Chasing Motes: A Physicist's introduction to Hopf Algebras

Hopf Algebras are examples of bialgebras, being both an algebra and coalgebra and are additionally equipped with an endomorphism known as an antipode which is analogous to the map of groups that takes elements to their inverse. These structures have been studied since 1941 first in the field of algebraic topology and have since spread to many fields of mathematics. More recently they have been applied to quantum mechanics and the combinatorics of renormalization of quantum field theories. In this talk I will introduce Hopf algebras for a very general audience; work through a couple of simple examples; and finally, discuss the Motic Hopf algebra and its relevance to my work in renormalization.