 27 / E-Mail Me

Senior Integrative Exercise (Comps)

My 2008-2009 comps group is studying geometric algebra (not to be confused with algebraic geometry). This is an enjoyable little neighborhood of mathematics with some important residents:

The list could keep going, but I have to end it somewhere, especially since my own understanding is limited. The connections to representation theory and physics, in particular, relate geometric algebra to just about everything in math. In short, if you're excited by the alleged interconnectedness of all of mathematics, then geometric algebra is a good spot from which to survey that interconnectedness. Here are some materials:

Update: The final product of the project was a classification of the irreducible representations of the double cover of the Poincaré group, and thus some aspect of the elementary particles of physics, following Eugene Wigner's 1939 paper.